A generalized advection dispersion equation
Indian Academy of Sciences (India)
Abdon Atangana
2014-02-01
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.
Advective Coalescence in Chaotic Flows
Energy Technology Data Exchange (ETDEWEB)
Nishikawa, Takashi; Toroczkai, Zoltan; Grebogi, Celso
2001-07-16
We investigate the reaction kinetics of small spherical particles with inertia, obeying coalescence type of reaction, B+B{yields}B , and being advected by hydrodynamical flows with time-periodic forcing. In contrast to passive tracers, the particle dynamics is governed by the strongly nonlinear Maxey-Riley equations, which typically create chaos in the spatial component of the particle dynamics, appearing as filamental structures in the distribution of the reactants. Defining a stochastic description supported on the natural measure of the attractor, we show that, in the limit of slow reaction, the reaction kinetics assumes a universal behavior exhibiting a t{sup -1} decay in the amount of reagents, which become distributed on a subset of dimension D{sub 2} , where D{sub 2} is the correlation dimension of the chaotic flow.
Chaotic advection, diffusion, and reactions in open flows
Energy Technology Data Exchange (ETDEWEB)
Tel, Tamas [Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, H-1518 Budapest, (Hungary); Karolyi, Gyoergy [Department of Civil Engineering Mechanics, Technical University of Budapest, Mueegyetem rpk. 3, H-1521 Budapest, (Hungary); Pentek, Aron [Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 (United States); Scheuring, Istvan [Department of Plant Taxonomy and Ecology, Research Group of Ecology and Theoretical Biology, Eoetvoes University, Ludovika ter 2, H-1083 Budapest, (Hungary); Toroczkai, Zoltan [Department of Physics, University of Maryland, College Park, Maryland 20742-4111 (United States); Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435 (United States); Grebogi, Celso [Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States); Kadtke, James [Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 (United States)
2000-03-01
We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.
Chaotic advection in blood flow.
Schelin, A B; Károlyi, Gy; de Moura, A P S; Booth, N A; Grebogi, C
2009-07-01
In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.
Onset of chaotic advection in open flows.
Biemond, J J Benjamin; de Moura, Alessandro P S; Károlyi, György; Grebogi, Celso; Nijmeijer, Henk
2008-07-01
In this paper we investigate the transition to chaos in the motion of particles advected by open flows with obstacles. By means of a topological argument, we show that the separation points on the surface of the obstacle imply the existence of a saddle point downstream from the obstacle, with an associated heteroclinic orbit. We argue that as soon as the flow becomes time periodic, these orbits give rise to heteroclinic tangles, causing passively advected particles to experience transient chaos. The transition to chaos thus coincides with the onset of time dependence in open flows with stagnant points, in contrast with flows with no stagnant points. We also show that the nonhyperbolic nature of the dynamics near the walls causes anomalous scalings in the vicinity of the transition. These results are confirmed by numerical simulations of the two-dimensional flow around a cylinder.
Influence of Ohmic Heating on Advection-Dominated Accretion Flows
Bisnovatyi-Kogan, G S
1997-01-01
Advection-dominated, high-temperature, quasi-spherical accretion flow onto a compact object of mass M, recently considered by a number of authors, assume that the dissipation of turbulent energy of the flow heats the ions and that a constant fraction f of the dissipated energy is advected inward. It is suggested that the efficiency of conversion of accretion energy to radiation can be very much smaller than unity. However, it is likely that the flows have an equipartition magnetic field with the result that dissipation of magnetic energy at a rate comparable to that for the turbulence must occur by Ohmic heating. We argue that this heating occurs as a result of plasma instabilities and that the relevant instabilities are current driven in response to the strong electric fields parallel to the magnetic field. We argue further that these instabilities heat predominantly the electrons. We analyze a model for the radial dependence of the ion and electron temperatures of a general, possibly quasi-spherical accreti...
A Toy Model for Advection Dominated Accretion Flows
Institute of Scientific and Technical Information of China (English)
汪定雄; 雷卫华; 肖看
2003-01-01
A toy disc model with advection dominated accretion on to a black hole is presented. The advection dominated accretion flows (ADAFs) are assumed to exist in the inner thick disc with rin ＜ r ＜ rout, and the disc is assumed to be geometrically thin for r ＞ rout. Compared with Paczynski's toy model the thick disc is not limited to be 100% advective. It turns out that the inner radius rin depends not only on the outer radius rout but also on the ADAF parameters f and ε. The effects of the inner thick disc on the radiation efficiency and the temperature profile of the outer thin disc are discussed in details.
Why Canonical Disks Cannot Produce Advection Dominated Flows
Molteni, D; Valenza, M A
2001-01-01
Using simple arguments we show that the canonical thin keplerian accretion disks cannot smoothly match any plain advection dominated flow (ADAF) model. By 'plain' ADAF model we mean the ones with zero cooling. The existence of sonic points in exact solutions is critical and imposes constraints that cannot be surpassed adopting 'reasonable' physical conditions at the hypothetical match point. Only the occurrence of new critical physical phenomena may produce a transition. We propose that exact advection models are a class of solutions which don't necessarily involve the standard thin cool disks and suggest a different scenario in which good ADAF solutions could eventually occur.
Advection-Based Sparse Data Management for Visualizing Unsteady Flow.
Guo, Hanqi; Zhang, Jiang; Liu, Richen; Liu, Lu; Yuan, Xiaoru; Huang, Jian; Meng, Xiangfei; Pan, Jingshan
2014-12-01
When computing integral curves and integral surfaces for large-scale unsteady flow fields, a major bottleneck is the widening gap between data access demands and the available bandwidth (both I/O and in-memory). In this work, we explore a novel advection-based scheme to manage flow field data for both efficiency and scalability. The key is to first partition flow field into blocklets (e.g. cells or very fine-grained blocks of cells), and then (pre)fetch and manage blocklets on-demand using a parallel key-value store. The benefits are (1) greatly increasing the scale of local-range analysis (e.g. source-destination queries, streak surface generation) that can fit within any given limit of hardware resources; (2) improving memory and I/O bandwidth-efficiencies as well as the scalability of naive task-parallel particle advection. We demonstrate our method using a prototype system that works on workstation and also in supercomputing environments. Results show significantly reduced I/O overhead compared to accessing raw flow data, and also high scalability on a supercomputer for a variety of applications.
Advection of nematic liquid crystals by chaotic flow
O'Naraigh, Lennon
2016-01-01
Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar two-dimensional geometry. The Landau-de Gennes equation coupled to an externally-prescribed flow field is the basis for the study: this is solved numerically in a periodic spatial domain. The focus is on a limiting case where the advection is passive, such that variations in the liquid-crystal properties do not feed back into the equation of motion for the uid velocity. The numerical simulations demonstrate that the coarsening of the liquid-crystal domains is arrested by the ow. The nature of the arrest is different depending on whether the flow is regular or chaotic. For the specific case where tumbling is important, the flow has a strong effect on the the liquid-crystal morphology: this provides a mechanism for controlling the shape of the liquid-crystal domains.
Samuel, Henri
2010-05-01
Advection is one of the major processes that commonly acts on various scales in nature (core formation, mantle convective stirring, multi-phase flows in magma chambers, salt diapirism ...). While this process can be modeled numerically by solving conservation equations, various geodynamic scenarios involve advection of quantities with sharp discontinuities. Unfortunately, in these cases modeling numerically pure advection becomes very challenging, in particular because sharp discontinuities lead to numerical instabilities, which prevent the local use of high order numerical schemes. Several approaches have been used in computational geodynamics in order to overcome this difficulty, with variable amounts of success. Despite the use of correcting filters or non-oscillatory, shock-preserving schemes, Eulerian (fixed grid) techniques generally suffer from artificial numerical diffusion. Lagrangian approaches (dynamic grids or particles) tend to be more popular in computational geodynamics because they are not prone to excessive numerical diffusion. However, these approaches are generally computationally expensive, especially in 3D, and can suffer from spurious statistical noise. As an alternative to these aforementioned approaches, I have applied a relatively recent Particle Level set method [Enright et al., 2002] for modeling advection of quantities with the presence of sharp discontinuities. I have adapted this improved method, which combines the best of Eulerian and Lagrangian approaches, and I have tested it against well known benchmarks and classical Geodynamic flows. In each case the Particle Level Set method accuracy equals or is better than other Eulerian and Lagrangian methods, and leads to significantly smaller computational cost, in particular in three-dimensional flows, where the reduction of computational time for modeling advection processes is most needed.
Modeling the advection of discontinuous quantities in Geophysical flows using Particle Level Sets
Aleksandrov, V.; Samuel, H.; Evonuk, M.
2010-12-01
Advection is one of the major processes that commonly acts on various scales in nature (core formation, mantle convective stirring, multi-phase flows in magma chambers, salt diapirism ...). While this process can be modeled numerically by solving conservation equations, various geodynamic scenarios involve advection of quantities with sharp discontinuities. Unfortunately, in these cases modeling numerically pure advection becomes very challenging, in particular because sharp discontinuities lead to numerical instabilities, which prevent the local use of high order numerical schemes. Several approaches have been used in computational geodynamics in order to overcome this difficulty, with variable amounts of success. Despite the use of correcting filters or non-oscillatory, shock-preserving schemes, Eulerian (fixed grid) techniques generally suffer from artificial numerical diffusion. Lagrangian approaches (dynamic grids or particles) tend to be more popular in computational geodynamics because they are not prone to excessive numerical diffusion. However, these approaches are generally computationally expensive, especially in 3D, and can suffer from spurious statistical noise. As an alternative to these aforementioned approaches, we have applied a relatively recent Particle Level set method [Enright et al., 2002] for modeling advection of quantities with the presence of sharp discontinuities. We have tested this improved method, which combines the best of Eulerian and Lagrangian approaches, against well known benchmarks and classical Geodynamic flows. In each case the Particle Level Set method accuracy equals or is better than other Eulerian and Lagrangian methods, and leads to significantly smaller computational cost, in particular in three-dimensional flows, where the reduction of computational time for modeling advection processes is most needed.
Authalic parameterization of general surfaces using Lie advection.
Zou, Guangyu; Hu, Jiaxi; Gu, Xianfeng; Hua, Jing
2011-12-01
Parameterization of complex surfaces constitutes a major means of visualizing highly convoluted geometric structures as well as other properties associated with the surface. It also enables users with the ability to navigate, orient, and focus on regions of interest within a global view and overcome the occlusions to inner concavities. In this paper, we propose a novel area-preserving surface parameterization method which is rigorous in theory, moderate in computation, yet easily extendable to surfaces of non-disc and closed-boundary topologies. Starting from the distortion induced by an initial parameterization, an area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms along the manifold, which yields equality of the area elements between the domain and the original surface at its final state. Existence and uniqueness of result are assured through an analytical derivation. Based upon a triangulated surface representation, we also present an efficient algorithm in line with discrete differential modeling. As an exemplar application, the utilization of this method for the effective visualization of brain cortical imaging modalities is presented. Compared with conformal methods, our method can reveal more subtle surface patterns in a quantitative manner. It, therefore, provides a competitive alternative to the existing parameterization techniques for better surface-based analysis in various scenarios.
Implementation of Two Component Advective Flow Solution in XSPEC
Debnath, Dipak; Mondal, Santanu
2014-01-01
Spectral and Temporal properties of black hole candidates can be explained reasonably well using Chakrabarti-Titarchuk solution of two component advective flow (TCAF). This model requires two accretion rates, namely, the Keplerian disk accretion rate and the halo accretion rate, the latter being composed of a sub-Keplerian, low angular momentum flow which may or may not develop a shock. In this solution, the relevant parameter is the relative importance of the halo (which creates the Compton cloud region) rate with respect to the Keplerian disk rate (soft photon source). Though this model has been used earlier to manually fit data of several black hole candidates quite satisfactorily, for the first time, we made it user friendly by implementing it into XSPEC software of GSFC/NASA. This enables any user to extract physical parameters of the accretion flows, such as two accretion rates, the shock location, the shock strength etc. for any black hole candidate. We provide some examples of fitting a few cases usin...
Standing Shock Instability in Advection-Dominated Accretion Flows
Le, Truong; Wolff, Michael T; Becker, Peter A; Putney, Joy
2015-01-01
Depending on the values of the energy and angular momentum per unit mass in the gas supplied at large radii, inviscid advection-dominated accretion flows can display velocity profiles with either pre-shock deceleration or pre-shock acceleration. Nakayama has shown that these two types of flow configurations are expected to have different stability properties. By employing the Chevalier & Imamura linearization method and the Nakayama instability boundary conditions, we discover that there are regions of parameters space where disk/shocks with outflows can be stable or unstable. In region of instability, we find that pre-shock deceleration is always unstable to the zeroth mode with zero frequency of oscillation, but is always stable to the fundamental and overtones. Furthermore, we also find that pre-shock acceleration is always unstable to the zeroth mode, and that the fundamental and overtones become increasingly less stable as the shock location moves away from the horizon when the disk half-height expan...
Chakrabarti, Sandip K
2016-01-01
An accretion flow around a black hole has a saddle type sonic point just outside the event horizon to guarantee that the flow enters the black hole supersonically. This feature exclusively present in strong gravity limit makes its marks in every observation of black hole candidates. Another physical sonic point is present (as in a Bondi flow) even in weak gravity. Every aspect of spectral or temporal properties of every black hole can be understood using this transonic or advective flow having more than one saddle type points. This most well known and generalized solution with viscosity and radiative transfer has been verified by numerical simulations also. Spectra, computed for various combinations of the standard Keplerian, and advective sub-Keplerian components match accurately with those from satellite observations. Standing, oscillating and propagatory oscillating shocks are produced due to centrifugal barrier of the advective component. The post-shock region acts as the Compton cloud producing the power...
Comments on the newly discovered advection dominated flows around black holes and neutron stars
Chakrabarti, S K
1995-01-01
We provide complete and global solutions of transonic flows around black holes, in presence of advection, rotation, heating and cooling. We show that for any degree of advection, there may exist two critical viscosity parameters \\alpha_{c1, c2} such that for \\alpha \\alpha_{c2}, the flow may again pass through the inner sonic point, depending on flow parameters. No new topologies emerge other than what we found earlier while studying viscous isothermal transonic flows. These findings indicate that the newly discovered advection dominated flows do not constitute any new solutions.
STANDING SHOCK INSTABILITY IN ADVECTION-DOMINATED ACCRETION FLOWS
Energy Technology Data Exchange (ETDEWEB)
Le, Truong [Department of Physics, Astronomy and Geology, Berry College, Mount Berry, GA 30149 (United States); Wood, Kent S.; Wolff, Michael T. [High Energy Space Environment Branch, Space Science Division, Naval Research Laboratory, Washington, DC 20375 (United States); Becker, Peter A. [Department of Physics and Astronomy, George Mason University, Fairfax, VA 22030 (United States); Putney, Joy, E-mail: tle@berry.edu [Department of Physics and Engineering, Washington and Lee University, Lexington, VA 24450 (United States)
2016-03-10
Depending on the values of the energy and angular momentum per unit mass in the gas supplied at large radii, inviscid advection-dominated accretion flows can display velocity profiles with either preshock deceleration or preshock acceleration. Nakayama has shown that these two types of flow configurations are expected to have different stability properties. By employing the Chevalier and Imamura linearization method and the Nakayama instability boundary conditions, we discover that there are regions of parameter space where disks/shocks with outflows can be stable or unstable. In regions of instability, we find that preshock deceleration is always unstable to the zeroth mode with zero frequency of oscillation, but is always stable to the fundamental mode and overtones. Furthermore, we also find that preshock acceleration is always unstable to the zeroth mode and that the fundamental mode and overtones become increasingly less stable as the shock location moves away from the horizon when the disk half-height expands above ∼12 gravitational radii at the shock radius. In regions of stability, we demonstrate the zeroth mode to be stable for the velocity profiles that exhibit preshock acceleration and deceleration. Moreover, for models that are linearly unstable, our model suggests the possible existence of quasi-periodic oscillations (QPOs) with ratios 2:3 and 3:5. These ratios are believed to occur in stellar and supermassive black hole candidates, for example, in GRS 1915+105 and Sgr A*, respectively. We expect that similar QPO ratios also exist in regions of stable shocks.
Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics
Tupikina, Liubov; López, Cristóbal; Hernández-García, Emilio; Marwan, Norbert; Kurths, Jürgen
2016-01-01
Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network's structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our r...
Update on Advection-Diffusion Purge Flow Model
Brieda, Lubos
2015-01-01
Gaseous purge is commonly used in sensitive spacecraft optical or electronic instruments to prevent infiltration of contaminants and/or water vapor. Typically, purge is sized using simplistic zero-dimensional models that do not take into account instrument geometry, surface effects, and the dependence of diffusive flux on the concentration gradient. For this reason, an axisymmetric computational fluid dynamics (CFD) simulation was recently developed to model contaminant infiltration and removal by purge. The solver uses a combined Navier-Stokes and Advection-Diffusion approach. In this talk, we report on updates in the model, namely inclusion of a particulate transport model.
Gusti, T. P.; Hertanti, D. R.; Bahsan, E.; Soeryantono, H.
2013-12-01
Particle-based numerical methods, such as Smoothed Particle Hydrodynamics (SPH), may be able to simulate some hydrodynamic and morphodynamic behaviors better than grid-based numerical methods. This study simulates hydrodynamics in meanders and advection and turbulent diffusion in straight river channels using Microsoft Excel and Visual Basic. The simulators generate three-dimensional data for hydrodynamics and one-dimensional data for advection-turbulent diffusion. Fluid at rest, sloshing, and helical flow are simulated in the river meanders. Spill loading and step loading are done to simulate concentration patterns associated with advection-turbulent diffusion. Results indicate that helical flow is formed due to disturbance in morphology and particle velocity in the stream and the number of particles does not have a significant effect on the pattern of advection-turbulent diffusion concentration.
Adaptive Computations for Partial Differential Equations Governing Advective Fluid Flows
1990-12-27
metry, Journal of Electroanalytical Chemistry 282 (1990), 1-26. 16. H.K. Dahle, M.S. Espedal, R.E. Ewing, and 0. Saevareid, Characteristic adap- tive sub... Electroanalytical Chemistry , (to appear). 36. E.L. Isaacson, D. Marchesin, B.J. Plohr, and J.B. Temple, Multiphase flow mod- els with singular Riemann problems
Impacts of photon bending on observational aspects of Two Component Advective Flow
Chatterjee, Arka
2016-01-01
Nature of photon trajectories in a curved spacetime around black holes are studied without constraining their motion to any plane. Impacts of photon bending are separately scrutinized for Keplerian and CENBOL components of Two Component Advective Flow (TCAF) model. Parameters like Red shift, Bolometric Flux, temperature profile and time of arrival of photons are also computed.
Manmoto, T; Kusunose, M
1997-01-01
The global structure of optically thin advection dominated accretion flows which are composed of two-temperature plasma around black holes is calculated. We adopt the full set of basic equations including the advective energy transport in the energy equation for the electrons. The spectra emitted by the optically thin accretion flows are also investigated. The radiation mechanisms which are taken into accout are bremsstrahlung, synchrotron emission, and Comptonization. The calculation of the spectra and that of the structure of the accretion flows are made to be completely consistent by calculating the radiative cooling rate at each radius. As a result of the advection domination for the ions, the heat transport from the ions to the electrons becomes practically zero and the radiative cooling balances with the advective heating in the energy equation of the electrons. Following up on the successful work of Narayan et al. (1995), we applied our model to the spectrum of Sgr A*. We find that the spectrum of Sgr ...
Smooth Transition from Shakura-Sunyaev Disc to Advection-Dominated Accretion Flow
Institute of Scientific and Technical Information of China (English)
林一清; 卢炬甫; 顾为民
2003-01-01
We solve a set of basic equations describing black hole accretion flows using the standard Runge-Kutta method and a bridging formula for the radiative cooling, and show that a smooth transition from a Shakura-Sunyaev disc to an advection-dominated accretion flow is realizable for the high-viscosity case, without the need of involving any extra mechanism of energy transport.
Partitioned coupling of advection-diffusion-reaction systems and Brinkman flows
Lenarda, Pietro; Paggi, Marco; Ruiz Baier, Ricardo
2017-09-01
We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-diffusion-reaction systems and incompressible, viscous flow. The space discretisation of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the differences in scales between the reaction, advection, and diffusion processes, considering the global system as a number of sequentially linked sets of partial differential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.
Advective and Conductive Heat Flow Budget Across the Wagner Basin, Northern Gulf of California
Neumann, F.; Negrete-Aranda, R.; Contreras, J.; Müller, C.; Hutnak, M.; Gonzalez-Fernandez, A.; Harris, R. N.; Sclater, J. G.
2015-12-01
In May 2015, we conducted a cruise across the northern Gulf of California, an area of continental rift basin formation and rapid deposition of sediments. The cruise was undertaken aboard the R/V Alpha Helix; our goal was to study variation in superficial conductive heat flow, lateral changes in the shallow thermal conductivity structure, and advective transport of heat across the Wagner basin. We used a Fielax heat flow probe with 22 thermistors that can penetrate up to 6 m into the sediment cover. The resulting data set includes 53 new heat flow measurements collected along three profiles. The longest profile (42 km) contains 30 measurements spaced 1-2 km apart. The western part of the Wagner basin (hanging wall block) exhibit low to normal conductive heat flow whereas the eastern part of the basin (foot wall block) heat flow is high to very high (up to 2500 mWm-2). Two other short profiles (12 km long each) focused on resolving an extremely high heat flow anomaly up to 15 Wm-2 located near the intersection between the Wagner bounding fault system and the Cerro Prieto fault. We hypothesize that the contrasting heat flow values observed across the Wagner basin are due to horizontal water circulation through sand layers and fault pathways of high permeability. Circulation appears to be from west (recharge zone) to east (discharge zone). Additionally, our results reveal strong vertical advection of heat due to dehydration reactions and compaction of fine grained sediments.
Directory of Open Access Journals (Sweden)
P. P. Ebner
2015-09-01
Full Text Available Snow at or close to the surface commonly undergoes temperature gradient metamorphism under advective flow, which alters its microstructure and physical properties. Time-lapse X-ray micro-tomography is applied to investigate the structural dynamics of temperature gradient snow metamorphism exposed to an advective airflow in controlled laboratory conditions. The sublimation of water vapor for saturated air flowing across the snow sample was experimentally determined via variations of the porous ice structure. The results showed that the exothermic gas-to-solid phase change is favorable vis-a-vis the endothermic solid-to-gas phase change, thus leading to more ice deposition than ice sublimation. Sublimation has a marked effect on the structural change of the ice matrix but diffusion of water vapor in the direction of the temperature gradient counteracted the mass transport of advection. Therefore, the total net ice change was negligible leading to a constant porosity profile. However, the strong reposition process of water molecules on the ice grains is relevant for atmospheric chemistry.
Modelling debris transport within glaciers by advection in a full-Stokes ice flow model
Wirbel, Anna; Jarosch, Alexander H.; Nicholson, Lindsey
2017-04-01
As mountain glaciers recede worldwide, an increasing proportion of the remaining glacierized area is expected to become debris covered. The spatio-temporal development of a surface debris cover has profound effects on the glacier behaviour and meltwater generation, yet little is known about how glacier dynamics influence the spatial distribution of an emerging debris cover. Motivated by this lack of understanding, we present a coupled model to simulate advection and resulting deformation of debris features within glaciers. The finite element model developed in python consists of an advection scheme coupled to a full-Stokes ice flow model, using FEniCS as the numerical framework. We show results from numerical tests that demonstrate its suitability to model advection-dominated transport of concentration in a divergence-free velocity field. The capabilities of the coupled model are demonstrated by simulating transport of debris features of different initial size, shape and location through modelled velocity fields of representative mountain glaciers. The results indicate that deformation of initial debris inputs, as a consequence of being transported through the glacier, plays an important role in determining the location and rate of debris emergence at the glacier surface. The presented work lays the foundation for comprehensive simulations of realistic patterns of debris cover, their spatial and temporal variability and the timescales over which debris covers can form.
Self-Similar Solutions for Viscous and Resistive Advection Dominated Accretion Flows
Indian Academy of Sciences (India)
Kazem Faghei
2012-03-01
In this paper, self-similar solutions of resistive advection dominated accretion flows (ADAF) in the presence of a pure azimuthal magnetic field are investigated. The mechanism of energy dissipation is assumed to be the viscosity and the magnetic diffusivity due to turbulence in the accretion flow. It is assumed that the magnetic diffusivity and the kinematic viscosity are not constant and vary by position and -prescription is used for them. In order to solve the integrated equations that govern the behavior of the accretion flow, a self-similar method is used. The solutions show that the structure of accretion flow depends on the magnetic field and the magnetic diffusivity. As the radial infall velocity and the temperature of the flow increase by magnetic diffusivity, the rotational velocity decreases. Also, the rotational velocity for all selected values of magnetic diffusivity and magnetic field is sub-Keplerian. The solutions show that there is a certain amount of magnetic field for which rotational velocity of the flow becomes zero. This amount of the magnetic field depends upon the gas properties of the disc, such as adiabatic index and viscosity, magnetic diffusivity, and advection parameters. The mass accretion rate increases by adding the magnetic diffusivity and the solutions show that in high magnetic pressure, the ratio of the mass accretion rate to the Bondi accretion rate is reduced with an increase in magnetic pressure. Also, the study of Lundquist and magnetic Reynolds numbers based on resistivity indicates that the linear growth of magnetorotational instability (MRI) of the flow reduces by resistivity. This property is qualitatively consistent with resistive magnetohydrodynamics (MHD) simulations.
The orientation field of fibers advected by a two-dimensional chaotic flow
Hejazi, Bardia; Mehlig, Bernhard; Voth, Greg
2016-11-01
We examine the orientation of slender fibers advected by a 2D chaotic flow. The orientation field of these fibers show fascinating structures called scar lines, where they rotate by π over short distances. We use the standard map as a convenient model to represent a time-periodic 2D incompressible fluid flow. To understand the fiber orientation field, we consider the stretching field, given by the eigenvalues and eigenvectors of the Cauchy-Green strain tensors. The eigenvector field is strongly aligned with the fibers over almost the entire field, but develops topological singularities at certain points which do not exist in the advected fiber field. The singularities are points that have experienced zero stretching, and the number of such points increases rapidly with time. A key feature of both the fiber orientation and the eigenvector field are the scar lines. We show that certain scar lines form from fluid elements that are initially stretched in one direction and then stretched in an orthogonal direction to cancel the initial stretching. The scar lines that satisfy this condition contain the singularities of the eigenvector field. These scar lines highlight the major differences between the passive director field and the much more widely studied passive scalar field.
Klotz, Lukasz; Lemoult, Gregoire; Wesfreid, Jose Eduardo
2015-11-01
We describe a new experimental set-up which allows us to study the sub-critical transition to turbulence in a two dimensional shear flow (including plane Couette, plane Couette-Poiseuille and plane Poiseuille flows). Our facility is an extension of a classical plane Couette experiment, in which one uses a single closed loop of plastic belt to generate the opposite sign velocity at each wall of the test section. However, in our case, we use two independent closed loops of plastic belt, one at each wall of the test section. The speed of these belts may be controlled separately. That enables to set two different velocities (in value and direction) as a boundary conditions at each of two test section's walls. In addition the pressure gradient in streamwise direction can be controlled. In particular, the plane Poiseuille flow with zero mean advection velocity can be created. We characterize by PIV the basic flow for different configurations. For a plane Poiseuille flows as base flow, we were able to observe for the first time the nearly stationary turbulent spots in this flow, with structures of characteristic wavelength ~ the distance between the two plates.
Mandal, S; Mandal, Samir; Chakrabarti, Sandip K.
2005-01-01
Centrifugal barrier supported boundary layer (CENBOL) of a black hole affects the spectrum exactly in the same way the boundary layer of a neutron star does. The CENBOL is produced due to standing or oscillating shock waves and these shocks accelerate electrons very efficiently and produce a power-law distribution. The accelerated particles in turn emit synchrotron radiation in presence of the magnetic field. We study the spectral properties of an accretion disk as a function of the shock strength, compression ratio, flow accretion rate and flow geometry. In the absence of a satisfactory description of magnetic fields inside the advective disk, we consider the presence of only stochastic fields and use the ratio of the field energy density to the gravitational energy density to be a parameter. Not surprisingly, stronger fields produce stronger humps due to synchrotron radiation. We not only include `conventional' synchrotron emission and Comptonization due to Maxwell-Bolzmann electrons in the gas, we also com...
An advective volume-balance model for flow in porous media
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2016-11-01
Volume-balance models are used by petroleum engineers to simulate multiphase and multicomponent flow phenomena in porous media and the extraction process in oil reservoirs. In these models, mass conservation equations and Darcy's law are supplemented by a balance condition for the pore and fluid volumes. This provides a pressure equation suitable for simulating a compressible flow within a compressible solid matrix. Here we present an alternative interpretation of the volume-balance condition that includes the advective transport within a consolidated porous media. We obtain a modified equation for the time evolution of the pressure field. Preliminary numerical tests of phase separation due to gravity suggest the model reproduces qualitatively the physical phenomena. Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Spreading of Advected Tracers in a Creeping Flow in a Rectangular Channel
Kaufman, Miron
2006-03-01
We have developed an analytical solution [M.Kaufman, 2003 AIChE Annual Meeting Conference Proceedings] of the Navier-Stokes equation for the two-dimensional incompressible flow in a rectangular cavity in the limit of zero Reynolds number. An analytical solution for the fluid velocity along the axis of a parallelepiped, again in the Stokes limit, is also known. In this work we combine the two solutions to get analytically the three-dimensional creeping flow inside a channel in the shape of a parallelepiped. We integrate numerically the velocity vector to get trajectories of tracers advected by the fluid. We analyze the spreading in space of the tracers by calculating the time evolution of the entropy.
Mukhopadhyay, Banibrata
2016-01-01
We show that the removal of angular momentum is possible in the presence of large scale magnetic stresses, arisen by fields much stronger than that required for magnetorotational instability, in geometrically thick, advective, sub-Keplerian accretion flows around black holes in steady-state, in the complete absence of alpha-viscosity. The efficiency of such angular momentum transfer via Maxwell stress, with the field well below its equipartition value, could be equivalent to that of alpha-viscosity, arisen via Reynolds stress, with $\\alpha=0.01-0.08$. We find in our simpler vertically averaged advective disk model that stronger the magnetic field and/or larger the vertical-gradient of azimuthal component of magnetic field, stronger the rate of angular momentum transfer is, which in turn may lead to a faster rate of outflowing matter, which has important implications to describe the hard spectral states of black hole sources. When the generic origin of alpha-viscosity is still being explored, mechanism of effi...
Anaerobic, Nitrate-Dependent Fe(II) Oxidation Under Advective Flow
Weber, K. A.; Coates, J. D.
2005-12-01
Microbially-catalyzed nitrate-dependent Fe(II) oxidation has been identified as a ubiquitous biogeochemical process contributing to anaerobic iron redox cycling in sedimentary environments. Most probable number enumeration revealed nitrate-dependent Fe(II) oxidizing microbial communities in groundwater and subsurface sediments in the order of 0 - 2.04 x 103 cells mL-1 and 2.39 x 102 - 1.17 x 103 cells (g wet sediment)-1, respectively. The efficacy of nitrate-dependent Fe(II) oxidation under advective flow was evaluated in a meso-scale column reactor packed with sterile low iron sand amended with subsurface sediments collected from the NABIR FRC background field site (10% mass/mass). Continuous flow of minimal medium mimicked the natural groundwater. Periodic FeCl2 and nitrate injections over a period of 49 days resulted in the retention of 95% of the iron (290 mmol). Extraction of solid-phase Fe revealed a net increase in Fe(III) of 160 mmol above background Fe(III) content indicating that 55% of the injected Fe(II) was oxidized. Differential solubility analysis of 0.5M HCl-extractable Fe and 3M HCl-extractable Fe indicated that the oxidation product was crystalline in nature as only 20% was soluble in 0.5M HCl. This formation of crystalline biogenic Fe(III) oxides is consistent with previous studies. Periodic injections of nitrate and acetate did not result in significant changes in Fe(II) or Fe(III) throughout a control column. Together these results demonstrate that native subsurface sediments harbor microbial communities capable of nitrate-dependent Fe(II) oxidation under advective flow. The biogenic formation of reactive Fe(III) oxide minerals capable of immobilizing heavy metals and radionuclides presents a plausible bioremediative strategy for contaminated subsurface environments.
Chaotic advection of finite-size bodies in a cavity flow
Vikhansky, A.
2003-07-01
We considered advection of neutrally buoyant discs in two-dimensional chaotic Stokes flow. The goal of the study is to explore a possibility to enhance laminar mixing in batch-flow mixers. Addition of freely moving bodies to periodically driven chaotic flow renders the flowfield nonperiodic [D. F. Zhang and D. A. Zumbrunnen, AIChE J. 42, 3301 (1996)], i.e., the Lagrangian chaos of the bodies motion induces Eulerian chaos of the flow that makes mixing more intensive. The presence of three bodies creates new topological features that do not exist in "pure" fluid. The trajectories of the discs in the augmented phase space tangle and form a braid that leads to so-called topological chaos [P. L. Boyland, H. Aref, and M. A. Stremler, J. Fluid Mech. 403, 277 (2000)]. Simulations were performed using a new variant of the immersed boundaries method that allows the direct numerical simulation of fluid-solid flows on a regular rectangular grid without explicit calculation of the forces that the particles exert on the fluid.
Iyer, Gautam; Kiselev, Alexander; Xu, Xiaoqian
2014-05-01
Consider a diffusion-free passive scalar θ being mixed by an incompressible flow u on the torus { T}^d . Our aim is to study how well this scalar can be mixed under an enstrophy constraint on the advecting velocity field. Our main result shows that the mix-norm ({\\Vert}{\\theta(t)}{\\Vert}_{H^{-1}}) is bounded below by an exponential function of time. The exponential decay rate we obtain is not universal and depends on the size of the support of the initial data. We also perform numerical simulations and confirm that the numerically observed decay rate scales similarly to the rigorous lower bound, at least for a significant initial period of time. The main idea behind our proof is to use the recent work of Crippa and De Lellis (2008 J. Reine Angew. Math. 616 15-46) making progress towards the resolution of Bressan's rearrangement cost conjecture.
Chatterjee, Arka; Ghosh, Himadri
2016-01-01
Two component advective flow (TCAF) successfully explains spectral and timing properties of black hole candidates. We study the nature of photon trajectories in the vicinity of a Schwarzschild black hole and incorporate this in predicting images of TCAF with a black hole at the Centre. We also compute the emitted spectra. We employ a Monte-Carlo simulation technique to achieve our goal. For accurate prediction of the image and the spectra, null trajectories are generated without constraining the motion to any specific plane. Red shift, bolometric flux and corresponding temperature have been calculated with appropriate relativistic consideration. The centrifugal barrier dominated boundary layer or CENBOL near the inner region of the disk which acts as the Compton cloud is appropriately modelled as a thick accretion disk in Schwarzschild geometry for the purpose of imaging and computing spectra. The variations of spectra and image with physical parameters such as the accretion rate ($\\dot{m}_d$) and inclination...
Institute of Scientific and Technical Information of China (English)
GONG Xiao-Long; WANG Ding-Xiong
2005-01-01
@@ We discuss jet production from an advection dominated accretion flow (ADAF) around a rotating black hole (BH) in an electromagnetic regime. An analytical expression for the jet power is derived by using an equivalent circuit in the BH magnetosphere. It turns out that a large fraction of jet powers is contributed from the inner region of the ADAF, and the jet power depends sensitively on the degree to which the flow is advection-dominated. In addition, we use our model to fit the strong jet powers of several BL Lac objects, which cannot be explained by virtue of the BZ process.
Hornby, P. G.
2005-12-01
Understanding chemical and thermal processes taking place in hydrothermal mineral deposition systems could well be a key to unlocking new mineral reserves through improved targeting of exploration efforts. To aid in this understanding it is very helpful to be able to model such processes with sufficient fidelity to test process hypotheses. To gain understanding, it is often sufficient to obtain semi-quantitative results that model the broad aspects of the complex set of thermal and chemical effects taking place in hydrothermal systems. For example, it is often sufficient to gain an understanding of where thermal, geometric and chemical factors converge to precipitate gold (say) without being perfectly precise about how much gold is precipitated. The traditional approach is to use incompressible Darcy flow together with the Boussinesq approximation. From the flow field, the heat equation is used to advect-conduct the heat. The flow field is also used to transport solutes by solving an advection-dispersion-diffusion equation. The reactions in the fluid and between fluid and rock act as source terms for these advection-dispersion equations. Many existing modelling systems that are used for simulating such systems use explicit time marching schemes and finite differences. The disadvantage of this approach is the need to work on rectilinear grids and the number of time steps required by the Courant condition in the solute transport step. The second factor can be particularly significant if the chemical system is complex, requiring (at a minimum) an equilibrium calculation at each grid point at each time step. In the approach we describe, we use finite elements rather than finite differences, and the pressure, heat and advection-dispersion equations are solved implicitly. The general idea is to put unconditional numerical stability of the time integration first, and let accuracy assume a secondary role. It is in this sense that the method is semi-quantiative. However
Volume of Fluid (VOF) type advection methods in two-phase flow: a comparative study
Aniszewski, Wojciech; Marek, Maciej
2014-01-01
In this paper, four distinct approaches to Volume of Fluid (VOF) computational method are compared. Two of the methods are the 'simplified' VOF formulations, in that they do not require geometrical interface reconstruction. The assessment is made possible by implementing all four approaches into the same code as a switchable options. This allows to rule out possible influence of other parts of numerical scheme, be it the discretisation of Navier-Stokes equations or chosen approximation of curvature, so that we are left with conclusive arguments because only one factor differs the compared methods. The comparison is done in the framework of CLSVOF (Coupled Level Set Volume of Fluid), so that all four methods are coupled with Level Set interface, which is used to compute pressure jump via the GFM (Ghost-Fluid Method). Results presented include static advections, full N-S solutions in laminar and turbulent flows. The paper is aimed at research groups who are implementing VOF methods in their computations or inte...
Temporal Variability from the Two-Component Advective Flow Solution and Its Observational Evidence
Dutta, Broja G.; Chakrabarti, Sandip K.
2016-09-01
In the propagating oscillatory shock model, the oscillation of the post-shock region, i.e., the Compton cloud, causes the observed low-frequency quasi-periodic oscillations (QPOs). The evolution of QPO frequency is explained by the systematic variation of the Compton cloud size, i.e., the steady radial movement of the shock front, which is triggered by the cooling of the post-shock region. Thus, analysis of the energy-dependent temporal properties in different variability timescales can diagnose the dynamics and geometry of accretion flows around black holes. We study these properties for the high-inclination black hole source XTE J1550-564 during its 1998 outburst and the low-inclination black hole source GX 339-4 during its 2006-07 outburst using RXTE/PCA data, and we find that they can satisfactorily explain the time lags associated with the QPOs from these systems. We find a smooth decrease of the time lag as a function of time in the rising phase of both sources. In the declining phase, the time lag increases with time. We find a systematic evolution of QPO frequency and hard lags in these outbursts. In XTE J1550-564, the lag changes from hard to soft (i.e., from a positive to a negative value) at a crossing frequency (ν c) of ˜3.4 Hz. We present possible mechanisms to explain the lag behavior of high and low-inclination sources within the framework of a single two-component advective flow model.
Mignone, A.; Flock, M.; Stute, M.; Kolb, S. M.; Muscianisi, G.
2012-09-01
Context. Explicit numerical computations of hypersonic or super-fast differentially rotating disks are subject to the time-step constraint imposed by the Courant condition, according to which waves cannot travel more than a fraction of a cell during a single time-step update. When the bulk orbital velocity largely exceeds any other wave speed (e.g., sound or Alfvén), as computed in the rest frame, the time step is considerably reduced and an unusually large number of steps may be necessary to complete the computation. Aims: We present a robust numerical scheme to overcome the Courant limitation by improving and extending the algorithm previously known as FARGO (fast advection in rotating gaseous objects) to the equations of magnetohydrodynamics (MHD) using a more general formalism. The proposed scheme conserves total angular momentum and energy to machine precision and works in cartesian, cylindrical, or spherical coordinates. The algorithm has been implemented in the next release of the PLUTO code for astrophysical gasdynamics and is suitable for local or global simulations of accretion or proto-planetary disk models. Methods: By decomposing the total velocity into an average azimuthal contribution and a residual term, the algorithm approaches the solution of the MHD equations through two separate steps corresponding to a linear transport operator in the direction of orbital motion and a standard nonlinear solver applied to the MHD equations written in terms of the residual velocity. Since the former step is not subject to any stability restriction, the Courant condition is computed only in terms of the residual velocity, leading to substantially larger time steps. The magnetic field is advanced in time using the constrained transport method in order to fulfill the divergence-free condition. Furthermore, conservation of total energy and angular momentum is enforced at the discrete level by properly expressing the source terms in terms of upwind Godunov fluxes
Kemner, K. M.; Boyanov, M.; Flynn, T. M.; O'Loughlin, E. J.; Antonopoulos, D. A.; Kelly, S.; Skinner, K.; Mishra, B.; Brooks, S. C.; Watson, D. B.; Wu, W. M.
2015-12-01
FeIII- and SO42--reducing microorganisms and the mineral phases they produce have profound implications for many processes in aquatic and terrestrial systems. In addition, many of these microbially-catalysed geochemical transformations are highly dependent upon introduction of reactants via advective and diffusive hydrological transport. We have characterized microbial communities from a set of static microcosms to test the effect of ethanol diffusion and sulfate concentration on UVI-contaminated sediment. The spatial distribution, valence states, and speciation of both U and Fe were monitored in situ throughout the experiment by synchrotron x-ray absorption spectroscopy, in parallel with solution measurements of pH and the concentrations of sulfate, ethanol, and organic acids. After reaction initiation, a ~1-cm thick layer of sediment near the sediment-water (S-W) interface became visibly dark. Fe XANES spectra of the layer were consistent with the formation of FeS. Over the 4 year duration of the experiment, U LIII-edge XANES indicated reduction of U, first in the dark layer and then throughout the sediment. Next, the microcosms were disassembled and samples were taken from the overlying water and different sediment regions. We extracted DNA and characterized the microbial community by sequencing 16S rRNA gene amplicons with the Illumina MiSeq platform and found that the community evolved from its originally homogeneous composition, becoming significantly spatially heterogeneous. We have also developed an x-ray accessible column to probe elemental transformations as they occur along the flow path in a porous medium with the purpose of refining reactive transport models (RTMs) that describe coupled physical and biogeochemical processes in environmental systems. The elemental distribution dynamics and the RTMs of the redox driven processes within them will be presented.
Lueptow, Richard M.; Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.
2013-11-01
We investigate chaotic advection and diffusion in competitive autocatalytic reactions. To study this subject, we use a computationally efficient method for solving advection-reaction-diffusion equations for periodic flows using a mapping method with operator splitting. In competitive autocatalytic reactions, there are two species, B and C, which both react autocatalytically with species A (A +B -->2B and A +C -->2C). If there is initially a small amount of spatially localized B and C and a large amount of A, all three species will be advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that the small scale interactions associated with the chaotic velocity field, specifically the local finite-time Lyapunov exponents (FTLEs), can accurately predict the final average concentrations of B and C after the reaction is complete. The species, B or C, that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If species B and C start in regions having similar FTLEs, their average concentrations at the end of the reaction will also be similar. Funded by NSF Grant CMMI-1000469.
Adam, A.; Pavlidis, D.; Percival, J. R.; Salinas, P.; Xie, Z.; Fang, F.; Pain, C. C.; Muggeridge, A. H.; Jackson, M. D.
2016-09-01
A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.
Energy Technology Data Exchange (ETDEWEB)
Costa-Cabral, M.C. [GKSS-Forschungszentrum Geesthacht GmbH (Germany). Inst. fuer Hydrophysik
1999-07-01
Current Lagrangian models for simulating advective transport of trace species in a discretized two-dimensional flow field use simplified descriptions of tracer sources, receptors and flow paths. When 'forward trajectories' are used, a diffuse source spread over a two-dimensional grid cell is treated as a single point source located at the cell's center, and its flow is projected in the downflow direction by a line. When 'backward trajectories' are used, each cell is treated as a point receptor and flow is projected back in time in the upflow direction by a line. In both cases, two-dimensional sources or receptors are treated as zero dimensional, and two-dimensional flow tubes are replaced by one-dimensional lines. While these simplifications may be acceptable in some cases, they can generate large errors when the flow field contains regions of considerable divergence of flow directions, or when fine scales are used. A new algorithm is introduced, called TUBES, which provides an exact solution to advective transport in a discretized two-dimensional flow field. TUBES uses two-dimensional flow tubes whose width expands and contracts over directionally divergent and convergent regions of the flow field, respectively. TUBES has applications in a wide variety of the earth sciences, including atmospheric science, oceanography, and surface and groundwater hydrology. (orig.) [German] Gegenwaertige Lagrange-Modelle zur Simulation advektiver Transporte von Tracern in einem diskretisierten zweidimensionalen Stroemungsfeld verwenden vereinfachte Beschreibungen der Quellen, Rezeptoren und Transportwege. Bei der Verwendung vorwaerts gerichteter Trajektorien ('forward trajectories') werden diffusive Quellen, die ueber eine zweidimensionale Gitterzelle verteilt sind, als Punktquelle behandelt, und der Transport mit der Stroemung erfolgt entlang einer Linie. Bei der Verwendung rueckwaerts gerichteter Trajektorien ('backward trajectories
Directory of Open Access Journals (Sweden)
J.-S. Chen
2011-04-01
Full Text Available This study presents a generalized analytical solution for one-dimensional solute transport in finite spatial domain subject to arbitrary time-dependent inlet boundary condition. The governing equation includes terms accounting for advection, hydrodynamic dispersion, linear equilibrium sorption and first order decay processes. The generalized analytical solution is derived by using the Laplace transform with respect to time and the generalized integral transform technique with respect to the spatial coordinate. Several special cases are presented and compared to illustrate the robustness of the derived generalized analytical solution. Result shows an excellent agreement. The analytical solutions of the special cases derived in this study have practical applications. Moreover, the derived generalized solution which consists an integral representation is evaluated by the numerical integration to extend its usage. The developed generalized solution offers a convenient tool for further development of analytical solution of specified time-dependent inlet boundary conditions or numerical evaluation of the concentration field for arbitrary time-dependent inlet boundary problem.
Spectral Properties of a Two Component and Two Temperature Advective Flow
Mandal, S; Mandal, Samir; Chakrabarti, Sandip K.
2005-01-01
Low angular momentum accretion flows very often have centrifugal pressure supported standing shock waves which can accelerate flow particles. The accelerated particles in turn emit synchrotron radiation in presence of magnetic fields. Efficient cooling of the electrons reduces its temperature in comparison to the protons. In this paper, we assume two temperature flows to explore this property of shocks and present an example of the emitted radiation spectrum.
A partially open porous media flow with chaotic advection: towards a model of coupled fields.
Metcalfe, Guy; Lester, Daniel; Ord, Alison; Kulkarni, Pandurang; Trefry, Mike; Hobbs, Bruce E; Regenaur-Lieb, Klaus; Morris, Jeffery
2010-01-13
In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.
Frontiers of chaotic advection
Aref, Hassan; Budišić, Marko; Cartwright, Julyan H E; Clercx, Herman J H; Feudel, Ulrike; Golestanian, Ramin; Gouillart, Emmanuelle; Guer, Yves Le; van Heijst, GertJan F; Krasnopolskaya, Tatyana S; MacKay, Robert S; Meleshko, Vyacheslav V; Metcalfe, Guy; Mezić, Igor; de Moura, Alessandro P S; Omari, Kamal El; Piro, Oreste; Speetjens, Michel F M; Sturman, Rob; Thiffeault, Jean-Luc; Tuval, Idan
2014-01-01
We review the present position of and survey future perspectives in the physics of chaotic advection; the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, micro-fluidics, biological flows, and large-scale dispersion of pollutants in oceanographic and atmospheric flows.
Impact of Calcium on Bacterial Reduction of U(VI) Under Advective Flow
Neiss, J.; Nico, P. S.; Stewart, B. D.; Fendorf, S.
2003-12-01
Due to mining and nuclear-production activities, uranium is now an environmental contaminant of great concern, the hazard of which can be diminished through reduction of the oxidized species, uranyl, to reduced phases such as uraninite. Recent evidence, however, illustrates the importance of uranyl speciation on the extent of reduction. In the presence of calcium, a Ca-UO2-CO3 complex is the dominant aqueous species, greatly limiting abiotic and biotic reduction of uranium. This species is, in fact, the most stable form of U(VI) in waters equilibrated with atmospheric carbon dioxide levels and calcium concentrations > 0.4 mM from pH 5 to 8. Here we explore the impact of calcium on uranium reduction rates and the concomitant biomineralization products of uranium and hydrous ferric oxide under dynamic flow conditions by a metal reducing bacterium, Shewanella putrefaciens. Using x-ray adsorption near edge structure (XANES) spectroscopy, we confirm the complete reduction of uranyl to the precipitated mineral uraninite in systems absent of calcium. While in contrast, minimal reduction transpires upon introduction of millimolar calcium concentration. Thus, calcium concentrations will have profound effects on bacterial reduction, and hence mobility, of uranium within surface and subsurface environments.
Temporal variability from the two-component advective flow solution and its observational evidence
Dutta, Broja G
2016-01-01
In the propagating oscillatory shock model, the oscillation of the post-shock region, i.e., the Compton cloud, causes the observed low-frequency quasi-periodic oscillations (QPOs). The evolution of QPO frequency is explained by the systematic variation of the Compton cloud size, i.e., the steady radial movement of the shock front, which is triggered by the cooling of the post-shock region. Thus, analysis of energy-dependent temporal properties in different variability time scales can diagnose the dynamics and geometry of accretion flows around black holes. We study these properties for the high inclination black hole source XTE J1550-564 during its 1998 outburst and the low-inclination black hole source GX 339-4 during its 2006-07 outburst using RXTE/PCA data, and we find that they can satisfactorily explain the time lags associated with the QPOs from these systems. We find a smooth decrease of the time lag as a function of time in the rising phase of both sources. In the declining phase the time lag increase...
Is There an Advection-Dominated Accretion Flow in Radio Galaxies with Double-Peaked Balmer Lines?
Nagao, T; Shioya, Y; Taniguchi, Y; Nagao, Tohru; Murayama, Takashi; Shioya, Yasuhiro; Taniguchi, Yoshiaki
2002-01-01
In order to examine the prediction that the broad-line radio galaxies (BLRGs) with double-peaked Balmer lines harbor an accretion disk characterized by an advection-dominated accretion flow (ADAF) in their nuclei, we investigate narrow emission-line flux ratios of the narrow-line regions which are photoionized by the nuclear continuum radiation. We compile data from the literature and confirm the pioneering work of Eracleous & Halpern that the BLRGs with the double-peaked Balmer emission exhibit larger flux ratios of both [O I]6300/[O III]5007 and [O II]3727/[O III]5007 than the BLRGs without the double-peaked Balmer emission. To examine whether or not these properties are attributed to the difference in the spectral energy distribution (SED) of the ionizing radiation between the BLRGs with and without the double-peaked Balmer emission, we perform photoionization model calculations using two types of input continuum radiation; one has the strong big blue bump which is expected for standard optically-thick...
Chatterjee, Arka; Chakrabarti, Sandip K.; Ghosh, Himadri
2017-03-01
Two-component advective flow (TCAF) successfully explains spectral and timing properties of black hole candidates. We study the nature of photon trajectories in the vicinity of a Schwarzschild black hole and incorporate this in predicting images of TCAF with a black hole at the Centre. We also compute the emitted spectra. We employ a Monte Carlo simulation technique to achieve our goal. For accurate prediction of the image and the spectra, null trajectories are generated without constraining the motion to any specific plane. Redshift, bolometric flux and corresponding temperature have been calculated with appropriate relativistic consideration. The CENtrifugal pressure supported BOundary Layer or CENBOL near the inner region of the disc, which acts as the Compton cloud, is appropriately modelled as a thick accretion disc in Schwarzschild geometry for the purpose of imaging and computing spectra. The variations of spectra and image with physical parameters such as the accretion rate (dot{m}_d) and inclination angle are presented. We show that the gravitational bending effects of photons do change the spectral shape to some extent.
1992-05-01
residual about four orders of magnitude. For the pr’esent example, this would amount to 7 steps using the exact linearization or 8-9 steps us- 10. ing...the flow about multi- ing first order upwind RHS in(5.9). Dashed line element airfoil configurations. Both of these im- depicts scheme run with exact ... linearization of plementations utilize locally structured meshes first order scheme on the LHS and second order to produce one-dimensional-like
Kurylyk, Barret L.; McKenzie, Jeffrey M; MacQuarrie, Kerry T. B.; Voss, Clifford I.
2014-01-01
Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.
Is There an Advection-dominated Accretion Flow in Radio Galaxies with Double-peaked Balmer Lines?
Nagao, Tohru; Murayama, Takashi; Shioya, Yasuhiro; Taniguchi, Yoshiaki
2002-03-01
In order to examine the prediction that the broad-line radio galaxies (BLRGs) with double-peaked Balmer lines harbor an accretion disk characterized by an advection-dominated accretion flow (ADAF) in their nuclei, we investigate narrow emission line flux ratios of the narrow-line regions (NLRs) which are photoionized by nuclear continuum radiation. We compile data from the literature and confirm the pioneering work of Eracleous & Halpern that the BLRGs with the double-peaked Balmer emission exhibit larger flux ratios of both [O I] λ6300/[O III] λ5007 and [O II] λ3727/[O III] λ5007 than the BLRGs without the double-peaked Balmer emission. To examine whether or not these properties are attributed to the difference in the spectral energy distribution (SED) of the ionizing radiation between the BLRGs with and without the double-peaked Balmer emission, we perform photoionization model calculations using two types of input continuum radiation; one has the strong big blue bump which is expected for standard optically thick accretion disks and the other does not exhibit a strong big blue bump as expected for optically thin ADAFs. We find that the data of the BLRGs with the double-peaked Balmer lines are consistent with the models adopting the SED without a strong big blue bump, while the data of the BLRGs without the double-peaked emission lines are well described by the models adopting the SED with a strong big blue bump. On the other hand, the observed differences in the NLR emission are hard to explain by the difference in the contribution of shocks. These results support the idea that the double-peaked Balmer lines arise at an outer region of an accretion disk which is illuminated by an inner, geometrically thick ADAF.
2005-01-01
The carbon metabolism in costal sediments is of major importance for the global carbon cycle. Costal sediments are also subjected to physical forcing generating water fluxes above and through the sediments, but how the physical affect the carbon metabolism is currently poorly known. In this study, the effect of advective pore water flow on degradation of organic matter in permeable sandy sediment was investigated in a laboratory study during wintertime. Sediments were collected from both brac...
Cholet, Cybèle; Charlier, Jean-Baptiste; Moussa, Roger; Steinmann, Marc; Denimal, Sophie
2017-07-01
The aim of this study is to present a framework that provides new ways to characterize the spatio-temporal variability of lateral exchanges for water flow and solute transport in a karst conduit network during flood events, treating both the diffusive wave equation and the advection-diffusion equation with the same mathematical approach, assuming uniform lateral flow and solute transport. A solution to the inverse problem for the advection-diffusion equations is then applied to data from two successive gauging stations to simulate flows and solute exchange dynamics after recharge. The study site is the karst conduit network of the Fourbanne aquifer in the French Jura Mountains, which includes two reaches characterizing the network from sinkhole to cave stream to the spring. The model is applied, after separation of the base from the flood components, on discharge and total dissolved solids (TDSs) in order to assess lateral flows and solute concentrations and compare them to help identify water origin. The results showed various lateral contributions in space - between the two reaches located in the unsaturated zone (R1), and in the zone that is both unsaturated and saturated (R2) - as well as in time, according to hydrological conditions. Globally, the two reaches show a distinct response to flood routing, with important lateral inflows on R1 and large outflows on R2. By combining these results with solute exchanges and the analysis of flood routing parameters distribution, we showed that lateral inflows on R1 are the addition of diffuse infiltration (observed whatever the hydrological conditions) and localized infiltration in the secondary conduit network (tributaries) in the unsaturated zone, except in extreme dry periods. On R2, despite inflows on the base component, lateral outflows are observed during floods. This pattern was attributed to the concept of reversal flows of conduit-matrix exchanges, inducing a complex water mixing effect in the saturated zone
Cornaton, F; 10.1016/j.advwatres.2005.10.009
2011-01-01
We present a methodology for determining reservoir groundwater age and transit time probability distributions in a deterministic manner, considering advective-dispersive transport in steady velocity fields. In a first step, we propose to model the statistical distribution of groundwater age at aquifer scale by means of the classical advection-dispersion equation for a conservative and nonreactive tracer, associated to proper boundary conditions. The evaluated function corresponds to the density of probability of the random variable age, age being defined as the time elapsed since the water particles entered the aquifer. An adjoint backward model is introduced to characterize the life expectancy distribution, life expectancy being the time remaining before leaving the aquifer. By convolution of these two distributions, groundwater transit time distributions, from inlet to outlet, are fully defined for the entire aquifer domain. In a second step, an accurate and efficient method is introduced to simulate the tr...
Fragile, P Chris
2008-01-01
(Abridged) We present one of the first physically-motivated two-dimensional general relativistic magnetohydrodynamic (GRMHD) numerical simulations of a radiatively-cooled black-hole accretion disk. The fiducial simulation combines a total-energy-conserving formulation with a radiative cooling function, which includes bremsstrahlung, synchrotron, and Compton effects. By comparison with other simulations we show that in optically thin advection-dominated accretion flows, radiative cooling can significantly affect the structure, without necessarily leading to an optically thick, geometrically thin accretion disk. We further compare the results of our radiatively-cooled simulation to the predictions of a previously developed analytic model for such flows. For the very low stress parameter and accretion rate found in our simulated disk, we closely match a state called the "transition" solution between an outer advection-dominated accretion flow and what would be a magnetically-dominated accretion flow (MDAF) in th...
Directory of Open Access Journals (Sweden)
E. Dellwik
2009-08-01
Full Text Available An analysis of flow angles from a fetch-limited beech forest site with clearings is presented. Flow angles and vertical velocities from two types of sonic anemometers as well as a ground based remote sensing lidar were analysed. Instead of using rotations, where zero-flow angles were assumed for neutral flow, the data from the instruments were interpreted in relation to the terrain.
Uncertainties regarding flow distortion and limited sampling time (statistical uncertainty were evaluated and found to be significant. Especially for one of the sonic anemometers, relatively small changes in the flow distortion correction could change the sign of mean vertical velocities taken during stable atmospheric stratification relative to the neutral flow. Despite the uncertainties, it was possible to some extent to relate both positive and negative mean flow angles to features in the terrain.
Conical and linear scans with a remote sensing lidar were evaluated for estimation of vertical velocities and flow angles. The results of the vertical conical scans were promising, and yielded negative flow angles for a sector where the forest is fetch-limited. However, more data and analysis is needed for a complete evaluation of the technique. The horizontal linear scans showed the variability of the mean wind speed field. A vertical velocity was calculated from different focusing distances, but this estimate yielded unrealistically high vertical velocities, due to neglect of the transversal wind component.
The vertical advection term was calculated using the measured mean flow angles at the mast and profile measurements of carbon dioxide, but it is not recommended to use in relation with the flux measurement as the vertical velocity measured at the mast is most likely not representative for the whole forest.
Striated populations in disordered environments with advection
Chotibut, Thiparat; Nelson, David R.; Succi, Sauro
2017-01-01
Growth in static and controlled environments such as a Petri dish can be used to study the spatial population dynamics of microorganisms. However, natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments. We investigate a generalized Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition. We analytically and numerically demonstrate that the non-equilibrium steady-state population density develops a flow-driven striation pattern. The striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity-independent value. Linear response theory is developed to study the statistics of the steady states. Theoretical predictions show excellent agreement with the numerical steady states of the generalized FKPP equation obtained from Lattice Boltzmann simulations. These findings suggest that, although the growth disorder can be spatially uncorrelated, correlated population structures with striations emerge naturally at sufficiently strong advection.
Symmetry constraints on generalizations of Bjorken flow
Gubser, Steven S
2010-01-01
I explain a generalization of Bjorken flow where the medium has finite transverse size and expands both radially and along the beam axis. If one assumes that the equations of viscous hydrodynamics can be used, with p=epsilon/3 and zero bulk viscosity, then the flow I describe can be developed into an exact solution of the relativistic Navier-Stokes equations. The local four-velocity in the flow is entirely determined by the assumption of symmetry under a subgroup of the conformal group.
DEFF Research Database (Denmark)
Cook, Perran L. M.; Wenzhofer, Frank; Glud, Ronnie N.;
2007-01-01
of O-2 distribution across ripples, and also deep subsurface O-2 pools, being observed. Mineralization pathways were predominantly aerobic when benthic mineralization rates were low and advective pore-water flow high as a result of well-developed sediment topography. By contrast, mineralization...... proceeded predominantly through sulfate reduction when benthic mineralization rates were high and advective pore-water flow low as a result of poorly developed topography. Previous studies of benthic mineralization in shallow sandy sediments have generally ignored these dynamics and, hence, have overlooked......We conducted four field campaigns to evaluate benthic O-2 consumption and the effect of advective pore-water flow in nearshore permeable sediments in the North Sea and Baltic Sea. Advective pore-water transport had a marked effect on the benthic exchange of O-2 and TCO2 in benthic chamber...
Fisher, J. C.; Ackerman, D. J.; Rousseau, J. P.; Rattray, G. W.
2009-12-01
Three-dimensional steady-state and transient models of groundwater flow and advective transport through the fractured basalts and interbedded sediments of the Eastern Snake River Plain (ESRP) aquifer were developed by the U.S. Geological Survey in cooperation with the U.S. Department of Energy. The model domain covers an area of 1,940 square miles that includes most of the Idaho National Laboratory (INL). A 50-year history of waste disposal at the INL has resulted in measurable concentrations of waste contaminants in the aquifer. Numerical models simulated 1980 steady-state conditions and transient flow for 1980-95. In the transient model, streamflow infiltration was the major stress. The models were calibrated using the parameter-estimation program incorporated in MODFLOW-2000. The steady-state model reasonably simulated the observed water-table altitude and gradients. Simulation of transient conditions reproduced changes in the flow system resulting from episodic infiltration from the Big Lost River. Analysis of simulations shows that flow is (1) dominantly horizontal through interflow zones in basalt, vertical anisotropy resulting from contrasts in hydraulic conductivity of different types of basalt and the interbedded sediments, (2) temporally variable due to streamflow infiltration from the Big Lost River, and (3) moving downward downgradient of the INL. Particle-tracking simulations were used to evaluate how simulated groundwater flow paths and travel times differ between the steady-state and transient flow models, and how well model-derived groundwater flow directions and velocities compare to independently-derived estimates. Particle tracking also was used to simulate the growth of tritium plumes originating at two INL facilities over a 16 year period under steady-state and transient flow conditions (1953-68). The shape, dimensions, and areal extent of these plumes were compared to a map of the plumes for 1968 from tritium releases beginning in 1952
General purpose flow solver applied to flow over hills
Energy Technology Data Exchange (ETDEWEB)
Soerensen, N.N.
1995-09-01
The present report describes the development a 2D and 3D finite-volume code in general curvilinear coordinates using the Basis 2D/3D platform by Michelsen. The codes are based on the Reynolds averaged incompressible isothermal Navier-Stokes equations and use primitive variables (U, V, W and P). The turbulence is modelled by the high Reynolds number {kappa} - {epsilon} model. Cartesian velocity components are used in a non-staggered arrangement following the methodology of Rhie. The equation system is solved using the SIMPLE method of Patankar and Spalding. Solution of the transport equations is obtained by a successive application of a TDMA solver in alternating direction. The solution of the pressure correction equation is accelerated using the multigrid tools from the Basis 2D/3D platform. Additionally a three-level grid sequence is implemented in order to minimize the overall solution time. Higher-order schemes (SUDS and QUICK) are implemented as explicit corrections to a first-order upwind difference scheme. In both the 2D and the 3D code it is possible to handle multiblock configurations. This feature is added in order to obtain a greater geometric flexibility. To mesh natural terrain in connection with atmospheric flow over complex terrain, a two- and a three-dimensional hyperbolic mesh generator are constructed. Additionally, a two- and a three-dimensional mesh generator based on a simple version of the transfinite interpolation technique are implemented. Several two-dimensional test cases are calculated e.g. laminar flow over a circular cylinder, turbulent channel flow, and turbulent flow over a backward facing step, all with satisfying results. In order to illustrate the application of the codes to atmospheric flow two cases are calculated, flow over a cube in a thick turbulent boundary-layer, and the atmospheric flow over the Askervein hill. (au) 13 tabs., 75 ills., 66 refs.
Finite-size particles, advection, and chaos: a collective phenomenon of intermittent bursting.
Medrano-T, Rene O; Moura, Alessandro; Tél, Tamás; Caldas, Iberê L; Grebogi, Celso
2008-11-01
We consider finite-size particles colliding elastically, advected by a chaotic flow. The collisionless dynamics has a quasiperiodic attractor and particles are advected towards this attractor. We show in this work that the collisions have dramatic effects in the system's dynamics, giving rise to collective phenomena not found in the one-particle dynamics. In particular, the collisions induce a kind of instability, in which particles abruptly spread out from the vicinity of the attractor, reaching the neighborhood of a coexisting chaotic saddle, in an autoexcitable regime. This saddle, not present in the dynamics of a single particle, emerges due to the collective particle interaction. We argue that this phenomenon is general for advected, interacting particles in chaotic flows.
Institute of Scientific and Technical Information of China (English)
Ya-Di Xu; Xin-Wu Cao
2009-01-01
It was found that advection-dominated accretion flow (ADAF)+thin disk model calculations can reproduce the observed spectral energy distributions (SEDs) of two low- luminosity active galactic nuclei (AGNs), provided they are accreting at ～ 0.01 - 0.03 Eddington rates and the thin disks are truncated to ADAFs at～ 100Rs (Rs is the Schwarzschild radius) for M81 and NGC 4579 (Quataert et al. 1999). However, the black hole masses adopted in their work are about one order of magnitude lower than recent measurements on these two sources. Adopting the well estimated black hole masses, our ADAF+thin disk model calculations can reproduce the observed SEDs of these two low- luminosity AGNs, if the black hole is accreting at 2.5 × 10-4 Eddington rates with the thin disk truncated at Rtr = 120Rs for M81 ((m) = 3.3 × 10-3 and Rtr = 80Rs are required for NGC 4579). The transition zones with temperature from the thin disk with 104 - 105 to～109 - 1010 K in the ADAF will inevitably emit thermal X-ray lines, which provides a useful diagnosis of their physical properties. The observed widths of the thermal X-ray iron lines at(～)6.8 keV are consistent with Doppler broadening by Keplerian motion of the gases in the transition zones at～100Rs. We use the structure of the transition zone between the ADAF and the thin disk derived by assuming the turbulent diffusive heat mechanism to calculate their thermal X-ray line emission with the standard software package Astrophysical Plasma Emission Code (APEC). Comparing them with the equivalent widths of the observed thermal X-ray iron lines in these two sources, we find that the turbulent diffusive heat mechanism seems to be unable to reproduce the ob- served thermal X-ray line emission. The test of the evaporation model for the accretion mode transition with the observed thermal X-ray line emission is briefly discussed.
Optimal convection cooling flows in general geometries
Alben, Silas
2016-01-01
We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of coordinates which are the pure conduction temperature and its harmonic conjugate. We find optimal flows for cooling a cylinder in an annular domain, a hot plate embedded in a cold surface, and a channel with hot interior and cold exterior. With a constraint of fixed kinetic energy, the optimal flows are all essentially the same in the conformal coordinates. In the physical coordinates, they consist of vortices ranging in size from the length of the hot surface to a small cutoff length at the interface of the hot and cold surfaces. With the constraint of fixed enstrophy (or fixed rate of viscous dissipation), a geometry-dependent metric factor appears in the equations. The conformal coordinates are useful here because they map the problems to a rectangular domain, facilitating num...
Modelling debris flows down general channels
Directory of Open Access Journals (Sweden)
S. P. Pudasaini
2005-01-01
Full Text Available This paper is an extension of the single-phase cohesionless dry granular avalanche model over curved and twisted channels proposed by Pudasaini and Hutter (2003. It is a generalisation of the Savage and Hutter (1989, 1991 equations based on simple channel topography to a two-phase fluid-solid mixture of debris material. Important terms emerging from the correct treatment of the kinematic and dynamic boundary condition, and the variable basal topography are systematically taken into account. For vanishing fluid contribution and torsion-free channel topography our new model equations exactly degenerate to the previous Savage-Hutter model equations while such a degeneration was not possible by the Iverson and Denlinger (2001 model, which, in fact, also aimed to extend the Savage and Hutter model. The model equations of this paper have been rigorously derived; they include the effects of the curvature and torsion of the topography, generally for arbitrarily curved and twisted channels of variable channel width. The equations are put into a standard conservative form of partial differential equations. From these one can easily infer the importance and influence of the pore-fluid-pressure distribution in debris flow dynamics. The solid-phase is modelled by applying a Coulomb dry friction law whereas the fluid phase is assumed to be an incompressible Newtonian fluid. Input parameters of the equations are the internal and bed friction angles of the solid particles, the viscosity and volume fraction of the fluid, the total mixture density and the pore pressure distribution of the fluid at the bed. Given the bed topography and initial geometry and the initial velocity profile of the debris mixture, the model equations are able to describe the dynamics of the depth profile and bed parallel depth-averaged velocity distribution from the initial position to the final deposit. A shock capturing, total variation diminishing numerical scheme is implemented to
Voronin, Lois M.; Cauller, Stephen J.
2017-07-31
flow to streams that eventually flow into the bay and groundwater discharge directly into the estuary and adjoining coastal wetlands— is summarized by quantity, travel time, and estimated nitrogen concentration. Simulated average groundwater discharge to streams in the watershed that flow into the BB-LEH estuary is approximately 400 million gallons per day. Particle-tracking results indicate that the travel time of 56 percent of this discharge is less than 7 years. Fourteen percent of the groundwater discharge to the streams in the BB-LEH watershed has a travel time of less than 7 years and originates in urban land. Analysis of flow-path simulations indicate that approximately 13 percent of the total groundwater flow through the study area discharges directly to the estuary and adjoining coastal wetlands (approximately 64 million gallons per day). The travel time of 19 percent of this discharge is less than 7 years. Ten percent of this discharge (1 percent of the total groundwater flow through the study area) originates in urban areas and has a travel time of less than 7 years. Groundwater that discharges to the streams that flow into the BB-LEH, in general, has shorter travel times, and a higher percentage of it originates in urban areas than does direct groundwater discharge to the Barnegat Bay–Little Egg Harbor estuary.The simulated average nitrogen concentration in groundwater that discharges to the Toms River, upstream from streamflow-gaging station 01408500 was computed and compared to summary concentrations determined from analysis of multiple surface-water samples. The nitrogen concentration in groundwater that discharges directly to the estuary and adjoining coastal wetlands is a current data gap. The particle tracking methodology used in this study provides an estimate of this concentration."
General purpose fast decoupled power flow
Energy Technology Data Exchange (ETDEWEB)
Nanda, J.; Bijwe, P.R.; Henry, J.; Bapi Raju, V. (Indian Inst. of Tech., New Delhi (IN). Dept. of Electrical Engineering)
1992-03-01
A general purpose fast decoupled power flow model (GFDPF) is presented that exhibits more or less best convergence properties for both well-behaved and ill-conditioned systems. In the proposed model, all network shunts such as line charging, external shunts at buses, shunts formed due to {pi} representation of off-nominal in-phase transformers etc. are treated as constant impedance loads. The effect of line resistances is considered while forming the (B') matrix and are ignored in forming the (B'') matrix. This model is tested on several systems for both well-behaved and ill-conditioned situations. A simple, efficient compensation technique is proposed to deal with Q-limit enforcements associated with bus-type switchings at voltage-controlled buses. The results demonstrate that the proposed GFDPF model exhibits more or less stable convergence behaviour for both well-behaved and ill-conditioned situations. (author).
Capillary deposition of advected floating particles
Dressaire, Emilie; Debaisieux, Aymeric; Gregori, Federico
2016-11-01
The deposition and aggregation of particles flowing through a confined environment can dramatically hinder the transport of suspensions. Yet, the mechanisms responsible for the deposition of particles in shear flow are not fully understood. Here, we use an experimental model system in which floating particles are advected on the surface of a water channel and deposited on fixed obstacles through attractive capillary effects. By varying the flow rate of the liquid, the wetting properties and size of the particles and obstacles, we can tune the magnitude of the capillary and hydrodynamic forces that determine the probability of deposition and the equilibrium position on the substrate. We show that arrays of obstacles can be designed to efficiently capture the floating particles advected by the flow.
A novel method for analytically solving a radial advection-dispersion equation
Lai, Keng-Hsin; Liu, Chen-Wuing; Liang, Ching-Ping; Chen, Jui-Sheng; Sie, Bing-Ruei
2016-11-01
An analytical solution for solute transport in a radial flow field has a variety of practical applications in the study of the transport in push-pull/divergent/convergent flow tracer tests, aquifer remediation by pumping and aquifer storage and recovery. However, an analytical solution for radial advective-dispersive transport has been proven very difficult to develop and relatively few in subsurface hydrology have made efforts to do so, because variable coefficients in the governing partial differential equations. Most of the solutions for radial advective-dispersive transport presented in the literature have generally been solved semi-analytically with the final concentration values being obtained with the help of a numerical Laplace inversion. This study presents a novel solution strategy for analytically solving the radial advective-dispersive transport problem. A Laplace transform with respect to the time variable and a generalized integral transform technique with respect to the spatial variable are first performed to convert the transient governing partial differential equations into an algebraic equation. Subsequently, the algebraic equation is solved using simple algebraic manipulations, easily yielding the solution in the transformed domain. The solution in the original domain is ultimately obtained by successive applications of the Laplace and corresponding generalized integral transform inversions. A convergent flow tracer test is used to demonstrate the robustness of the proposed method for deriving an exact analytical solution to the radial advective-dispersive transport problem. The developed analytical solution is verified against a semi-analytical solution taken from the literature. The results show perfect agreement between our exact analytical solution and the semi-analytical solution. The solution method presented in this study can be applied to create more comprehensive analytical models for a great variety of radial advective
Energy Technology Data Exchange (ETDEWEB)
Gjesdal, Thor
1997-12-31
This thesis discusses the development and application of efficient numerical methods for the simulation of fluid flows, in particular the flow of incompressible fluids. The emphasis is on practical aspects of algorithm development and on application of the methods either to linear scalar model equations or to the non-linear incompressible Navier-Stokes equations. The first part deals with cell centred multigrid methods and linear correction scheme and presents papers on (1) generalization of the method to arbitrary sized grids for diffusion problems, (2) low order method for advection-diffusion problems, (3) attempt to extend the basic method to advection-diffusion problems, (4) Fourier smoothing analysis of multicolour relaxation schemes, and (5) analysis of high-order discretizations for advection terms. The second part discusses a multigrid based on pressure correction methods, non-linear full approximation scheme, and papers on (1) systematic comparison of the performance of different pressure correction smoothers and some other algorithmic variants, low to moderate Reynolds numbers, and (2) systematic study of implementation strategies for high order advection schemes, high-Re flow. An appendix contains Fortran 90 data structures for multigrid development. 160 refs., 26 figs., 22 tabs.
A General Thermal Equilibrium Discharge Flow Model
Institute of Scientific and Technical Information of China (English)
ZHAO; Min-fu; ZHANG; Dong-xu; LV; Yu-feng
2015-01-01
In isentropic and thermal equilibrium assumptions,a discharge flow model was derived,which unified the rules of normal temperature water discharge,high temperature and high pressure water discharge,two-phase critical flow,saturated steam and superheated steam critical
Optically-thick accretion discs with advection
Institute of Scientific and Technical Information of China (English)
陈林红; 吴枚; 尚仁成
2002-01-01
The structures of optically-thick accretion discs with radial advection have been investigated by the iteration and integration algorithms. The advective cooling term changes mostly the inner part of disc solution, and even results in an optically-thick advection-dominated accretion flow (ADAF). Three distinct branches-the outer Shakura-Sunyaev disc (SSD), the inner ADAF and the middle transition layer-are found for a super-Eddington disc. The SSD-ADAF transition radius can be estimated as 18(M/ME)RG where RG is the Schwarzschild radius, M is the mass accretion rate and ME is the Eddington accretion rate. SSD solutions calculated with the iteration and integration methods are identical, while ADAF solutions obtained by these two methods differ greatly. Detailed algorithms and their differences have been analysed. The iteration algorithm is not self-consistent, since it implies that the dimensionless advection factor ξ is invariant, but in the inner ADAF region the variation of ξ is not negligible. The integration algorithm is always effective for the whole region of an optically-thick disc if the accretion rate is no smaller than 10-4ME. For optically-thin discs, the validity of these two algorithms is different. We suggest that the integration method be employed to calculate the global solution of a disc model without assuming ξ to be a constant. We also discuss its application to the emergent continuum spectrum in order to explain observational facts.
LAYER DEPENDENT ADVECTION IN CMAQ
The advection methods used in CMAQ require that the Courant-Friedrichs-Lewy (CFL) condition be satisfied for numerical stability and accuracy. In CMAQ prior to version 4.3, the ADVSTEP algorithm established CFL-safe synchronization and advection timesteps that were uniform throu...
An explicit high order method for fractional advection diffusion equations
Sousa, Ercília
2014-12-01
We propose a high order explicit finite difference method for fractional advection diffusion equations. These equations can be obtained from the standard advection diffusion equations by replacing the second order spatial derivative by a fractional operator of order α with 1convergence of the numerical method through consistency and stability. The order of convergence varies between two and three and for advection dominated flows is close to three. Although the method is conditionally stable, the restrictions allow wide stability regions. The analysis is confirmed by numerical examples.
Directory of Open Access Journals (Sweden)
Taohua Liu
2017-01-01
Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(KlogK. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.
Concave Generalized Flows with Applications to Market Equilibria
Vegh, Laszlo A
2011-01-01
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give the first polynomial time combinatorial algorithm for solving corresponding optimization problems, finding a epsilon-approximate solution in O(m(m+\\log n)\\log(MUm/epsilon)) arithmetic operations and value oracle queries, where M and U are upper bounds on simple parameters. For (linear) generalized flows, our algorithm can be seen as a variant of the highest-gain augmenting path algorithm by Goldfarb, Jin and Orlin. We show that this general convex programming model serves as a common framework for several market equilibrium problems, including the linear Fisher market model and its various extensions. Our result immediately enables us to extend these market models to more general settings and to solve some open problems in the literature.
High Order Semi-Lagrangian Advection Scheme
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Magnetic field advection in two interpenetrating plasma streams
Energy Technology Data Exchange (ETDEWEB)
Ryutov, D. D.; Kugland, N. L.; Levy, M. C.; Plechaty, C.; Ross, J. S.; Park, H. S. [Lawrence Livermore National Laboratory, Livermore, California 94551 (United States)
2013-03-15
Laser-generated colliding plasma streams can serve as a test-bed for the study of various astrophysical phenomena and the general physics of self-organization. For streams of a sufficiently high kinetic energy, collisions between the ions of one stream with the ions of the other stream are negligible, and the streams can penetrate through each other. On the other hand, the intra-stream collisions for high-Mach-number flows can still be very frequent, so that each stream can be described hydrodynamically. This paper presents an analytical study of the effects that these interpenetrating streams have on large-scale magnetic fields either introduced by external coils or generated in the plasma near the laser targets. Specifically, a problem of the frozen-in constraint is assessed and paradoxical features of the field advection in this system are revealed. A possibility of using this system for studies of magnetic reconnection is mentioned.
Anderson-Witting transport coefficients for flows in general relativity
Ambrus, Victor E
2016-01-01
The transport coefficients induced by the Anderson-Witting approximation of the collision term in the relativistic Boltzmann equation are derived for close to equilibrium flows in general relativity. Using the tetrad formalism, it is shown that the expression for these coefficients is the same as that obtained on flat space-time, in agreement with the generalized equivalence principle.
Analytical Solutions of the Space-Time Fractional Derivative of Advection Dispersion Equation
Directory of Open Access Journals (Sweden)
Abdon Atangana
2013-01-01
Full Text Available Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in porous medium. A space-time fractional advection-dispersion equation (FADE is a generalization of the classical ADE in which the first-order space derivative is replaced with Caputo or Riemann-Liouville derivative of order , and the second-order space derivative is replaced with the Caputo or the Riemann-Liouville fractional derivative of order . We derive the solution of the new equation in terms of Mittag-Leffler functions using Laplace transfrom. Some examples are given. The results from comparison let no doubt that the FADE is better in prediction than ADE.
GENERALIZED VARIATIONAL OPTIMAZATION ANALYSIS FOR 2-D FLOW FIELD
Institute of Scientific and Technical Information of China (English)
HUANG Si-xun; XU Ding-hua; LAN Wei-ren; TENG Jia-jun
2005-01-01
The Variational Optimization Analysis Method (VOAM) for 2-D flow field suggested by Sasaki was reviewed first. It is known that the VOAM can be used efficiently in most cases. However, in the cases where there are high frequency noises in 2-D flow field, it appears to be inefficient. In the present paper, based on Sasaki's VOAM, a Generalized Variational Optimization Analysis Method (GVOAM) was proposed with regularization ideas, which could deal well with flow fields containing high frequency noises. A numerical test shows that observational data can be both variationally optimized and filtered, and therefore the GVOAM is an efficient method.
General Separations Area (GSA) Groundwater Flow Model Update: Hydrostratigraphic Data
Energy Technology Data Exchange (ETDEWEB)
Bagwell, L. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Bennett, P. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Flach, G. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2017-02-21
This document describes the assembly, selection, and interpretation of hydrostratigraphic data for input to an updated groundwater flow model for the General Separations Area (GSA; Figure 1) at the Department of Energy’s (DOE) Savannah River Site (SRS). This report is one of several discrete but interrelated tasks that support development of an updated groundwater model (Bagwell and Flach, 2016).
FLUENT/BFC - A general purpose fluid flow modeling program for all flow speeds
Dvinsky, Arkady S.
FLUENT/BFC is a fluid flow modeling program for a variety of applications. Current capabilities of the program include laminar and turbulent flows, subsonic and supersonic viscous flows, incompressible flows, time-dependent and stationary flows, isothermal flows and flows with heat transfer, Newtonian and power-law fluids. The modeling equations in the program have been written in coordinate system invariant form to accommodate the use of boundary-conforming, generally nonorthogonal coordinate systems. The boundary-conforming coordinate system can be generated using both an internal grid generator, which is an integral part of the code, and external application-specific grid generators. The internal grid generator is based on a solution of a system of elliptic partial differential equations and can produce grids for a wide variety of two- and three-dimensional geometries.
A remapped particle-mesh semi-Lagrangian advection scheme
Cotter, C.J.; Frank, J.E.; Reich, S.
2007-01-01
We describe the remapped particle-mesh advection method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In addition to the conservation property, the remapped pa
Advective - dispersive contaminant transport towards a pumping well
Kooten, van J.J.A.
1996-01-01
In this thesis we describe an analytical approximation method for predicting the advective- dispersive transport of a contaminant towards a pumping well. The groundwater flow is assumed to be stationary and essentially horizontal. Due to dispersion contaminant transport is a stochastic pr
Theory of advection-driven long range biotic transport
We propose a simple mechanistic model to examine the effects of advective flow on the spread of fungal diseases spread by wind-blown spores. The model is defined by a set of two coupled non-linear partial differential equations for spore densities. One equation describes the long-distance advectiv...
A computational method for sharp interface advection
Roenby, Johan; Bredmose, Henrik; Jasak, Hrvoje
2016-11-01
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists of two parts. First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face-interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple two-dimensional and three-dimensional interface advection problems on both structured and unstructured meshes. The results are very satisfactory in terms of volume conservation, boundedness, surface sharpness and efficiency. The isoAdvector method was implemented as an OpenFOAM extension and is published as open source.
A Computational Method for Sharp Interface Advection
Roenby, Johan; Jasak, Hrvoje
2016-01-01
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists in two parts: First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step. Second, from the reconstructed surface, we model the motion of the face-interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total volume of fluid transported across the face. The method was tested on simple 2D and 3D interface advection problems ...
Dynamics of generalized Gaussian polymeric structures in random layered flows
Katyal, Divya; Kant, Rama
2015-04-01
We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron-de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent α . Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of α , the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.
Fast multigrid solution of the advection problem with closed characteristics
Energy Technology Data Exchange (ETDEWEB)
Yavneh, I. [Israel Inst. of Technology, Haifa (Israel); Venner, C.H. [Univ. of Twente, Enschede (Netherlands); Brandt, A. [Weizmann Inst. of Science, Rehovot (Israel)
1996-12-31
The numerical solution of the advection-diffusion problem in the inviscid limit with closed characteristics is studied as a prelude to an efficient high Reynolds-number flow solver. It is demonstrated by a heuristic analysis and numerical calculations that using upstream discretization with downstream relaxation-ordering and appropriate residual weighting in a simple multigrid V cycle produces an efficient solution process. We also derive upstream finite-difference approximations to the advection operator, whose truncation terms approximate {open_quotes}physical{close_quotes} (Laplacian) viscosity, thus avoiding spurious solutions to the homogeneous problem when the artificial diffusivity dominates the physical viscosity.
Nucleosynthesis in Advective Accretion Disks Around Galactic and Extra-Galactic Black Holes
Mukhopadhyay, B
1998-01-01
We compute the nucleosynthesis of materials inside advective disks around black holes. We show that composition of incoming matter can change significantly depending on the accretion rate and accretion disks. These works are improvements on the earlier works in thick accretion disks of Chakrabarti, Jin & Arnett (1987) in presence of advection in the flow.
Coupling of Active Motion and Advection Shapes Intracellular Cargo Transport
Trong, P Khuc; Goldstein, R E; 10.1103/PhysRevLett.109.028104
2012-01-01
Intracellular cargo transport can arise from passive diffusion, active motor-driven transport along cytoskeletal filament networks, and passive advection by fluid flows entrained by such motor/cargo motion. Active and advective transport are thus intrinsically coupled as related, yet different representations of the same underlying network structure. A reaction-advection-diffusion system is used here to show that this coupling affects the transport and localization of a passive tracer in a confined geometry. For sufficiently low diffusion, cargo localization to a target zone is optimized either by low reaction kinetics and decoupling of bound and unbound states, or by a mostly disordered cytoskeletal network with only weak directional bias. These generic results may help to rationalize subtle features of cytoskeletal networks, for example as observed for microtubules in fly oocytes.
Generalized primary/secondary flow analysis of viscous flow around bodies at incidence
Govindan, T. R.; Briley, W. R.; Chang, Ming-Shun
1991-01-01
Generalized primary/secondary flow equations, which are an approximation to the Navier-Stokes equations, have been utilized to compute the three-dimensional viscous flow around bodies at incidence. Two features central to the approximations in the primary/secondary flow equations are a locally specified primary flow direction and a decomposition of the secondary velocity field. For the flow around a body at incidence, the local primary flow direction is aligned with streamlines for the potential flow around the body at zero degrees incidence. A sequentially decoupled implicit algorithm exploits the form of the primary/secondary flow equations for fast run times. Computed solutions for flow around an ogive cylinder at incidence and an unappended submarine hull in drift have been presented. These solutions show the generation of strong lee-side vortices which are a source of propulsor inlet distortion and a side-force on the body. Computed solutions agree well with available experimental data. The combined efficiency and accuracy of the approximate equations and solution algorithm make this approach attractive for computing viscous flow around bodies at incidence.
The effect of magnetic resistivity in advection dominated accretion disk with poloidal magnetic
Directory of Open Access Journals (Sweden)
J Ghanbari
2009-12-01
Full Text Available In this work, we carry out self –similar solutions of viscous-resistive accretion flows around a magnetized compact object. We consider an axi-symmetric, rotating, isothermal steady accretion flow, which contains a poloidal magnetic field of the central star. The dominant mechanism of energy dissipation is assumed to be the turbulence viscosity and magnetic diffusivity due to the magnetic field of the central star. We explore the effect of viscosity, magnetic diffusivity and advection on a rotating disk. We show that dynamical quantities of advection dominated accretion flows (ADAFs are sensitive to the advection, viscosity and magnetic diffusivity parameters.
A computational method for sharp interface advection
DEFF Research Database (Denmark)
Roenby, Johan; Bredmose, Henrik; Jasak, Hrvoje
2016-01-01
We devise a numerical method for passive advection of a surface, such as the interface between two incompressible fluids, across a computational mesh. The method is called isoAdvector, and is developed for general meshes consisting of arbitrary polyhedral cells. The algorithm is based on the volume...... of fluid (VOF) idea of calculating the volume of one of the fluids transported across the mesh faces during a time step. The novelty of the isoAdvector concept consists of two parts. First, we exploit an isosurface concept for modelling the interface inside cells in a geometric surface reconstruction step....... Second, from the reconstructed surface, we model the motion of the face–interface intersection line for a general polygonal face to obtain the time evolution within a time step of the submerged face area. Integrating this submerged area over the time step leads to an accurate estimate for the total...
Memory effects in chaotic advection of inertial particles
Daitche, Anton; Tél, Tamás
2014-07-01
A systematic investigation of the effect of the history force on particle advection is carried out for both heavy and light particles. General relations are given to identify parameter regions where the history force is expected to be comparable with the Stokes drag. As an illustrative example, a paradigmatic two-dimensional flow, the von Kármán flow is taken. For small (but not extremely small) particles all investigated dynamical properties turn out to heavily depend on the presence of memory when compared to the memoryless case: the history force generates a rather non-trivial dynamics that appears to weaken (but not to suppress) inertial effects, it enhances the overall contribution of viscosity. We explore the parameter space spanned by the particle size and the density ratio, and find a weaker tendency for accumulation in attractors and for caustics formation. The Lyapunov exponent of transients becomes larger with memory. Periodic attractors are found to have a very slow, {{t}^{-1/2}} type convergence towards the asymptotic form. We find that the concept of snapshot attractors is useful to understand this slow convergence: an ensemble of particles converges exponentially fast towards a snapshot attractor, which undergoes a slow shift for long times.
Memory Effects in Chaotic Advection of Inertial Particles
Daitche, Anton
2014-01-01
A systematic investigation of the effect of the history force on particle advection is carried out for both heavy and light particles. General relations are given to identify parameter regions where the history force is expected to be comparable with the Stokes drag. As an illustrative example, a paradigmatic two-dimensional flow, the von K\\'arm\\'an flow is taken. For small (but not extremely small) particles all investigated dynamical properties turn out to heavily depend on the presence of memory when compared to the memoryless case: the history force generates a rather nontrivial dynamics that appears to weaken (but not to suppress) inertial effects, it enhances the overall contribution of viscosity. We explore the parameter space spanned by the particle size and the density ratio, and find a weaker tendency for accumulation in attractors and for caustics formation. The Lyapunov exponent of transients becomes larger with memory. Periodic attractors are found to have a very slow, $t^{-1/2}$ type convergence...
The role of advection in a two-species competition model
Averill, Isabel; Lou, Yuan
2017-01-01
The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence of multiple populations, in contrast with the situation of weak advection where coexistence may not be possible. The transition of the dynamics from weak to strong advection is generally difficult to determine. In this work the authors consider a mathematical model of two competing populations in a spatially varying but temporally constant environment, where both species have the same population dynamics but different dispersal strategies: one species adopts random dispersal, while the dispersal strategy for the other species is a combination of random dispersal and advection upward along the resource gradient. For any given diffusion rates the authors consider the bifurcation diagram of positive steady states by u...
A general mixture model for sediment laden flows
Liang, Lixin; Yu, Xiping; Bombardelli, Fabián
2017-09-01
A mixture model for general description of sediment-laden flows is developed based on an Eulerian-Eulerian two-phase flow theory, with the aim at gaining computational speed in the prediction, but preserving the accuracy of the complete two-fluid model. The basic equations of the model include the mass and momentum conservation equations for the sediment-water mixture, and the mass conservation equation for sediment. However, a newly-obtained expression for the slip velocity between phases allows for the computation of the sediment motion, without the need of solving the momentum equation for sediment. The turbulent motion is represented for both the fluid and the particulate phases. A modified k-ε model is used to describe the fluid turbulence while an algebraic model is adopted for turbulent motion of particles. A two-dimensional finite difference method based on the SMAC scheme was used to numerically solve the mathematical model. The model is validated through simulations of fluid and suspended sediment motion in steady open-channel flows, both in equilibrium and non-equilibrium states, as well as in oscillatory flows. The computed sediment concentrations, horizontal velocity and turbulent kinetic energy of the mixture are all shown to be in good agreement with available experimental data, and importantly, this is done at a fraction of the computational efforts required by the complete two-fluid model.
Maximum estimates for generalized Forchheimer flows in heterogeneous porous media
Celik, Emine; Hoang, Luan
2017-02-01
This article continues the study in [4] of generalized Forchheimer flows in heterogeneous porous media. Such flows are used to account for deviations from Darcy's law. In heterogeneous media, the derived nonlinear partial differential equation for the pressure can be singular and degenerate in the spatial variables, in addition to being degenerate for large pressure gradient. Here we obtain the estimates for the L∞-norms of the pressure and its time derivative in terms of the initial and the time-dependent boundary data. They are established by implementing De Giorgi-Moser's iteration in the context of weighted norms with the weights specifically defined by the Forchheimer equation's coefficient functions. With these weights, we prove suitable weighted parabolic Poincaré-Sobolev inequalities and use them to facilitate the iteration. Moreover, local in time L∞-bounds are combined with uniform Gronwall-type energy inequalities to obtain long-time L∞-estimates.
Thermal power system analysis using a generalized network flow model
Energy Technology Data Exchange (ETDEWEB)
Kumar, John Arun [Former Senior Design Engineer, Power System Analysis and Control Group, Bharat Heavy Electricals Limited, New Delhi (India); Chebiyam, Radhakrishna [Former Director, Academic Staff College, JNT University, Hyderabad-72 (India)
2012-07-01
This paper analyzes an Integrated Thermal Power System using a Multiperiod Generalized Network Flow Model. The thermal system analysis is carried out by taking into account the complex dynamics involved in utilizing multiple energy carriers (coal, diesel and natural gas). The model comprises energy source nodes, energy transformation nodes, energy storage nodes, energy demand nodes and their interconnections. The solution to the integrated energy system problem involves the evaluation of energy flows that meet the electricity demand at minimum total cost, while satisfying system constraints. This is illustrated through the India case study using a minimum time-step of one hour. MATLAB based software was developed for carrying out this study. TOMLAB/CPLEX software was utilized for obtaining the optimal solution. The model and the methodology utilized for conducting the study would be of interest to those involved in integrated energy system planning for a country or a region.
General spectral flow formula for fixed maximal domain
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
2005-01-01
We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow...... of the resulting continuous family of (unbounded) self-adjoint Fredholm operators in terms of the Maslov index of two related curves of Lagrangian spaces. One curve is given by the varying domains, the other by the Cauchy data spaces. We provide rigorous definitions of the underlying concepts of spectral theory...... and symplectic analysis and give a full (and surprisingly short) proof of our General Spectral Flow Formula for the case of fixed maximal domain. As a side result, we establish local stability of weak inner unique continuation property (UCP) and explain its role for parameter dependent spectral theory....
Calculation of turbulent reactive flows in general orthogonal coordinates
Lai, M. K. Y.
1992-02-01
The mathematical and numerical methodology for an extended and enhanced version of the TURCOM computer code, called TURCOM-BFC, is presented. This code solves the conservation equations of multi-component chemically reactive and turbulent flows in general curvilinear orthogonal coordinates. The k-epsilon turbulence submodel is used. Flame chemistry assumes a number of species and chemical reactions. The latter are subdivided into finite-rate reaction steps and a one-step irreversible reaction, whose rate is controlled by a combination of mixing and global kinetics. Both the SIMPLE and PISO algorithms are implemented to solve the system of equations. The capability of TURCOM-BFC is tested and demonstrated by predicting 3-dimensional combustion flow inside a reaction furnace, where both polar-cylindrical and bipolar coordinates are used.
Generalized transport coefficients for inelastic Maxwell mixtures under shear flow
Garzó, Vicente; Trizac, Emmanuel
2015-11-01
The Boltzmann equation framework for inelastic Maxwell models is considered to determine the transport coefficients associated with the mass, momentum, and heat fluxes of a granular binary mixture in spatially inhomogeneous states close to the simple shear flow. The Boltzmann equation is solved by means of a Chapman-Enskog-type expansion around the (local) shear flow distributions fr(0 ) for each species that retain all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the transport processes instead of the conventional scalar coefficients. These tensors are given in terms of the solutions of a set of coupled equations, which can be analytically solved as functions of the shear rate a , the coefficients of restitution αr s, and the parameters of the mixture (masses, diameters, and composition). Since the reference distribution functions fr(0 ) apply for arbitrary values of the shear rate and are not restricted to weak dissipation, the corresponding generalized coefficients turn out to be nonlinear functions of both a and αr s. The dependence of the relevant elements of the three diffusion tensors on both the shear rate and dissipation is illustrated in the tracer limit case, the results showing that the deviation of the generalized transport coefficients from their forms for vanishing shear rates is in general significant. A comparison with the previous results obtained analytically for inelastic hard spheres by using Grad's moment method is carried out, showing a good agreement over a wide range of values for the coefficients of restitution. Finally, as an application of the theoretical expressions derived here for the transport coefficients, thermal diffusion segregation of an intruder immersed in a granular gas is also studied.
A new Remesh-Lagrange technique for advecting temperature that minimizes numerical diffusion
Hasenclever, J.; Phipps Morgan, J.; Shi, C.
2007-12-01
The proper treatment of heat-advection is a generally underappreciated problem within CFD, yet particularly critical for calculating physically sound erosion in plume-lithosphere interactions and temperature sensitive melting processes. Typically, Eulerian (fixed-mesh) codes have been preferred to solve for fluid flow and they are almost essential for finite-difference-based algorithms. Unfortunately, the Eulerian approach introduces numerical artifacts into the solution of the advection-diffusion heat transport problem that can only be suppressed by adding 'too-diffusive' artificial diffusion to the equations, as for example in the Smolarkiewicz formulation for heat advection. We have developed a 'Remesh-Lagrange' method using a partly deforming finite element mesh and find it to be significantly more accurate than our previous methods. In several test scenarios we show the large improvement in accuracy that can be obtained by using a Lagrangian approach for 10-30 time steps (depending upon the distortion of the finite elements in the deformed Lagrangian mesh) and then regridding to the initial mesh. When an element becomes too distorted the nodes connected to it become fixed and we switch from Lagrange to a Semi-Lagrange formulation for these nodes. Instead of the standard 'linear backward' Semi-Lagrange we are also experimenting with a more accurate interpolation scheme for an unstructured mesh that additionally includes the nodal derivatives of the temperature field when calculating the value at the Semi-Lagrange traceback point. The same bicubic interpolation method for an unstructured grid is used to remesh the 'too-distorted' Lagrange grid back to the initial undistorted mesh. We compare the Remesh-Lagrange technique against the following Eulerian methods in a series of 2-D numerical experiments advecting stripes and Gaussian peaks in steady circulating flow: linear back-interpolation Semi-Lagrange method; bicubic back-interpolation Semi-Lagrange method
DEFF Research Database (Denmark)
Binning, Philip John; Postma, Diederik Jan; Russel, T.F.;
2007-01-01
at depth in the unsaturated zone, a pressure gradient is created between the reactive zone and the ground surface, causing a substantial advective air flow into the subsurface. To determine the balance between advective and diffusive transport, a one-dimensional multicomponent unsaturated zone gas...... flows at steady state. However, greater pressure gradients are found in low-permeability soils. In transient cases, advective fluxes depend on the initial conditions and can be far greater than diffusive fluxes. In contrast to steady state conditions the transient case is sensitive to other model...
Epi-two-dimensional flow and generalized enstrophy
Yoshida, Zensho
2016-01-01
The conservation of the enstrophy ($L^2$ norm of the vorticity $\\omega$) plays an essential role in the physics and mathematics of two-dimensional (2D) Euler fluids. Generalizing to compressible ideal (inviscid and barotropic) fluids, the generalized enstrophy $\\int_{\\Sigma(t)} f(\\omega/\\rho)\\rho\\, d^2 x$, ($f$ an arbitrary smooth function, $\\rho$ the density, and $\\Sigma(t)$ an arbitrary 2D domain co-moving with the fluid) is a constant of motion, and plays the same role. On the other hand, for the three-dimensional (3D) ideal fluid, the helicity $\\int_{M} {V}\\cdot\\omega\\,d^3x$, ($V$ the flow velocity, $\\omega=\
Advective-diffusive transport in microflows
Anderson, Patrick; Speetjens, Michel; Gorodetskyi, Oleksandr
2014-11-01
Advective-diffusive transport in microflows is studied by means of the diffusive mapping method, a recent extension of the mapping method by Gorodetskyi et al. (Phys. Fluids 24, 2012) that includes molecular diffusion. This greatly expands the application area of the mapping technique and makes the powerful concepts of eigenmode decomposition and spectral analysis of scalar transport accessible to an important class of flows: inline micromixers with diffusion. The staggered herringbone micro-mixer is adopted as a prototypical three-dimensional micro mixer. Simulations with the diffusive mapping method are in close agreement with experimental observations in literature and expose a strong impact of diffusion on the transport. Diffusion enables crossing of Lagrangian transport barriers and thus smoothens concentration gradients and accelerates homogenization. Spectral analysis of the mapping matrix reveals this already occurs on a modal level in that individual eigenmodes progressively smoothen and spread out across transport barriers with stronger diffusion. Concurrently, the corresponding eigenvalues diminish and thus fundamentally alter the mixing process by invariably causing homogenization, irrespective of the Lagrangian flow structure.
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-31
This conference day was jointly organized by the `university group of thermal engineering (GUT)` and the French association of thermal engineers. This book of proceedings contains 7 papers entitled: `energy spectra of a passive scalar undergoing advection by a chaotic flow`; `analysis of chaotic behaviours: from topological characterization to modeling`; `temperature homogeneity by Lagrangian chaos in a direct current flow heat exchanger: numerical approach`; ` thermal instabilities in a mixed convection phenomenon: nonlinear dynamics`; `experimental characterization study of the 3-D Lagrangian chaos by thermal analogy`; `influence of coherent structures on the mixing of a passive scalar`; `evaluation of the performance index of a chaotic advection effect heat exchanger for a wide range of Reynolds numbers`. (J.S.)
A Generalized Minimum Cost Flow Model for Multiple Emergency Flow Routing
Directory of Open Access Journals (Sweden)
Jianxun Cui
2014-01-01
Full Text Available During real-life disasters, that is, earthquakes, floods, terrorist attacks, and other unexpected events, emergency evacuation and rescue are two primary operations that can save the lives and property of the affected population. It is unavoidable that evacuation flow and rescue flow will conflict with each other on the same spatial road network and within the same time window. Therefore, we propose a novel generalized minimum cost flow model to optimize the distribution pattern of these two types of flow on the same network by introducing the conflict cost. The travel time on each link is assumed to be subject to a bureau of public road (BPR function rather than a fixed cost. Additionally, we integrate contraflow operations into this model to redesign the network shared by those two types of flow. A nonconvex mixed-integer nonlinear programming model with bilinear, fractional, and power components is constructed, and GAMS/BARON is used to solve this programming model. A case study is conducted in the downtown area of Harbin city in China to verify the efficiency of proposed model, and several helpful findings and managerial insights are also presented.
Logically rectangular mixed methods for Darcy flow on general geometry
Energy Technology Data Exchange (ETDEWEB)
Arbogast, T.; Keenan, P.T.; Wheeler, M.F.; Yotov, I. [Rice Univ., Houston, TX (United States)
1995-12-31
The authors consider an expanded mixed finite element formulation (cell centered finite difference) for Darcy flow with a tensor absolute permeability. The reservoir can be geometrically general with internal features, but the computational domain is rectangular. The method is defined on a curvilinear grid that need not be orthogonal, obtained by mapping the rectangular, computational grid. The original flow problem becomes a similar problem with a modified permeability on the computational grid. Quadrature rules turn the mixed method into a cell-centered finite difference method with a 9 point stencil in 2-D and 19 in 3-D. As shown by theory and experiment, if the modified permeability on the computational domain is smooth, then the convergence rate is optimal and both pressure and velocity are superconvergent at certain points. If not, Lagrange multiplier pressures can be introduced on boundaries of elements so that optimal convergence is retained. This modification presents only small changes in the solution process; in fact, the same parallel domain decomposition algorithms can be applied with little or no change to the code if the modified permeability is smooth over the subdomains. This Lagrange multiplier procedure can be used to extend the difference scheme to multi-block domains, and to give a coupling with unstructured grids. In all cases, the mixed formulation is locally conservative. Computational results illustrate the advantage and convergence of this method.
Verification of Advective Bar Elements Implemented in the Aria Thermal Response Code.
Energy Technology Data Exchange (ETDEWEB)
Mills, Brantley [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
A verification effort was undertaken to evaluate the implementation of the new advective bar capability in the Aria thermal response code. Several approaches to the verification process were taken : a mesh refinement study to demonstrate solution convergence in the fluid and the solid, visually examining the mapping of the advective bar element nodes to the surrounding surfaces, and a comparison of solutions produced using the advective bars for simple geometries with solutions from commercial CFD software . The mesh refinement study has shown solution convergence for simple pipe flow in both temperature and velocity . Guidelines were provided to achieve appropriate meshes between the advective bar elements and the surrounding volume. Simulations of pipe flow using advective bars elements in Aria have been compared to simulations using the commercial CFD software ANSYS Fluent (r) and provided comparable solutions in temperature and velocity supporting proper implementation of the new capability. Verification of Advective Bar Elements iv Acknowledgements A special thanks goes to Dean Dobranich for his guidance and expertise through all stages of this effort . His advice and feedback was instrumental to its completion. Thanks also goes to Sam Subia and Tolu Okusanya for helping to plan many of the verification activities performed in this document. Thank you to Sam, Justin Lamb and Victor Brunini for their assistance in resolving issues encountered with running the advective bar element model. Finally, thanks goes to Dean, Sam, and Adam Hetzler for reviewing the document and providing very valuable comments.
Toward enhanced subsurface intervention methods using chaotic advection.
Trefry, Michael G; Lester, Daniel R; Metcalfe, Guy; Ord, Alison; Regenauer-Lieb, Klaus
2012-01-01
Many intervention activities in the terrestrial subsurface involve the need to recover/emplace distributions of scalar quantities (e.g. dissolved phase concentrations or heat) from/in volumes of saturated porous media. These scalars can be targeted by pump-and-treat methods or by amendment technologies. Application examples include in-situ leaching for metals, recovery of dissolved contaminant plumes, or utilizing heat energy in geothermal reservoirs. While conventional pumping methods work reasonably well, costs associated with maintaining pumping schedules are high and improvements in efficiency would be welcome. In this paper we discuss how transient switching of the pressure at different wells can intimately control subsurface flow, generating a range of "programmed" flows with various beneficial characteristics. Some programs produce chaotic flows which accelerate mixing, while others create encapsulating flows which can isolate fluid zones for lengthy periods. In a simplified model of an aquifer subject to balanced pumping, chaotic flow topologies have been predicted theoretically and verified experimentally using Hele-Shaw cells. Here, a survey of the key characteristics of chaotic advection is presented. Mathematical methods are used to show how these characteristics may translate into practical situations involving regional flows and heterogeneity. The results are robust to perturbations, and withstand significant aquifer heterogeneity. It is proposed that chaotic advection may form the basis of new efficient technologies for groundwater interventions. Crown Copyright © 2011. Published by Elsevier B.V. All rights reserved.
Effect of advection on transient ion concentration-polarization phenomenon
Rosentsvit, Leon; Park, Sinwook; Yossifon, Gilad
2017-08-01
Here, we studied the effect of advection on the transient ion concentration-polarization phenomenon in microchannel-membrane systems. Specifically, the temporal evolution of the depletion layer in a system that supports net flow rates with varying Péclet values was examined. Experiments complemented with simplified analytical one-dimensional semi-infinite modeling and numerical simulations demonstrated either suppression or enhancement of the depletion layer propagation against or with the direction of the net flow, respectively. Of particular interest was the third-species fluorescent dye ion concentration-polarization dynamics which was further explained using two-dimensional numerical simulations that accounted for the device complex geometry.
Influence of advective bio-irrigation on carbon and nitrogen cycling in sandy sediments
Na, T.; Gribsholt, B.; Galaktionov, O. S.; T. Lee; Meysman, F. J. R.
2008-01-01
In sandy sediments, the burrow ventilation activity of benthic macrofauna can generate substantial advective flows within the sediment surrounding their burrows. Here we investigated the effects of such advective bio-irrigation on carbon and nitrogen cycling in sandy sediments. To this end, we combined a range of complementary experimental and modelling approaches in a microcosm study of the lugworm Arenicola marina (Polychaeta: Annelida). Bio-irrigation rates were determined using uranine as...
Ghosh, Shubhrangshu
2016-01-01
The correlated and coupled dynamics of accretion and outflow around black holes (BHs) are essentially governed by the fundamental laws of conservation as outflow extracts matter, momentum and energy from the accretion region. Here we analyzed a robust form of 2.5-dimensional viscous, resistive, advective magnetized accretion-outflow coupling in BH systems, in the mean field magnetohydrodynamical (MHD) regime. We solve the complete set of coupled MHD conservation equations self-consistently, through invoking a generalized polynomial expansion in two dimensions. We perform a critical analysis of accretion-outflow region and provide a complete quasi-analytical family of solutions for advective flows. We obtain the physical plausible outflow solutions at high turbulent viscosity parameter $\\alpha \\, (\\ge 0.3)$, and at a reduced scale-height, as magnetic stresses compress or squeeze the flow region. We found that the value of the large-scale poloidal magnetic field $\\bar B_P$ is enhanced with increasing geometrica...
Turbulent dynamo with advective magnetic helicity flux
Del Sordo, Fabio; Brandenburg, Axel
2012-01-01
Many astrophysical bodies harbor magnetic fields that are thought to be sustained by dynamo processes. However, it has been argued that the production of large-scale magnetic fields by a mean-field dynamo is strongly suppressed at large magnetic Reynolds numbers owing to the conservation of magnetic helicity. This phenomenon is known as catastrophic quenching. Advection of magnetic field toward the outer boundaries and away from the dynamo is expected to alleviate such quenching. Examples are stellar and galactic winds. Such advection might be able to overcome the constraint imposed by the conservation of magnetic helicity, transporting a fraction of it outside the domain in which the dynamo operates. We study how the dynamo process is affected by advection. In particular, we study the relative roles played by advective and diffusive fluxes of magnetic helicity. We do this by performing direct numerical simulations of a turbulent dynamo of alpha^2 type driven by forced turbulence in a Cartesian domain in the ...
Discounted cash flow valuation methods: Examples of perpetuities, constant growth and general case
Fernandez, Pablo
2005-01-01
This paper explores the discounted cash flow valuation methods. We start the paper with the simplest case: no-growth, perpetual-life companies. Then we will study the continuous growth case and, finally, the general case. The different concepts of cash flow used in company valuation are defined: equity cash flow (ECF), free cash flow (FCF), and capital cash flow (CCF). Then the appropriate discount rate is determined for each cash flow, depending on the valuation method used. Our starting poi...
Discounted cash flow valuation methods: Examples of perpetuities, constant growth and general case
Fernandez, Pablo
2005-01-01
This paper explores the discounted cash flow valuation methods. We start the paper with the simplest case: no-growth, perpetual-life companies. Then we will study the continuous growth case and, finally, the general case. The different concepts of cash flow used in company valuation are defined: equity cash flow (ECF), free cash flow (FCF), and capital cash flow (CCF). Then the appropriate discount rate is determined for each cash flow, depending on the valuation method used. Our starting poi...
A Method for Measuring Subcanopy CO2 Advection
Staebler, R. M.; Fitzjarrald, D. R.
2004-12-01
Underestimation of nocturnal CO2 respiration under calm conditions remains an unsolved problem at many forest flux stations, and several groups are currently investigating the direct measurement of horizontal advection of CO2. This presentation will describe a systematic, relatively low-cost methodology developed to determine whether horizontal mean transport of CO2 accounts for the missing CO2 at the Harvard Forest (Petersham, MA). This methodology includes the characterization of subcanopy motions, determining the appropriate size of the subcanopy network required to make the measurements, developing a method of integrating the measurements in the vertical, and determining the required averaging time. Measurements were conducted over 4 years and produced data for 310 nights covering all seasons. Subcanopy flows were decoupled from the flows aloft 75% of the time. Conditions conducive to the generation of negative buoyancy near the forest floor, necessary for drainage flows to develop, were given in 92% of all nights. The occurrence of nocturnal drainage flows correlated well with "missing flux" problems ("deficit nights"), prompting us to propose an improvement on the commonly used friction velocity criterion (which requires u* to be larger than some empirical cut-off for the eddy fluxes to be considered credible). The "negative buoyancy forcing fraction", i.e. negative buoyancy as a fraction of the sum of the dynamic driving forces, can be shown to predict deficit nights significantly better than the u* cut-off. The appropriate horizontal size of the network of wind and CO2 sensors at the Harvard Forest was shown to be on the order of 100 m, ensuring that sensors were generally observing coherent processes on this scale or larger and thus displaying some correlation. Horizontal transport of CO2 was found to be restricted to the bottom ~10 m of the forest, facilitating the development of a method of integrating the horizontal CO2 gradients in the vertical
Advection equation analysed by two-timing method
Vladimirov, V A
2016-01-01
The aim of this paper is to study and classify the multiplicity of distinguished limits and asymptotic solutions for the advection equation with a general oscillating velocity field with the systematic use of the two-timing method. Our results are: (i) the dimensionless advection equation contains two independent small parameters, which represent the ratio of two characteristic time-scales and the spatial amplitudes of oscillations; the scaling of the variables and parameters contains Strouhal number; (ii) an infinite sequence of distinguished limits has been identified; this sequence corresponds to the successive degenerations of a drift velocity; (iii) we have derived the averaged and oscillatory equations for the first four distinguished limits; derivations are performed up to the forth orders in small parameters; (v) we have shown, that each distinguish limit solution generates an infinite number of parametric solutions; these solutions differ from each other by the slow time-scale and the amplitude of pr...
GENERALIZED FLOW LAWS OF POLYPHASE ROCKS: AN OVERVIEW
Institute of Scientific and Technical Information of China (English)
JI; Shao-cheng; FAN; Wei-ming; WANG; Yue-jun
2002-01-01
Rheological properties of polyphase rocks play an important role in the dynamics of the lithosphere and asthenosphere. However, such fundamental issues have not been well resolved. A theoretical analysis has been made to develop expressions for the flow laws of polyphase rocks in terms of the volume fractions and flow laws of their constituent phases. The flow strengths predicted by the proposed model for common crustal and upper mantle rocks such as granite, diorite, diabase and lherzolite, and for synthetic two-phase composites such as forsterite-enstatite and water ice-ammonia dehydrate aggregates are in good agreement with previously determined experimental values. The proposed theoretical model allows one to calculate, to the first approximation, the flow laws of a large number of polyphase rocks at geologic conditions based on the experimentally determined flow laws of a relatively small number of monomineralic aggregates.
Heinle, B.; Cardiff, M. A.
2016-12-01
The presence of fractures plays an essential role in hydrogeologic transport, as well as geothermal and hydrocarbon industries, as fractures introduce new pathways for flow and transport in host rocks. Transport through these features is often highly non-Fickian, due to the combination of both heterogeneous advection and matrix diffusion. Fracture aperture distributions and contact areas control the ability of fluids to flow through a fracture, and to interact with host rock. The heterogeneous nature of these fracture apertures often lead to preferential fluid pathways that control the prevalence of advective and diffusive processes within the fracture network. To understand how preferential fluid pathways affect these transport processes in detail, an innovative approach is introduced for visualizing advective and diffusive phenomena through the use of thermochromic liquid crystals (TLCs). An artificial fracture with the ability to have its surface roughness altered is constructed and heterogeneous flow and diffusion of heat is observed directly using these TLCs. The surfaces are digitized and simulated in COMSOL Multiphysics where particle tracing is used to determine arrival time curves in the absence of host rock diffusion. The resulting combination of the visual results from lab experiments and particle statistics from the computer model provide a unique method for assessing the impact of both heterogeneous advection and matrix-diffusion on tracer breakthrough in fractures, across a variety of fracture geometries. Figure 1. Image of advective (left) and diffusive (right) phenomena occurring simultaneously as fluid flows through the artificial fracture.
Webb, G. M.; Dasgupta, B.; McKenzie, J. F.; Hu, Q.; Zank, G. P.
2014-03-01
In this paper advected invariants and conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics are obtained using Lie dragging techniques. There are different classes of invariants that are advected or Lie dragged with the flow. Simple examples are the advection of the entropy S (a 0-form), and the conservation of magnetic flux (an invariant 2-form advected with the flow). The magnetic flux conservation law is equivalent to Faraday's equation. The gauge condition for the magnetic helicity to be advected with the flow is determined. Different variants of the helicity in ideal fluid dynamics and MHD including: fluid helicity, cross helicity and magnetic helicity are investigated. The fluid helicity conservation law and the cross-helicity conservation law in MHD are derived for the case of a barotropic gas. If the magnetic field lies in the constant entropy surface, then the gas pressure can depend on both the entropy and the density. In these cases the conservation laws are local conservation laws. For non-barotropic gases, we obtain nonlocal conservation laws for fluid helicity and cross helicity by using Clebsch variables. These nonlocal conservation laws are the main new results of the paper. Ertel's theorem and potential vorticity, the Hollman invariant, and the Godbillon-Vey invariant for special flows for which the magnetic helicity is zero are also discussed.
Energy Technology Data Exchange (ETDEWEB)
Lichtner, P.C.; Helgeson, H.C.
1986-06-20
A general formulation of multi-phase fluid flow coupled to chemical reactions was developed based on a continuum description of porous media. A preliminary version of the computer code MCCTM was constructed which implemented the general equations for a single phase fluid. The computer code MCCTM incorporates mass transport by advection-diffusion/dispersion in a one-dimensional porous medium coupled to reversible and irreversible, homogeneous and heterogeneous chemical reactions. These reactions include aqueous complexing, oxidation/reduction reactions, ion exchange, and hydrolysis reactions of stoichiometric minerals. The code MCCTM uses a fully implicit finite difference algorithm. The code was tested against analytical calculations. Applications of the code included investigation of the propagation of sharp chemical reaction fronts, metasomatic alteration of microcline at elevated temperatures and pressures, and ion-exchange in a porous column. Finally numerical calculations describing fluid flow in crystalline rock in the presence of a temperature gradient were compared with experimental results for quartzite.
Visualizing Vector Fields Using Line Integral Convolution and Dye Advection
Shen, Han-Wei; Johnson, Christopher R.; Ma, Kwan-Liu
1996-01-01
We present local and global techniques to visualize three-dimensional vector field data. Using the Line Integral Convolution (LIC) method to image the global vector field, our new algorithm allows the user to introduce colored 'dye' into the vector field to highlight local flow features. A fast algorithm is proposed that quickly recomputes the dyed LIC images. In addition, we introduce volume rendering methods that can map the LIC texture on any contour surface and/or translucent region defined by additional scalar quantities, and can follow the advection of colored dye throughout the volume.
Local and nonlocal advection of a passive scalar
Scott, R. K.
2006-11-01
Passive and active scalar mixing is examined in a simple one-parameter family of two-dimensional flows based on quasi-geostrophic dynamics, in which the active scalar, the quasi-geostrophic potential vorticity, is confined to a single horizontal surface (so-called surface quasi-geostrophic dynamics) and in which a passive scalar field is also advected by the (horizontal, two-dimensional) velocity field at a finite distance from the surface. At large distances from the surface the flow is determined by the largest horizontal scales, the flow is spectrally nonlocal, and a chaotic advection-type regime dominates. At small distances, z, scaling arguments suggest a transition wavenumber kc˜1/2z, where the slope of the passive scalar spectrum changes from k-5/3, determined by local dynamics, to k-1, determined by nonlocal dynamics, analogous to the transition to a k-1 slope in the Batchelor regime in three-dimensional turbulence. Direct numerical simulations reproduce the qualitative aspects of this transition. Other characteristics of the simulated scalar fields, such as the relative dominance of coherent or filamentary structures, are also shown to depend strongly on the degree of locality.
A general theory of wave interactions in layered flows
Guha, Anirban
2016-01-01
Using kinematics, we propose a theory of non-modal interactions between the interfaces of a 2D, inviscid, multi-layered fluid system. Specifically, a $3$-interface problem with kinematic and geometric symmetry is explored. Repetitive, extremely short bursts of very high wave growth/decay-rates are observed in the parameter ranges where normal-mode theory predicts stability. The underlying dynamical system predicts chaotic outcomes for some initial conditions. For realistic multi-layered flows, such instabilities of finite amplitude may alter the mean flow to a noisy, unpredictable state.
Solving the Advection-Diffusion Equations in Biological Contexts using the Cellular Potts Model
Dan, D; Chen, K; Glazier, J A; Dan, Debasis; Mueller, Chris; Chen, Kun; Glazier, James A.
2005-01-01
The Cellular Potts Model (CPM) is a robust, cell-level methodology for simulation of biological tissues and morphogenesis. Both tissue physiology and morphogenesis depend on diffusion of chemical morphogens in the extra-cellular fluid or matrix (ECM). Standard diffusion solvers applied to the cellular potts model use finite difference methods on the underlying CPM lattice. However, these methods produce a diffusing field tied to the underlying lattice, which is inaccurate in many biological situations in which cell or ECM movement causes advection rapid compared to diffusion. Finite difference schemes suffer numerical instabilities solving the resulting advection-diffusion equations. To circumvent these problems we simulate advection-diffusion within the framework of the CPM using off-lattice finite-difference methods. We define a set of generalized fluid particles which detach advection and diffusion from the lattice. Diffusion occurs between neighboring fluid particles by local averaging rules which approxi...
Webb, Gary M; McKenzie, James F; Hu, Qiang; Zank, Gary P
2013-01-01
In this paper we discuss conservation laws in ideal magnetohydrodynamics (MHD) and gas dynamics associated with advected invariants. The invariants in some cases, can be related to fluid relabelling symmetries associated with the Lagrangian map. There are different classes of invariants that are advected or Lie dragged with the flow. Simple examples are the advection of the entropy S (a 0-form), and the conservation of magnetic flux (an invariant 2-form advected with the flow). The magnetic flux conservation law is equivalent to Faraday's equation. We discuss the gauge condition required for the magnetic helicity to be advected with the flow. The conditions for the cross helicity to be an invariant are discussed. We discuss the different variants of helicity in fluid dynamics and in MHD, including: fluid helicity, cross helicity and magnetic helicity. The fluid helicity conservation law and the cross helcity conservation law in MHD are derived for the case of a barotropic gas. If the magnetic field lies in th...
A generalized Forchheimer radial flow model for constant-rate tests
Liu, Ming-Ming; Chen, Yi-Feng; Zhan, Hongbin; Hu, Ran; Zhou, Chuang-Bing
2017-09-01
Models used for data interpretation of constant-rate tests (CRTs) are commonly derived with the assumption of Darcian flow in an idealized integer flow dimension, where the non-Darcian nature of fluid flow and the complexity of flow geometry are disregarded. In this study, a Forchheimer's law-based analytical model is proposed with the assumption of buildup (or drawdown) decomposition for characterizing the non-Darcian flow in a generalized radial formation where the flow dimension n may become non-integer. The proposed model immediately reduces to Barker's (1988) model for Darcian flow in the generalized radial formation and to Mathias et al.'s (2008) model for non-Darcian flow in a two-dimensional confined aquifer. A comparison with numerical simulations shows that the proposed model behaves well at late times for flow dimension n > 1.5. The proposed model is finally applied for data interpretation of the constant-rate pumping tests performed at Ploemeur (Le Borgne et al., 2004), showing that the intrinsic hydraulic conductivity of formations will be underestimated and the specific storage will be overestimated if the non-Darcian effect is ignored. The proposed model is an extension of the generalized radial flow (GRF) model based on Forchheimer's law, which would be of significance for data interpretation of CRTs in aquifers of complex flow geometry in which non-Darcian flow occurs.
Metamorphism during temperature gradient with undersaturated advective airflow in a snow sample
Ebner, Pirmin Philipp; Schneebeli, Martin; Steinfeld, Aldo
2016-04-01
Snow at or close to the surface commonly undergoes temperature gradient metamorphism under advective flow, which alters its microstructure and physical properties. Time-lapse X-ray microtomography is applied to investigate the structural dynamics of temperature gradient snow metamorphism exposed to an advective airflow in controlled laboratory conditions. Cold saturated air at the inlet was blown into the snow samples and warmed up while flowing across the sample with a temperature gradient of around 50 K m-1. Changes of the porous ice structure were observed at mid-height of the snow sample. Sublimation occurred due to the slight undersaturation of the incoming air into the warmer ice matrix. Diffusion of water vapor opposite to the direction of the temperature gradient counteracted the mass transport of advection. Therefore, the total net ice change was negligible leading to a constant porosity profile. However, the strong recrystallization of water molecules in snow may impact its isotopic or chemical content.
Generalized second-order slip boundary condition for nonequilibrium gas flows
Guo, Zhaoli; Qin, Jishun; Zheng, Chuguang
2014-01-01
It is a challenging task to model nonequilibrium gas flows within a continuum-fluid framework. Recently some extended hydrodynamic models in the Navier-Stokes formulation have been developed for such flows. A key problem in the application of such models is that suitable boundary conditions must be specified. In the present work, a generalized second-order slip boundary condition is developed in which an effective mean-free path considering the wall effect is used. By combining this slip scheme with certain extended Navier-Stokes constitutive relation models, we obtained a method for nonequilibrium gas flows with solid boundaries. The method is applied to several rarefied gas flows involving planar or curved walls, including the Kramers' problem, the planar Poiseuille flow, the cylindrical Couette flow, and the low speed flow over a sphere. The results show that the proposed method is able to give satisfied predictions, indicating the good potential of the method for nonequilibrium flows.
Generalized Method of Variational Analysis for 3-D Flow
Institute of Scientific and Technical Information of China (English)
兰伟仁; 黄思训; 项杰
2004-01-01
The generalized method of variational analysis (GMVA) suggested for 2-D wind observations by Huang et al. is extended to 3-D cases. Just as in 2-D cases, the regularization idea is applied. But due to the complexity of the 3-D cases, the vertical vorticity is taken as a stable functional. The results indicate that wind observations can be both variationally optimized and filtered. The efficiency of GMVA is also checked in a numerical test. Finally, 3-D wind observations with random disturbances are manipulated by GMVA after being filtered.
Reactive particles in random flows.
Károlyi, György; Tél, Tamás; de Moura, Alessandro P S; Grebogi, Celso
2004-04-30
We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically.
Edmondson, J K
2014-01-01
Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and the generating vector field, and is provided for from two equivalent perspectives: a Lagrangian specification with respect to a generalized parameter, and an Eulerian specification making explicit the evolution dynamics. Furthermore, we provide explicit non-trivial conditions which govern the transformation properties of the referential gradient object.
Distributed Parallel Particle Advection using Work Requesting
Energy Technology Data Exchange (ETDEWEB)
Muller, Cornelius; Camp, David; Hentschel, Bernd; Garth, Christoph
2013-09-30
Particle advection is an important vector field visualization technique that is difficult to apply to very large data sets in a distributed setting due to scalability limitations in existing algorithms. In this paper, we report on several experiments using work requesting dynamic scheduling which achieves balanced work distribution on arbitrary problems with minimal communication overhead. We present a corresponding prototype implementation, provide and analyze benchmark results, and compare our results to an existing algorithm.
A cryogenic circulating advective multi-pass absorption cell
Stockett, M. H.; Lawler, J. E.
2012-03-01
A novel absorption cell has been developed to enable a spectroscopic survey of a broad range of polycyclic aromatic hydrocarbons (PAH) under astrophysically relevant conditions and utilizing a synchrotron radiation continuum to test the still controversial hypothesis that these molecules or their ions could be carriers of the diffuse interstellar bands. The cryogenic circulating advective multi-pass absorption cell resembles a wind tunnel; molecules evaporated from a crucible or injected using a custom gas feedthrough are entrained in a laminar flow of cryogenically cooled buffer gas and advected into the path of the synchrotron beam. This system includes a multi-pass optical White cell enabling absorption path lengths of hundreds of meters and a detection sensitivity to molecular densities on the order of 107 cm-3. A capacitively coupled radio frequency dielectric barrier discharge provides ionized and metastable buffer gas atoms for ionizing the candidate molecules via charge exchange and the Penning effect. Stronger than expected clustering of PAH molecules has slowed efforts to record gas phase PAH spectra at cryogenic temperatures, though such clusters may play a role in other interstellar phenomena.
OBSERVATION OF MAGNETIC RECONNECTION DRIVEN BY GRANULAR SCALE ADVECTION
Energy Technology Data Exchange (ETDEWEB)
Zeng Zhicheng; Cao Wenda [Center for Solar-Terrestrial Research, New Jersey Institute of Technology, 323 Martin Luther King Blvd., Newark, NJ 07102 (United States); Ji Haisheng [Big Bear Solar Observatory, 40386 North Shore Lane, Big Bear City, CA 92314 (United States)
2013-06-01
We report the first evidence of magnetic reconnection driven by advection in a rapidly developing large granule using high spatial resolution observations of a small surge event (base size {approx} 4'' Multiplication-Sign 4'') with the 1.6 m aperture New Solar Telescope at the Big Bear Solar Observatory. The observations were carried out in narrowband (0.5 A) He I 10830 A and broadband (10 A) TiO 7057 A. Since He I 10830 A triplet has a very high excitation level and is optically thin, its filtergrams enable us to investigate the surge from the photosphere through the chromosphere into the lower corona. Simultaneous space data from the Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory were used in the analysis. It is shown that the surge is spatio-temporally associated with magnetic flux emergence in the rapidly developing large granule. During the development of the granule, its advecting flow ({approx}2 km s{sup -1}) squeezed the magnetic flux into an intergranular lane area, where a magnetic flux concentration was formed and the neighboring flux with opposite magnetic polarity was canceled. During the cancellation, the surge was produced as absorption in He I 10830 A filtergrams while simultaneous EUV brightening occurred at its base. The observations clearly indicate evidence of a finest-scale reconnection process driven by the granule's motion.
Semi-Lagrangian advection-propagation (SLAP) scheme for three-dimensional interface tracking
Aldredge, R. C.
2010-06-01
A fully three-dimensional semi-Lagrangian scheme is developed for computing the evolution of advected self-propagating surfaces (e.g., premixed flames) governed by a level-set advection-propagation equation. The scheme provides third-order spatial accuracy and shape preservation. Example numerical simulations of three-dimensional front propagation are presented to illustrate the capability of the scheme of capturing cusp formation and associated surface-area annihilation as well as the formation and consumption of detached closed-surface pockets behind fronts propagating in highly vortical flow.
Huang, Y.H.; Saiers, J.E.; Harvey, J.W.; Noe, G.B.; Mylon, S.
2008-01-01
The movement of particulate matter within wetland surface waters affects nutrient cycling, contaminant mobility, and the evolution of the wetland landscape. Despite the importance of particle transport in influencing wetland form and function, there are few data sets that illuminate, in a quantitative way, the transport behavior of particulate matter within surface waters containing emergent vegetation. We report observations from experiments on the transport of 1 ??m latex microspheres at a wetland field site located in Water Conservation Area 3A of the Florida Everglades. The experiments involved line source injections of particles inside two 4.8-m-long surface water flumes constructed within a transition zone between an Eleocharis slough and Cladium jamaicense ridge and within a Cladium jamaicense ridge. We compared the measurements of particle transport to calculations of two-dimensional advection-dispersion model that accounted for a linear increase in water velocities with elevation above the ground surface. The results of this analysis revealed that particle spreading by longitudinal and vertical dispersion was substantially greater in the ridge than within the transition zone and that particle capture by aquatic vegetation lowered surface water particle concentrations and, at least for the timescale of our experiments, could be represented as an irreversible, first-order kinetics process. We found generally good agreement between our field-based estimates of particle dispersion and water velocity and estimates determined from published theory, suggesting that the advective-dispersive transport of particulate matter within complex wetland environments can be approximated on the basis of measurable properties of the flow and aquatic vegetation. Copyright 2008 by the American Geophysical Union.
Generalization of the one-dimensional ideal plasma flow with spherical waves
Energy Technology Data Exchange (ETDEWEB)
Golovin, Sergey V [Queen' s University, Kingston, Ontario K7 L 3N6 (Canada)
2006-06-09
We give a description of the ideal plasma flow, which is governed by an exact partially invariant solution of the magnetohydrodynamics equations. The solution generalizes known one-dimensional flow with spherical waves. The generalization consists in addition of the special tangent vector components of the velocity and the magnetic field at any plasma particle. In the special case of zeroth tangential component the solution coincides with the classical one-dimensional one. This paper describes a three-dimensional picture of the plasma flow, governed by the obtained solution.
Lester, D R; Metcalfe, Guy
2016-01-01
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the porescale generate chaotic advection, involving exponential stretching and folding of fluid elements,the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit t...
Symmetries of the Euler compressible flow equations for general equation of state
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-10-15
The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.
A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems
Geissert, Matthias; Hieber, Matthias; Nguyen, Thieu Huy
2016-06-01
This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier-Stokes-Oseen flow, the Navier-Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein-Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.
Using the stress function in the flow of generalized Newtonian fluids through pipes and slits
Sochi, Taha
2015-01-01
We use a generic and general numerical method to obtain solutions for the flow of generalized Newtonian fluids through circular pipes and plane slits. The method, which is simple and robust can produce highly accurate solutions which virtually match any analytical solutions. The method is based on employing the stress, as a function of the pipe radius or slit thickness dimension, combined with the rate of strain function as represented by the fluid rheological constitutive relation that correlates the rate of strain to stress. Nine types of generalized Newtonian fluids are tested in this investigation and the solutions obtained from the generic method are compared to the analytical solutions which are obtained from the Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was obtained in all the investigated cases. All the required quantities of the flow which include local viscosity, rate of strain, flow velocity profile and volumetric flow rate, as well as shear stress, can be obtained from ...
Multiple anisotropic collisions for advection-diffusion Lattice Boltzmann schemes
Ginzburg, Irina
2013-01-01
This paper develops a symmetrized framework for the analysis of the anisotropic advection-diffusion Lattice Boltzmann schemes. Two main approaches build the anisotropic diffusion coefficients either from the anisotropic anti-symmetric collision matrix or from the anisotropic symmetric equilibrium distribution. We combine and extend existing approaches for all commonly used velocity sets, prescribe most general equilibrium and build the diffusion and numerical-diffusion forms, then derive and compare solvability conditions, examine available anisotropy and stable velocity magnitudes in the presence of advection. Besides the deterioration of accuracy, the numerical diffusion dictates the stable velocity range. Three techniques are proposed for its elimination: (i) velocity-dependent relaxation entries; (ii) their combination with the coordinate-link equilibrium correction; and (iii) equilibrium correction for all links. Two first techniques are also available for the minimal (coordinate) velocity sets. Even then, the two-relaxation-times model with the isotropic rates often gains in effective stability and accuracy. The key point is that the symmetric collision mode does not modify the modeled diffusion tensor but it controls the effective accuracy and stability, via eigenvalue combinations of the opposite parity eigenmodes. We propose to reduce the eigenvalue spectrum by properly combining different anisotropic collision elements. The stability role of the symmetric, multiple-relaxation-times component, is further investigated with the exact von Neumann stability analysis developed in diffusion-dominant limit.
Generalized Flow Tracing for the Analysis of Networked Renewable Electricity Systems
Hörsch, Jonas; Becker, Sarah; Schramm, Stefan; Greiner, Martin
2016-01-01
Flow allocation methods represent a valuable tool set to analyze the power flows in networked electricity systems. Based on this flow allocation, the costs associated with the usage of the underlying network infrastructure can be assigned to the users of the electricity system. This paper presents a generalization of the flow tracing method that is applicable to arbitrary compositions of inflow appearing naturally in aggregated networks. The composition of inflow is followed from net-generating sources through the network and assigns corresponding shares of the total power flow as well as of the outflow to the net-consuming sinks. We showcase the analytical power of this method for a scenario based on the IEEE 118 bus network and emphasize the need of appropriate aggregating measures, which allow to integrate over whole time series of fluctuating flow patterns.
Energy Technology Data Exchange (ETDEWEB)
Azreg-Ainou, Mustapha [Baskent University, Engineering Faculty, Ankara (Turkey)
2017-01-15
We present new accretion solutions of a polytropic perfect fluid onto an f(R)-gravity de Sitter-like black hole. We consider two f(R)-gravity models and obtain finite-period cyclic flows oscillating between the event and cosmological horizons as well as semi-cyclic critical flows executing a two-way motion from and back to the same horizon. Besides the generalizations and new solutions presented in this work, a corrigendum to Eur. Phys. J. C (2016) 76:280 is provided. (orig.)
Directory of Open Access Journals (Sweden)
Taha Sochi
2015-01-01
Full Text Available We use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational principle and hence it is totally independent of our previous approach which is based on this principle. Instead, the method applies a very generic and general optimization approach which can be justified by the Dirichlet principle although this is not the only possible theoretical justification. The results that were obtained from the new method using nine types of fluid are in total agreement, within certain restrictions, with the results obtained from the traditional methods of fluid mechanics as well as the results obtained from the previous variational approach. In addition to being a useful method in its own for resolving the flow field in circular pipes and plane slits, the new variational method lends more support to the old variational method as well as for the use of variational principles in general to resolve the flow of generalized Newtonian fluids and obtain all the quantities of the flow field which include shear stress, local viscosity, rate of strain, speed profile, and volumetric flow rate.
Parallel algorithms for semi-lagrangian advection
Malevsky, A. V.; Thomas, S. J.
1997-08-01
Numerical time step limitations associated with the explicit treatment of advection-dominated problems in computational fluid dynamics are often relaxed by employing Eulerian-Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to find the departure point of a fluid particle arriving at a Eulerian grid point. The value of the advected field at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation influence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high-order ODE solver involving multiple interpolations of the velocity field.
Chen, Miawjane; Yan, Shangyao; Wang, Sin-Siang; Liu, Chiu-Lan
2015-02-01
An effective project schedule is essential for enterprises to increase their efficiency of project execution, to maximize profit, and to minimize wastage of resources. Heuristic algorithms have been developed to efficiently solve the complicated multi-mode resource-constrained project scheduling problem with discounted cash flows (MRCPSPDCF) that characterize real problems. However, the solutions obtained in past studies have been approximate and are difficult to evaluate in terms of optimality. In this study, a generalized network flow model, embedded in a time-precedence network, is proposed to formulate the MRCPSPDCF with the payment at activity completion times. Mathematically, the model is formulated as an integer network flow problem with side constraints, which can be efficiently solved for optimality, using existing mathematical programming software. To evaluate the model performance, numerical tests are performed. The test results indicate that the model could be a useful planning tool for project scheduling in the real world.
Comparison of different computer platforms for running the Versatile Advection Code
Toth, G.; Keppens, R.; Sloot, P.; Bubak, M.; Hertzberger, B.
1998-01-01
The Versatile Advection Code is a general tool for solving hydrodynamical and magnetohydrodynamical problems arising in astrophysics. We compare the performance of the code on different computer platforms, including work stations and vector and parallel supercomputers. Good parallel scaling can be a
Directory of Open Access Journals (Sweden)
J Ghanbari
2009-12-01
Full Text Available Dynamics of stationary axisymmetric configuration of the viscous accreting fluids surrounding a non-rotating compact object in final stages of accretion flow is presented here. For the special case of thin disk approximation, the relativistic fluid equations ignoring self-gravity of the disk are derived in Schwarzschild geometry. For two different state equations, two sets of self-consistent analytical solutions of fully relativistic fluid equations are obtained separately. The effect of bulk viscosity coefficient on the physical functions are investigated for each state equation, as well as the bounds that exert on the free parameters due to the condition of accretion flow in the last stages. The solutions found show that the radial and azimuthal velocities, density and pressure of the fluid increase inwards for both state equations. Also, viscosity has no effect on the velocities and density distributions in both state equations. Two state equations show different types of behavior with respect to the bulk viscosity coefficient. For p=K state equation, if there is no bulk viscosity, the pressure remains constant throughout the disk, whereas with increasing bulk viscosity the pressure falls off in the inner regions but soon stabilizes at an almost constant value. However, for p=ρc2 state equation, the pressure is never constant, even in the absence of bulk viscosity. The larger the value of ηb, the higher the value of pressure in the inner regions.
Institute of Scientific and Technical Information of China (English)
沈孟育; 刘秋生; 张增产
1996-01-01
An efficient numerical method for calculating the three-dimensional transonic flows in turbomachinery is proposed. Instead of the Euler equation, streamsurface-governing equations are deduced in the generalized von Mises coordinate system to reflect the flow feature in turbomachinery. Its main advantage is that it is easier to specify more reasonable initial values, i.e. initial streamsurface position, thus accelerating the convergence rate of the iteration process. Moreover, to use the generalized von Mises coordinates makes the present method capable of incorporating the calculation of the flow field, design and modification of the blade contour into a unified algorithm. A rotated finite difference scheme for the streamsurface-governing equations is constructed, and a new measure is presented to deal with the double-value problem of the velocity and density caused by the application of the stream functions as coordinates in the transonic flow. Three test cases were considered with the present approach
Pressure Gradient Influence on MHD Flow for Generalized Burgers’ Fluid with Slip Condition
Directory of Open Access Journals (Sweden)
Ghada H. Ibraheem,
2014-07-01
Full Text Available This paper presents a research for magnetohydrodynamic (MHD flow of an incompressible generalized Burgers' fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is introduced to establish the constitutive relationship of the generalized Burgers' fluid. By using the discrete Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear stress are obtained in terms of Fox H- function for the following two problems: (i flow due to a constant pressure gradient, and (ii flow due to due to a sinusoidal pressure gradient. The solutions for no – slip condition and no magnetic field, can be derived as special cases of our solutions. Furthermore, the effects of various parameters on the velocity distribution characteristics are analyzed and discussed in detail. Comparison between the two cases is also made.
Magnetic resonance microscopy analysis of advective transport in a biofilm reactor.
Gjersing, Erica L; Codd, Sarah L; Seymour, Joseph D; Stewart, Philip S
2005-03-30
In this article we present magnetic resonance microscopy (MRM) characterization of the advective transport in a biofilm capillary reactor. The biofilm generates non-axial flows that are up to 20% of the maximum axial velocity. The presence of secondary velocities of this magnitude alters the mass transport in the bioreactor relative to non-biofilm fouled reactors and questions the applicability of empirical mass transfer coefficient approaches. The data are discussed in the context of simulations and models of biofilm transport and conceptual aspects of transport modeling in complex flows are also discussed. The variation in the residence time distribution due to biofilm growth is calculated from the measured propagator of the motion. Dynamical systems methods applied to model fluid mixing in complex flows are indicated as a template for extending mass transport theory to quantitatively incorporate microscale data on the advection field into macroscale mass transfer models.
Interfacial wave behavior in oil-water channel flows: Prospects for a general understanding
Energy Technology Data Exchange (ETDEWEB)
McCready, M.J.; Uphold, D.D.; Gifford, K.A. [Univ. of Notre Dame, IN (United States)
1997-12-31
Oil-water pressure driven channel flow is examined as a model for general two-layer flows where interfacial disturbances are important. The goal is to develop sufficient understanding of this system so that the utility and limitations of linear and nonlinear theories can be known a priori. Experiments show that sometimes linear stability is useful at predicting the steady or dominant evolving waves. However in other situations there is no agreement between the linearly fastest growing wave and the spectral peak. An interesting preliminary result is that the bifurcation to interfacial waves is supercritical for all conditions that were studied for an oil-water channel flow, gas-liquid channel flow and two-liquid Couette flow. However, three different mechanisms are dominant for each of these three situations.
An exact solution of unsteady Couette flow of generalized second grade fluid
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The fractional calculus approach is introduced into the rheological constitutive model of a generalized second grade fluid. A constitutive model with fractional derivative is developed for the generalized second grade fluid. Unsteady Couette flow of the generalized second grade fluid is studied by using the method of the discrete inverse Laplace transform and generalized Mittag-Leffler function. And then an exact solution is obtained for this problem with arbitrary fractional derivative. This provides a new analytical tool for the study of viscoelastic fluid mechanics.
Reiter, M. A.
2004-12-01
60m to 120m, the expression representing horizontal advection is a generally preferred fit to the T log. Perhaps horizontal liquid flow through perched water zones, steps in the ground water table elevation caused by normal faulting, horizontal variations in barometric pressure effects at depth, and sub horizontal vapor flow moving around permeability barriers on its way to the surface, promote horizontal advection at the Tome and Mesa del Sol sites.
Cellwise conservative unsplit advection for the volume of fluid method
DEFF Research Database (Denmark)
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
2015-01-01
We present a cellwise conservative unsplit (CCU) advection scheme for the volume of fluid method (VOF) in 2D. Contrary to other schemes based on explicit calculations of the flux balances, the CCU advection adopts a cellwise approach where the pre-images of the control volumes are traced backward......We present a cellwise conservative unsplit (CCU) advection scheme for the volume of fluid method (VOF) in 2D. Contrary to other schemes based on explicit calculations of the flux balances, the CCU advection adopts a cellwise approach where the pre-images of the control volumes are traced...
Electrohydrodynamic migration of a spherical drop in a general quadratic flow
Mandal, Shubhadeep; Chakraborty, Suman
2015-01-01
We investigate the motion of a spherical drop in a general quadratic flow acted upon by an arbitrarily oriented externally applied uniform electric field. The drop and media are considered to be leaky dielectrics. The flow field affects the distribution of charges on the drop surface, which leads to alteration in the electric field, thereby affecting the velocity field through the Maxwell stress on the fluid-fluid interface. The two-way coupled electrohydrodynamics is central towards dictating the motion of the drop in the flow field. We analytically address the electric potential distribution and Stokesian flow field in and around the drop in a general quadratic flow for small electric Reynolds number (which is the ratio of the charge relaxation time scale to the convective time scale). As a special case, we consider a drop in an unbounded cylindrical Poiseuille flow and show that, an otherwise absent, cross-stream drop migration may be obtained in the presence of a uniform electric field. Depending on the d...
Slip effects on a generalized Burgers’ fluid flow between two side walls with fractional derivative
Directory of Open Access Journals (Sweden)
Shihao Han
2016-01-01
Full Text Available This paper presents a research for the 3D flow of a generalized Burgers’ fluid between two side walls generated by an exponential accelerating plate and a constant pressure gradient, where the no-slip assumption between the exponential accelerating plate and the Burgers’ fluid is no longer valid. The governing equations of the generalized Burgers’ fluid flow are established by using the fractional calculus approach. Exact analytic solutions for the 3D flow are established by employing the Laplace transform and the finite Fourier sine transform. Furthermore, some 3D and 2D figures for the fluid velocity and shear stress are plotted to analyze and discuss the effects of various parameters.
Generalized Fleming-Viot processes with immigration via stochastic flows of partitions
Foucart, Clément
2011-01-01
The generalized Fleming-Viot processes were defined in 1999 by Donnelly and Kurtz using a particle model and by Bertoin and Le Gall in 2003 using stochastic flows of bridges. In both methods, the key argument used to characterize these processes is the duality between these processes and exchangeable coalescents. A larger class of coalescent processes, called distinguished coalescents, was set up recently to incorporate an immigration phenomenon in the underlying population. The purpose of this article is to define and characterize a class of probability-measure valued processes called the generalized Fleming-Viot processes with immigration. We consider some stochastic flows of partitions of Z_{+}, in the same spirit as Bertoin and Le Gall's flows, replacing roughly speaking, composition of bridges by coagulation of partitions. Identifying at any time a population with the integers $\\mathbb{N}:=\\{1,2,...\\}$, the formalism of partitions is effective in the past as well as in the future especially when there ar...
Energy Technology Data Exchange (ETDEWEB)
Zhao, Guangpu [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Jian, Yongjun, E-mail: jianyj@imu.edu.cn [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Chang, Long [School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, Inner Mongolia 010051 (China); Buren, Mandula [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China)
2015-08-01
By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed.
Oscillations in a flexible channel flow of a generalized Newtonian fluid
Goswami, Prakash; Chakraborty, Suman
2016-01-01
We study the flow of a generalized Newtonian fluid, characterized by a power-law model, through a channel consisting of a wall with a flexible membrane under longitudinal tension. It is assumed that at steady state the flow through the channel admits a constant flux unidirectional flow profile, while for the unsteady case, we employ the long wave approximation and use a set of reduced equations to describe the variation of the shape of the membrane (assumed to be massless and elastic) and the variation of the fluid-flux. By means of asymptotic expansion, multiscale analysis and full numerical solutions of the pertinent governing equations, we show that depending upon the Reynolds number and the membrane stress, the flow behaviour for a shear-thinning, shear-thickening and Newtonian fluid may be markedly different, being oscillatory for one while chaotic for the other. The results presented herein hold practical relevance for several biologically relevant processes involving transport of rheologically complex ...
Institute of Scientific and Technical Information of China (English)
ZhuDetong
2004-01-01
This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems. Using the duality theory of the linear programming and convex theory, the generalized directional derivative of the general multicommodity minimal cost flow problems is derived. The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.
Advective Accretion Disks around Black Holes with Account of Magnetic Fields
Bisnovatyi-Kogan, G. S.
2002-09-01
Accretion disc theory was first developed as a theory with the local heat balance, where the whole energy produced by a viscous heating was emitted to the sides of the disc. One of the most important new invention of this theory was a phenomenological treatment of the turbulent viscosity, known as "alpha" prescription, when the (rφ) component of the stress tensor was approximated by (αP) with a unknown constant α. This prescription played the role in the accretion disc theory as well important as the mixing-length theory of convection for stellar evolution. Sources of turbulence in the accretion disc are discussed, including nonlinear hydrodynamic turbulence, convection and magnetic field role. In parallel to the optically thick geometrically thin accretion disc models, a new branch of the optically thin accretion disc models was discovered, with a larger thickness for the same total luminosity. The choice between these solutions should be done of the base of a stability analysis. The ideas underlying the necessity to include advec-tion into the accretion disc theory are presented and first models with advection are reviewed. The present status of the solution for a low-luminous optically thin accretion disc model with advection is discussed and the limits for an advection dominated accretion flows (ADAF) imposed by the presence of magnetic field are analyzed.
Effect of Ionic Advection on Electroosmosis over Charge Surfaces: Beyond the Weak Field Limit
Ghosh, Uddipta
2015-01-01
The present study deals with the effect of ionic advection on electroosmotic flow over charge modulated surfaces in a generalized paradigm when the classically restrictive "weak field" limit may be relaxed. Going beyond the commonly portrayed weak field limit (i.e, the externally applied electric field is over-weighed by the surface-induced electrical potential, towards charge distribution in an electrified wall-adhering layer) for electroosmotic transport, we numerically solve the coupled full set of Poisson-Nernst-Planck (PNP) and Navier-Stokes equations, in a semi-infinite domain, bounded at the bottom by a charged wall. Further, in an effort to obtain deeper physical insight, we solve the simplified forms of the relevant governing equations for low surface potential in two separate asymptotic limits: (i) a regular perturbation solution for Low Ionic Peclet number (Pe), where Pe is employed as the gauge function and (ii) a matched asymptotic solution for O(1) Pe in the Thin Electric Double Layer (EDL) limi...
Wu, Chung-Hua
1993-01-01
This report represents a general theory applicable to axial, radial, and mixed flow turbomachines operating at subsonic and supersonic speeds with a finite number of blades of finite thickness. References reflect the evolution of computational methods used, from the inception of the theory in the 50's to the high-speed computer era of the 90's. Two kinds of relative stream surfaces, S(sub 1) and S(sub 2), are introduced for the purpose of obtaining a three-dimensional flow solution through the combination of two-dimensional flow solutions. Nonorthogonal curvilinear coordinates are used for the governing equations. Methods of computing transonic flow along S(sub 1) and S(sub 2) stream surfaces are given for special cases as well as for fully three-dimensional transonic flows. Procedures pertaining to the direct solutions and inverse solutions are presented. Information on shock wave locations and shapes needed for computations are discussed. Experimental data from a Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt e.V. (DFVLR) rotor and from a Chinese Academy of Sciences (CAS) transonic compressor rotor are compared with the computed flow properties.
Quantifying streambed advection and conduction heat fluxes
Caissie, Daniel; Luce, Charles H.
2017-02-01
Groundwater and accompanying heat fluxes are particularly relevant for aquatic habitats as they influence living conditions both within the river and streambed. This study focuses on the theory and the development of new equations to estimate conduction and advection heat fluxes into and out of the bed, correcting some earlier misunderstandings and adding parameterizations that extend our understanding of timing of heat fluxes. The new heat flux equations are illustrated using Catamaran Brook (New Brunswick, Canada) stream/streambed temperature data. We show important relationships between fluxes when the surface water temperature (1) follows a sinusoidal function superimposed on a steady state condition (constant deep streambed temperature) and (2) when sinusoidal variations in stream temperature at two frequencies (annual and diel) are superimposed. When the stream temperature is used as a prescribed boundary condition, the contribution of bed fluid fluxes to stream temperature occurs through the effects of conductive thermal gradients, not through direct contribution/mixing of cold/warm water. Boundary conditions can be modified, however, to account for direct contribution of cold/warm water (e.g., localized upwelling) and consequences for the conduction heat flux. Equations developed allow for prediction of conductive fluxes to the bed during summer driven by diel and annual temperature fluctuations of the stream water and good agreement was observed between analytic solutions and field data. Results from this study provide a better insight into groundwater and heat fluxes which will ultimately result in better stream temperature models and a better management of fisheries resources.
Boundary value problem for one-dimensional fractional differential advection-dispersion equation
Directory of Open Access Journals (Sweden)
Khasambiev Mokhammad Vakhaevich
2014-07-01
Full Text Available An equation commonly used to describe solute transport in aquifers has attracted more attention in recent years. After a formal study of some aspects of the advection-diffusion equation, basically from the mathematical point of view with the solution of a differential equation with fractional derivative, the main interest to this problem shifted onto physical aspects of the dynamical system, such as the total energy and the dynamical response. In this regard it should be pointed out that the interaction with environment is expressed in terms of stochastic arrow of time. This allows one also to reach a progress in one more issue. Formerly the equation of advection-diffusion was not obtained from any physical principles. However, mainly the success concerns linear fractional systems. In fact, there are many cases in which linear treatments are not sufficient. The more general systems described by nonlinear fractional differential equations have not been studied enough. The ordinary calculus brings out clearly that essentially new phenomena occur in nonlinear systems, which generally cannot occur in linear systems. Due to vast range of application of the fractional advection-dispersion equation, a lot of work has been done to find numerical solution and fundamental solution of this equation. The research on the analytical solution of initial-boundary problem for space-fractional advection-dispersion equation is relatively new and is still at an early stage of development. In this paper, we will take use of the method of variable separation to solve space-fractional advection-dispersion equation with initial boundary data.
Ricci flow, Killing spinors, and T-duality in generalized geometry
Garcia-Fernandez, Mario
2016-01-01
We introduce a notion of Ricci flow in generalized geometry, extending a previous definition by Gualtieri on exact Courant algebroids. Special stationary points of the flow are given by solutions to first-order differential equations, the Killing spinor equations, which encompass special holonomy metrics with solutions of the Strominger system. Our main result investigates a method to produce new solutions of the Ricci flow and the Killing spinor equations. For this, we consider T-duality between possibly topologically distinct torus bundles endowed with Courant structures, and demonstrate that solutions of the equations are exchanged under this symmetry. As applications, we give a mathematical explanation of the dilaton shift in string theory and prove that the Strominger system is preserved by T-duality.
Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces
Directory of Open Access Journals (Sweden)
Eiji Onodera
2008-05-01
Full Text Available We study the structure of differential equations of one-dimensional dispersive flows into compact Riemann surfaces. These equations geometrically generalize two-sphere valued systems modeling the motion of vortex filament. We define a generalized Hasimoto transform by constructing a good moving frame, and reduce the equation with values in the induced bundle to a complex valued equation which is easy to handle. We also discuss the relationship between our reduction and the theory of linear dispersive partial differential equations.
Classical and generalized Horton laws for peak flows in rainfall-runoff events.
Gupta, Vijay K; Ayalew, Tibebu B; Mantilla, Ricardo; Krajewski, Witold F
2015-07-01
The discovery of the Horton laws for hydrologic variables has greatly lagged behind geomorphology, which began with Robert Horton in 1945. We define the classical and the generalized Horton laws for peak flows in rainfall-runoff events, which link self-similarity in network geomorphology with river basin hydrology. Both the Horton laws are tested in the Iowa River basin in eastern Iowa that drains an area of approximately 32 400 km(2) before it joins the Mississippi River. The US Geological Survey continuously monitors the basin through 34 stream gauging stations. We select 51 rainfall-runoff events for carrying out the tests. Our findings support the existence of the classical and the generalized Horton laws for peak flows, which may be considered as a new hydrologic discovery. Three different methods are illustrated for estimating the Horton peak-flow ratio due to small sample size issues in peak flow data. We illustrate an application of the Horton laws for diagnosing parameterizations in a physical rainfall-runoff model. The ideas and developments presented here offer exciting new directions for hydrologic research and education.
Generalized Mean-Flow Theory of Wave-Current-Bottom Interactions
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The interaction between waves, currents and bottoms in estuarine and coastal regions is ubiquitious, in particular the dynamic mechanism of waves on large-scale slowly varying currents. The wave action concept may be extended and applicated to the study of the mechanism. Considering the effects of moving bottoms and starting from the Navier-Stokes equation of motion of a viscous fluid including the Coriolis force, a generalized mean-flow model theory for the nearshore region, that is, a set of mean-flow equations and their generalized wave action equation involving the three new kinds of actions termed respectively as the current wave action, the bottom wave action and the dissipative wave action which can be applied to arbitrary depth over moving bottoms and ambient currents with a typical vertical structure, is developed by vertical integration and time-averaging over a wave period, thus extending the classical concept, wave action, from the ideal averaged flow conservative system to the real averaged flow dissipative dynamical system, and having a large range of application.
Chinyoka, T.; Makinde, O. D.
2013-01-01
The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively. PMID:23956691
Chu, M. S.; Guo, Wenfeng
2016-06-01
The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the "electrostatic continua." Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic
Flow dynamics around downwelling submarine canyons
Directory of Open Access Journals (Sweden)
J. M. Spurgin
2014-05-01
Full Text Available Flow dynamics around a downwelling submarine canyon were analysed with the Massachusetts Institute of Technology general circulation model. Blanes Canyon (Northwest Mediterranean was used for topographic and initial forcing conditions. Fourteen scenarios were modelled with varying forcing conditions. Rossby number and Burger number were used to determine the significance of Coriolis acceleration and stratification (respectively and their impacts on flow dynamics. A new non-dimensional parameter (χ was introduced to determine the significance of vertical variations in stratification. Some simulations do see brief periods of upwards displacement of water during the 10 day model period, however, the presence of the submarine canyon is found to enhance downwards advection of density in all model scenarios. High Burger numbers lead to negative vorticity and a trapped anticyclonic eddy within the canyon, as well as an increased density anomaly. Low Burger numbers lead to positive vorticity, cyclonic circulation and weaker density anomalies. Vertical variations in stratification affect zonal jet placement. Under the same forcing conditions, the zonal jet is pushed offshore in more uniformly stratified domains. Offshore jet location generates upwards density advection away from the canyon, while onshore jets generate downwards density advection everywhere within the model domain. Increasing Rossby values across the canyon axis, as well as decreasing Burger values, increase negative vertical flux at shelf break depth (150 m. Increasing Rossby numbers lead to stronger downwards advection of a passive tracer (nitrate as well as stronger vorticity within the canyon. Results from previous studies were explained within this new dynamic framework.
Flow dynamics around downwelling submarine canyons
Directory of Open Access Journals (Sweden)
J. M. Spurgin
2014-10-01
Full Text Available Flow dynamics around a downwelling submarine canyon were analysed with the Massachusetts Institute of Technology general circulation model. Blanes Canyon (northwestern Mediterranean was used for topographic and initial forcing conditions. Fourteen scenarios were modelled with varying forcing conditions. Rossby and Burger numbers were used to determine the significance of Coriolis acceleration and stratification (respectively and their impacts on flow dynamics. A new non-dimensional parameter (χ was introduced to determine the significance of vertical variations in stratification. Some simulations do see brief periods of upwards displacement of water during the 10-day model period; however, the presence of the submarine canyon is found to enhance downwards advection of density in all model scenarios. High Burger numbers lead to negative vorticity and a trapped anticyclonic eddy within the canyon, as well as an increased density anomaly. Low Burger numbers lead to positive vorticity, cyclonic circulation, and weaker density anomalies. Vertical variations in stratification affect zonal jet placement. Under the same forcing conditions, the zonal jet is pushed offshore in more uniformly stratified domains. The offshore jet location generates upwards density advection away from the canyon, while onshore jets generate downwards density advection everywhere within the model domain. Increasing Rossby values across the canyon axis, as well as decreasing Burger values, increase negative vertical flux at shelf break depth (150 m. Increasing Rossby numbers lead to stronger downwards advection of a passive tracer (nitrate, as well as stronger vorticity within the canyon. Results from previous studies are explained within this new dynamic framework.
Flow dynamics around downwelling submarine canyons
Spurgin, J. M.; Allen, S. E.
2014-10-01
Flow dynamics around a downwelling submarine canyon were analysed with the Massachusetts Institute of Technology general circulation model. Blanes Canyon (northwestern Mediterranean) was used for topographic and initial forcing conditions. Fourteen scenarios were modelled with varying forcing conditions. Rossby and Burger numbers were used to determine the significance of Coriolis acceleration and stratification (respectively) and their impacts on flow dynamics. A new non-dimensional parameter (χ) was introduced to determine the significance of vertical variations in stratification. Some simulations do see brief periods of upwards displacement of water during the 10-day model period; however, the presence of the submarine canyon is found to enhance downwards advection of density in all model scenarios. High Burger numbers lead to negative vorticity and a trapped anticyclonic eddy within the canyon, as well as an increased density anomaly. Low Burger numbers lead to positive vorticity, cyclonic circulation, and weaker density anomalies. Vertical variations in stratification affect zonal jet placement. Under the same forcing conditions, the zonal jet is pushed offshore in more uniformly stratified domains. The offshore jet location generates upwards density advection away from the canyon, while onshore jets generate downwards density advection everywhere within the model domain. Increasing Rossby values across the canyon axis, as well as decreasing Burger values, increase negative vertical flux at shelf break depth (150 m). Increasing Rossby numbers lead to stronger downwards advection of a passive tracer (nitrate), as well as stronger vorticity within the canyon. Results from previous studies are explained within this new dynamic framework.
Wheeler, M.F.
2010-09-06
For many years there have been formulations considered for modeling single phase ow on general hexahedra grids. These include the extended mixed nite element method, and families of mimetic nite di erence methods. In most of these schemes either no rate of convergence of the algorithm has been demonstrated both theoret- ically and computationally or a more complicated saddle point system needs to be solved for an accurate solution. Here we describe a multipoint ux mixed nite element (MFMFE) method [5, 2, 3]. This method is motivated from the multipoint ux approximation (MPFA) method [1]. The MFMFE method is locally conservative with continuous ux approximations and is a cell-centered scheme for the pressure. Compared to the MPFA method, the MFMFE has a variational formulation, since it can be viewed as a mixed nite element with special approximating spaces and quadrature rules. The framework allows han- dling of hexahedral grids with non-planar faces by applying trilinear mappings from physical elements to reference cubic elements. In addition, there are several multi- scale and multiphysics extensions such as the mortar mixed nite element method that allows the treatment of non-matching grids [4]. Extensions to the two-phase oil-water ow are considered. We reformulate the two- phase model in terms of total velocity, capillary velocity, water pressure, and water saturation. We choose water pressure and water saturation as primary variables. The total velocity is driven by the gradient of the water pressure and total mobility. Iterative coupling scheme is employed for the coupled system. This scheme allows treatments of di erent time scales for the water pressure and water saturation. In each time step, we rst solve the pressure equation using the MFMFE method; we then Center for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; mfw@ices.utexas.edu. yCenter for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; gxue
Directory of Open Access Journals (Sweden)
Mandana Samari Kermani
2016-01-01
Full Text Available The interaction of spherical solid particles with turbulent eddies in a 3-D turbulent channel flow with friction Reynolds number was studied. A generalized lattice Boltzmann equation (GLBE was used for computation of instantaneous turbulent flow field for which large eddy simulation (LES was employed. The sub-grid-scale (SGS turbulence effects were simulated through a shear-improved Smagorinsky model (SISM, which can predict turbulent near wall region without any wall function. Statistical properties of particles behavior such as root mean square (RMS velocities were studied as a function of dimensionless particle relaxation time ( by using a Lagrangian approach. Combination of SISM in GLBE with particle tracking analysis in turbulent channel flow is novelty of the present work. Both GLBE and SISM solve the flow field equations locally. This is an advantage of this method and makes it easy implementing. Comparison of the present results with previous available data indicated that SISM in GLBE is a reliable method for simulation of turbulent flows which is a key point to predict particles behavior correctly.
General slip regime permeability model for gas flow through porous media
Zhou, Bo; Jiang, Peixue; Xu, Ruina; Ouyang, Xiaolong
2016-07-01
A theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by converging-diverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, "Effective correlation of apparent gas permeability in tight porous media," Transp. Porous Media 82, 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model.
Merks, R.M.H.; Hoekstra, A.G.; Sloot, P.M.A.
2002-01-01
We numerically validate the moment propagation method for advection-diffusion in a Lattice Boltzmann simulation against the analytic Taylor-Aris prediction for dispeion in a three dimensional Poiseuille flow. Good agreement between simulation and teh tehory is found, with relative errors smaller tha
Predicting salt advection in groundwater from saline aquaculture ponds
Verrall, D. P.; Read, W. W.; Narayan, K. A.
2009-01-01
SummaryThis paper predicts saltwater advection in groundwater from leaky aquaculture ponds. A closed form solution for the potential function, stream function and velocity field is derived via the series solutions method. Numerically integrating along different streamlines gives the location (or advection front) of saltwater throughout the domain for any predefined upper time limit. Extending this process produces a function which predicts advection front location against time. The models considered in this paper are easily modified given knowledge of the required physical parameters.
Designing for chaos: applications of chaotic advection at the microscale.
Stremler, Mark A; Haselton, F R; Aref, Hassan
2004-05-15
Chaotic advection can play an important role in efficient microfluidic mixers. We discuss a design paradigm that exploits chaotic advection and illustrate by two recent examples, namely enhancing gene expression profiling and constructing an in-line microfluidic mixing channel, how application of this paradigm has led to successful micromixers. We suggest that 'designing for chaos', that is, basing practical mixer design on chaotic advection analysis, is a promising approach to adopt in this developing field which otherwise has little to guide it and is constrained by issues of scale and manufacturability.
Signatures of fractal clustering of aerosols advected under gravity.
Vilela, Rafael D; Tél, Tamás; de Moura, Alessandro P S; Grebogi, Celso
2007-06-01
Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example, at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension D(0) of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.
Contribution of Advective and Non-advective Heat Fluxes to the Heat Budget of a Shallow Lagoon
Directory of Open Access Journals (Sweden)
Rodríguez-Rodríguez Miguel
2005-01-01
Full Text Available The heat budget in a shallow lagoon has been established from field measurements at a bihourly scale. Information on the main advective and non-advective heat fluxes were collected during year 2003 at Nueva lagoon (AlmerÃa, Southern Spain. Heat storage data was obtained from a thermistor chain located in the deepest part of the lagoon and meteorological information was acquired using an automatic meteorological station placed near the lagoon's shore. In addition, estimation of evaporation was inferred from climatic approaches. Inputs of heat energy were dominated by radiative fluxes, with received net radiation accounting on average for around 95% of the non-advective total gains and radiation losses accounting for around 70% of the non-advective total losses. Sensible heat transfer from/to the atmosphere constituted the second energy input (4% and output (20%, although heat losses by evaporation were also significant. Conduction of heat into the sediments was a relatively constant form of energy loss but constitutes a minor contribution on the overall heat budget. Considerable variability was evident in non-advective heat fluxes at different time scales, from diel to seasonal. In relation to advective heat fluxes, groundwater and irrigation surpluses added to the heat storage of Nueva lagoon, whereas heat advected via precipitation was negligible.
Advective-diffusive mass transfer in fractured porous media with variable rock matrix block size.
Sharifi Haddad, Amin; Hassanzadeh, Hassan; Abedi, Jalal
2012-05-15
Traditional dual porosity models do not take into account the effect of matrix block size distribution on the mass transfer between matrix and fracture. In this study, we introduce the matrix block size distributions into an advective-diffusive solute transport model of a divergent radial system to evaluate the mass transfer shape factor, which is considered as a first-order exchange coefficient between the fracture and matrix. The results obtained lead to a better understanding of the advective-diffusive mass transport in fractured porous media by identifying two early and late time periods of mass transfer. Results show that fractured rock matrix block size distribution has a great impact on mass transfer during early time period. In addition, two dimensionless shape factors are obtained for the late time, which depend on the injection flow rate and the distance of the rock matrix from the injection point.
DEFF Research Database (Denmark)
Santos, Isaac R.; Eyre, Bradley D.; Glud, Ronnie N.
2012-01-01
Porewater flow enhances mineralization rates in organic-poor permeable sands. Here, a series of sediment column experiments were undertaken to assess the potential effect of advective porewater transport on denitrification in permeable carbonate sands collected from Heron Island (Great Barrier Reef...... consumption and N-2 production. The N:O-2 slope of 0.114 implied that about 75% of all the nitrogen mineralized was denitrified. A 4-fold increase in sediment column length (from 10 to 40 cm) resulted in an overall increase in oxygen consumption (1.6-fold), TCO2 production (1.8-fold), and denitrification (1...... enhance the development of microniches (i.e., steep oxygen gradients) within porous carbonate sands, perhaps providing optimum conditions for denitrification. The denitrification peak fell within the broad range of advection rates (often on scales of 1-100 L m(-2) h(-1)) typically found on continental...
A Hybrid Advection Scheme for Conserving Angular Momentum on a Refined Cartesian Mesh
Byerly, Zachary D; Tohline, Joel E; Marcello, Dominic C
2014-01-01
We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable axisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios, and quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima (1986) and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. (1994). When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the...
A general approach for modeling the motion of rigid and deformable ellipsoids in ductile flows
Jiang, Dazhi
2012-01-01
A general approach for modeling the motion of rigid or deformable objects in viscous flows is presented. It is shown that the rotation of a 3D object in a viscous fluid, regardless of the mechanical property and shape of the object, is defined by a common and simple differential equation, dQ/dt=-Θ˜Q, where Q is a matrix defined by the orientation of the object and Θ˜ is the angular velocity tensor of the object. The difference between individual cases lies only in the formulation for the angular velocity. Thus the above equation, together with Jeffery's theory for the angular velocity of rigid ellipsoids, describes the motion of rigid ellipsoids in viscous flows. The same equation, together with Eshelby's theory for the angular velocity of deformable ellipsoids, describes the motion of deformable ellipsoids in viscous flows. Both problems are solved here numerically by a general approach that is much simpler conceptually and more economic computationally, compared to previous approaches that consider the problems separately and require numerical solutions to coupled differential equations about Euler angles or spherical (polar coordinate) angles. A Runge-Kutta approximation is constructed for solving the above general differential equation. Singular cases of Eshelby's equations when the object is spheroidal or spherical are handled in this paper in a much simpler way than in previous work. The computational procedure can be readily implemented in any modern mathematics application that handles matrix operations. Four MathCad Worksheets are provided for modeling the motion of a single rigid or deformable ellipsoid immersed in viscous fluids, as well as the evolution of a system of noninteracting rigid or deformable ellipsoids embedded in viscous flows.
An advection-based model to increase the temporal resolution of PIV time series.
Scarano, Fulvio; Moore, Peter
A numerical implementation of the advection equation is proposed to increase the temporal resolution of PIV time series. The method is based on the principle that velocity fluctuations are transported passively, similar to Taylor's hypothesis of frozen turbulence. In the present work, the advection model is extended to unsteady three-dimensional flows. The main objective of the method is that of lowering the requirement on the PIV repetition rate from the Eulerian frequency toward the Lagrangian one. The local trajectory of the fluid parcel is obtained by forward projection of the instantaneous velocity at the preceding time instant and backward projection from the subsequent time step. The trajectories are approximated by the instantaneous streamlines, which yields accurate results when the amplitude of velocity fluctuations is small with respect to the convective motion. The verification is performed with two experiments conducted at temporal resolutions significantly higher than that dictated by Nyquist criterion. The flow past the trailing edge of a NACA0012 airfoil closely approximates frozen turbulence, where the largest ratio between the Lagrangian and Eulerian temporal scales is expected. An order of magnitude reduction of the needed acquisition frequency is demonstrated by the velocity spectra of super-sampled series. The application to three-dimensional data is made with time-resolved tomographic PIV measurements of a transitional jet. Here, the 3D advection equation is implemented to estimate the fluid trajectories. The reduction in the minimum sampling rate by the use of super-sampling in this case is less, due to the fact that vortices occurring in the jet shear layer are not well approximated by sole advection at large time separation. Both cases reveal that the current requirements for time-resolved PIV experiments can be revised when information is poured from space to time. An additional favorable effect is observed by the analysis in the frequency
A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks
Majumdar, Alok; Bailey, John W.; Schallhorn, Paul; Steadman, Todd
1998-01-01
This paper describes a general purpose computer program for analyzing steady state and transient flow in a complex network. The program is capable of modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal. The program's preprocessor allows the user to interactively develop a fluid network simulation consisting of nodes and branches. Mass, energy and specie conservation equations are solved at the nodes; the momentum conservation equations are solved in the branches. The program contains subroutines for computing "real fluid" thermodynamic and thermophysical properties for 33 fluids. The fluids are: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride and ammonia. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. Seventeen different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include: pipe flow, flow through a restriction, non-circular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, and a Joule-Thompson device. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. This paper also illustrates the application and verification of the code by comparison with Hardy Cross method for steady state flow and analytical solution for unsteady flow.
New complex variable meshless method for advection-diffusion problems
Institute of Scientific and Technical Information of China (English)
Wang Jian-Fei; Cheng Yu-Min
2013-01-01
In this paper,an improved complex variable meshless method (ICVMM) for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square (ICVMLS) approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for two-point boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency.
Anomalous scaling of a scalar field advected by turbulence
Energy Technology Data Exchange (ETDEWEB)
Kraichnan, R.H. [Robert H. Kraichnan, Inc., Santa Fe, NM (United States)
1995-12-31
Recent work leading to deduction of anomalous scaling exponents for the inertial range of an advected passive field from the equations of motion is reviewed. Implications for other turbulence problems are discussed.
Cavitating flow during water hammer using a generalized interface vaporous cavitation model
Sadafi, Mohamadhosein; Riasi, Alireza; Nourbakhsh, Seyed Ahmad
2012-10-01
In a transient flow simulation, column separation may occur when the calculated pressure head decreases to the saturated vapor pressure head in a computational grid. Abrupt valve closure or pump failure can result in a fast transient flow with column separation, potentially causing problems such as pipe failure, hydraulic equipment damage, cavitation or corrosion. This paper reports a numerical study of water hammer with column separation in a simple reservoir-pipeline-valve system and pumping station. The governing equations for two-phase transient flow in pipes are solved based on the method of characteristics (MOC) using a generalized interface vaporous cavitating model (GIVCM). The numerical results were compared with the experimental data for validation purposes, and the comparison indicated that the GIVCM describes the experimental results more accurately than the discrete vapor cavity model (DVCM). In particular, the GIVCM correlated better with the experimental data than the DVCM in terms of timing and pressure magnitude. The effects of geometric and hydraulic parameters on flow behavior in a pumping station with column separation were also investigated in this study.
Energy Technology Data Exchange (ETDEWEB)
Hoffmann Jensen, B.
2003-12-01
The goal of this brief report is to express the model equations for an incompressible flow which is horizontally homogeneous. It is intended as a computationally inexpensive starting point of a more complete solution for neutral atmospheric flow over complex terrain. This idea was set forth by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employed to allow a robust and consistent numerical procedure. An invariant tensor form of the model equations is utilized expressing the flow variables in a transformed coordinate system in which they are horizontally homogeneous. The model utilizes the k - e model with limited mixing length by Apsley and Castro (1997). This turbulence closure reflects the fact that the atmosphere is only neutral up to a certain height. The horizontally homogeneous flow model is a part of a perturbation solver under development which is hoped to be more accurate than the current standard program WAsP by Troen and Petersen (1989) while achieving a high speed of execution. (au)
Generalized multiscale finite element method for non-Newtonian fluid flow in perforated domain
Chung, E. T.; Iliev, O.; Vasilyeva, M. V.
2016-10-01
In this work, we consider a non-Newtonian fluid flow in perforated domains. Fluid flow in perforated domains have a multiscale nature and solution techniques for such problems require high resolution. In particular, the discretization needs to honor the irregular boundaries of perforations. This gives rise to a fine-scale problems with many degrees of freedom which can be very expensive to solve. In this work, we develop a multiscale approach that attempt to solve such problems on a coarse grid by constructing multiscale basis functions. We follow Generalized Multiscale Finite Element Method (GMsFEM) [1, 2] and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems [3, 4]. We show that with a few basis functions in each coarse block, one can accurately approximate the solution, where each coarse block can contain many small inclusions.
Burkhardt, Z.; Ramachandran, N.; Majumdar, A.
2017-01-01
Fluid Transient analysis is important for the design of spacecraft propulsion system to ensure structural stability of the system in the event of sudden closing or opening of the valve. Generalized Fluid System Simulation Program (GFSSP), a general purpose flow network code developed at NASA/MSFC is capable of simulating pressure surge due to sudden opening or closing of valve when thermodynamic properties of real fluid are available for the entire range of simulation. Specifically GFSSP needs an accurate representation of pressure-density relationship in order to predict pressure surge during a fluid transient. Unfortunately, the available thermodynamic property programs such as REFPROP, GASP or GASPAK does not provide the thermodynamic properties of Monomethylhydrazine (MMH). This paper will illustrate the process used for building a customized table of properties of state variables from available properties and speed of sound that is required by GFSSP for simulation. Good agreement was found between the simulations and measured data. This method can be adopted for modeling flow networks and systems with other fluids whose properties are not known in detail in order to obtain general technical insight. Rigorous code validation of this approach will be done and reported at a future date.
Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.
2014-04-01
In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous media. While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods. Typically, approaches are limited to Dirichlet boundary conditions. In this paper, Brinkman penalization is extended for generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. This Characteristic-Based Volume Penalization (CBVP) method is a comprehensive approach to conditions on immersed boundaries, providing for homogeneous and inhomogeneous Dirichlet, Neumann, and Robin boundary conditions on hyperbolic and parabolic equations. This CBVP method can be used to impose boundary conditions for both integrated and non-integrated variables in a systematic manner that parallels the prescription of exact boundary conditions. Furthermore, the method does not depend upon a physical model, as with porous media approach for Brinkman penalization, and is therefore flexible for various physical regimes and general evolutionary equations. Here, the method is applied to scalar diffusion and to direct numerical simulation of compressible, viscous flows. With the Navier-Stokes equations, both homogeneous and inhomogeneous Neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder. Theoretical and numerical examination shows that the error from penalized Neumann and Robin boundary conditions can be rigorously controlled through an a priori penalization parameter η. The error on a transient boundary is found to converge as O
Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface
Institute of Scientific and Technical Information of China (English)
M. Sajid; K. Mahmood; Z. Abbas
2012-01-01
We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface.The power law non-Newtonian fluid is considered as a lubricant.The lubrication layer is thin and assumed to have a variable thickness.The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization.The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order RungeKutta method.The results are discussed to see the influence of pertinent parameters.The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.%We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface. The power law non-Newtonian fluid is considered as a lubricant. The lubrication layer is thin and assumed to have a variable thickness. The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization. The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge Kutta method. The results arc discussed to see the influence of pertinent parameters. The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.
Berenstein, Igal; Bullara, Domenico; De Decker, Yannick
2014-09-01
This paper studies the spatiotemporal dynamics of a reaction-diffusion-advection system corresponding to an extension of the Oregonator model, which includes two inhibitors instead of one. We show that when the reaction-diffusion, two-dimensional problem displays stationary patterns the addition of a plug flow can induce the emergence of new types of stationary structures. These patterns take the form of spots or arcs, the size and the spacing of which can be controlled by the flow.
On the MHD flow of fractional generalized Burgers' fluid with modified Darcy's law
Institute of Scientific and Technical Information of China (English)
T. Hayat; M. Khan; S. Asghar
2007-01-01
This work is concerned with applying the fractional calculus approach to the magnetohydrodynamic(MHD) pipe flow of a fractional generalized Burgers' fluid in a porous space by using modified Darcy's relationship. The fluid is electrically conducting in the presence of a constant applied magnetic field in the transverse direction. Exact solution for the velocity distribution is developed with the help of Fourier transform for fractional calculus. The solutions for a Navier-Stokes, second grade, Maxwell, Oldroyd-B and Burgers' fluids appear as the limiting cases of the present analysis.
Indian Academy of Sciences (India)
M H Mkwizu; O D Makinde; Yaw Nkansah-Gyekye
2015-10-01
This work investigates the effects of convective cooling on entropy generation in a transient generalized Couette flow of water-based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both First and Second Laws of thermodynamics are utilised to analyse the problem. The model partial differential equations for momentum and energy balance are tackled numerically using a semidiscretization finite difference method together with Runge–Kutta Fehlberg integration scheme. Graphical results on the effects of parameter variation on velocity, temperature, skin friction, Nusselt number, entropy generation rate, irreversibility ratio and Bejan number are presented and discussed.
DEFF Research Database (Denmark)
Jørgensen, Bo Hoffmann
2003-01-01
by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...... equations is utilized expressing the flow variables in a transformed coordinate system in which they are horizontally homogeneous. The model utilizes the k - emodel with limited mixing length by Apsley and Castro (1997). This turbulence closure reflects the fact that the atmosphere is only neutral up...
Institute of Scientific and Technical Information of China (English)
HUANG Rui Xin
2014-01-01
Gravitational Potential Energy (GPE) change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps:stirring and sub-scale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stir-ring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordi-nates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eule-rian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.
Directory of Open Access Journals (Sweden)
Eric T. Chung
2015-12-01
Full Text Available In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation. We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration to solve the coupled system. We use the mixed framework, which allows mass conservation. Our main contributions are: (1 the development of a mass conservative GMsFEM for the coupled flow and transport; (2 the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation. We present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation.
An improved parallel SPH approach to solve 3D transient generalized Newtonian free surface flows
Ren, Jinlian; Jiang, Tao; Lu, Weigang; Li, Gang
2016-08-01
In this paper, a corrected parallel smoothed particle hydrodynamics (C-SPH) method is proposed to simulate the 3D generalized Newtonian free surface flows with low Reynolds number, especially the 3D viscous jets buckling problems are investigated. The proposed C-SPH method is achieved by coupling an improved SPH method based on the incompressible condition with the traditional SPH (TSPH), that is, the improved SPH with diffusive term and first-order Kernel gradient correction scheme is used in the interior of the fluid domain, and the TSPH is used near the free surface. Thus the C-SPH method possesses the advantages of two methods. Meanwhile, an effective and convenient boundary treatment is presented to deal with 3D multiple-boundary problem, and the MPI parallelization technique with a dynamic cells neighbor particle searching method is considered to improve the computational efficiency. The validity and the merits of the C-SPH are first verified by solving several benchmarks and compared with other results. Then the viscous jet folding/coiling based on the Cross model is simulated by the C-SPH method and compared with other experimental or numerical results. Specially, the influences of macroscopic parameters on the flow are discussed. All the numerical results agree well with available data, and show that the C-SPH method has higher accuracy and better stability for solving 3D moving free surface flows over other particle methods.
Chung, Eric
2015-12-11
In this paper, we develop a mass conservative multiscale method for coupled flow and transport in heterogeneous porous media. We consider a coupled system consisting of a convection-dominated transport equation and a flow equation. We construct a coarse grid solver based on the Generalized Multiscale Finite Element Method (GMsFEM) for a coupled system. In particular, multiscale basis functions are constructed based on some snapshot spaces for the pressure and the concentration equations and some local spectral decompositions in the snapshot spaces. The resulting approach uses a few multiscale basis functions in each coarse block (for both the pressure and the concentration) to solve the coupled system. We use the mixed framework, which allows mass conservation. Our main contributions are: (1) the development of a mass conservative GMsFEM for the coupled flow and transport; (2) the development of a robust multiscale method for convection-dominated transport problems by choosing appropriate test and trial spaces within Petrov-Galerkin mixed formulation. We present numerical results and consider several heterogeneous permeability fields. Our numerical results show that with only a few basis functions per coarse block, we can achieve a good approximation.
Institute of Scientific and Technical Information of China (English)
NIU Junchuan; GE Peiqi; HOU Cuirong; LIM C W; SONG Kongjie
2009-01-01
For estimating the vibration transmission accurately and performing vibration control efficiently in isolation systems, a novel general model is presented to predict the power flow transmitted into the complicate flexible bases of laminated beams. In the model, the laminated beam bases are simulated by the first-order shear deformation laminated plate theory, which is relatively simple and economic but accurate in predicting the vibration solutions of flexible isolation systems with laminated beam bases in comparison with classical laminated beam theories and higher order theories. On the basis of the presented model, substructure technique and variational principle are employed to obtain the governing equation of the isolation system and the power flow solution. Then, the vibration characteristics of the flexible isolation systems with laminated bases are investigated. Several numerical examples are given to show the validity and efficiency of the presented model. It is concluded that the presented model is the extension of the classical one and it can obtain more accurate power flow solutions.
ALGEBRAIC GENERALIZATION OF THE CASH FLOW STATEMENT: REFLECTIONS BY MEANS OF AN ALGEBRAIC ALGORITHM
Directory of Open Access Journals (Sweden)
José Roberto Kassai
2012-09-01
Full Text Available Starting on January 1, 2008 it became mandatory for all Brazilian public companies and private companies with net worth greater than two million reais (about one million dollars as of this writing to publish a cash flow statement (CFS as part of their financial statements, making this statement another important source of information for investors. This article proposes an algebraic generalization for the CFS. Working papers can help fill in a gap in teaching about cash flow statements and produce an indirect method and a direct method, side by side with their equivalence highlighted, in a single matrix by means of algebraic algorithms. This study is normative in nature and stresses the transversal relationship between accounting and mathematics, showing that accounting reports and their structures can be seen as matrices and be subjected to algebraic deductions about the events recorded by double entries. As a result, we demonstrate a mathematical algorithm with matrices and submatrices and a script in the format of working papers, compatible with the normative orientations of the Federal Accounting Council (CFS and Brazilian legislation, permitting formulation of clear, reliable and effective cash flow statements.
Anco, S C
2010-01-01
A moving frame formulation of non-stretching geometric curve flows in Euclidean space is used to derive a 1+1 dimensional hierarchy of integrable SO(3)-invariant vector models containing the Heisenberg ferromagnetic spin model as well as a model given by a spin-vector version of the mKdV equation. These models describe a geometric realization of the NLS hierarchy of soliton equations whose bi-Hamiltonian structure is shown to be encoded in the Frenet equations of the moving frame. This derivation yields an explicit bi-Hamiltonian structure, recursion operator, and constants of motion for each model in the hierarchy. A generalization of these results to geometric surface flows is presented, where the surfaces are non-stretching in one direction while stretching in all transverse directions. Through the Frenet equations of a moving frame, such surface flows are shown to encode a hierarchy of 2+1 dimensional integrable SO(3)-invariant vector models, along with their bi-Hamiltonian structure, recursion operator, ...
Effect of advection on variations in zooplankton at a single location near Cabo Nazca, Peru
Energy Technology Data Exchange (ETDEWEB)
Smith, S L; Brink, K H; Santander, H; Cowles, T J; Huyer, A
1980-04-01
Temporal variations in the biomass and species composition of zooplankton at a single midshelf station in an upwelling area off Peru can be explained to a large extent by onshore-offshore advection in the upper 20 m of the water column. During periods of strong or sustained near-surface onshore flow, peaks in biomass of zooplankton were observed at midshelf and typically oceanic species of copepod were collected. In periods of offshore flow at the surface, a copepod capable of migrating into oxygen-depleted layers deeper than 30 m was collected. A simple translocation model of advection applied to the cross-shelf distribution of Paracalanus parvus suggests that the fluctuations in P. pavus observed in the midshelf time-series were closely related to onshore-offshore flow in the upper 20 m. Fluctuations in abundance of the numerically dominant copepod, Acartia tonsa, were apparently affected by near surface flow also. The population age-structure suggests that A. tonsa was growing at maximal rates, due in part to its positive feeding response to the dinoflagellate/diatom assemblage of phytoplankton.
Lester, D. R.; Trefry, M. G.; Metcalfe, G.
2016-11-01
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the pore scale generate chaotic advection-involving exponential stretching and folding of fluid elements-the mechanisms by which it arises and implications of microscopic chaos for macroscopic dispersion and mixing. Prohibited in steady 2D flow due to topological constraints, these phenomena are ubiquitous due to the topological complexity inherent to all 3D porous media. Consequently 3D porous media flows generate profoundly different fluid deformation and mixing processes to those of 2D flow. The interplay of chaotic advection and broad transit time distributions can be incorporated into a continuous-time random walk (CTRW) framework to predict macroscopic solute mixing and spreading. We show how these results may be generalised to real porous architectures via a CTRW model of fluid deformation, leading to stochastic models of macroscopic dispersion and mixing which both honour the pore-scale kinematics and are directly conditioned on the pore-scale architecture.
Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation
Frønsdal, Christian
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
Modelling uncertainty in incompressible flow simulation using Galerkin based generalized ANOVA
Chakraborty, Souvik; Chowdhury, Rajib
2016-11-01
This paper presents a new algorithm, referred to here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA) for modelling input uncertainties and its propagation in incompressible fluid flow. The proposed approach utilizes ANOVA to represent the unknown stochastic response. Further, the unknown component functions of ANOVA are represented using the generalized polynomial chaos expansion (PCE). The resulting functional form obtained by coupling the ANOVA and PCE is substituted into the stochastic Navier-Stokes equation (NSE) and Galerkin projection is employed to decompose it into a set of coupled deterministic 'Navier-Stokes alike' equations. Temporal discretization of the set of coupled deterministic equations is performed by employing Adams-Bashforth scheme for convective term and Crank-Nicolson scheme for diffusion term. Spatial discretization is performed by employing finite difference scheme. Implementation of the proposed approach has been illustrated by two examples. In the first example, a stochastic ordinary differential equation has been considered. This example illustrates the performance of proposed approach with change in nature of random variable. Furthermore, convergence characteristics of GG-ANOVA has also been demonstrated. The second example investigates flow through a micro channel. Two case studies, namely the stochastic Kelvin-Helmholtz instability and stochastic vortex dipole, have been investigated. For all the problems results obtained using GG-ANOVA are in excellent agreement with benchmark solutions.
Round window membrane intracochlear drug delivery enhanced by induced advection.
Borkholder, David A; Zhu, Xiaoxia; Frisina, Robert D
2014-01-28
Delivery of therapeutic compounds to the inner ear via absorption through the round window membrane (RWM) has advantages over direct intracochlear infusions; specifically, minimizing impact upon functional hearing measures. However, previous reports show that significant basal-to-apical concentration gradients occur, with the potential to impact treatment efficacy. Here we present a new approach to inner ear drug delivery with induced advection aiding distribution of compounds throughout the inner ear in the murine cochlea. Polyimide microtubing was placed near the RWM niche through a bullaostomy into the middle ear cavity allowing directed delivery of compounds to the RWM. We hypothesized that a posterior semicircular canalostomy would induce apical flow from the patent cochlear aqueduct to the canalostomy due to influx of cerebral spinal fluid. To test this hypothesis, young adult CBA/CaJ mice were divided into two groups: bullaostomy approach only (BA) and bullaostomy+canalostomy (B+C). Cochlear function was evaluated by distortion product otoacoustic emission (DPOAE) and auditory brainstem response (ABR) thresholds during and after middle ear infusion of salicylate in artificial perilymph (AP), applied near the RWM. The mice recovered for 1week, and were re-tested. The results demonstrate there was no significant impact on auditory function utilizing the RWM surgical procedure with or without the canalostomy, and DPOAE thresholds were elevated reversibly during the salicylate infusion. Comparing the threshold shifts for both methods, the B+C approach had more of a physiological effect than the BA approach, including at lower frequencies representing more apical cochlear locations. Unlike mouse cochleostomies, there was no deleterious auditory functional impact after 1week recovery from surgery. The B+C approach had more drug efficacy at lower frequencies, underscoring potential benefits for more precise control of delivery of inner ear therapeutic compounds.
Vertex centred Discretization of Two-Phase Darcy flows on General Meshes
Directory of Open Access Journals (Sweden)
Herbin Raphaèle
2012-04-01
Full Text Available This paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG, already introduced for single phase diffusive problems in [9], to multiphase Darcy flows. The convergence of the VAG scheme is proved for a simplified two-phase Darcy flow model, coupling an elliptic equation for the pressure and a linear hyperbolic equation for the saturation. The ability for the VAG scheme to efficiently deal with highly heterogeneous media and complex meshes is exhibited on immiscible and miscible two phase Darcy flow models. Cet article porte sur la discrétisation des flux de Darcy polyphasiques au sein de milieux poreux hétérogènes et anisotropes, dans des maillages tridimensionnels généraux utilisés dans le contexte de la simulation de réservoir ou de bassin. Un schéma avec inconnues aux sommets [9], qui a l’avantage d’être inconditionnellement coercif et symétrique, est généralisé au cas des écoulements de Darcy polyphasiques. La convergence du schéma est démontrée sur un modèle diphasique simplifié, couplant une équation elliptique pour la pression à une équation hyperbolique linéaire pour la saturation. On illustre ensuite la capacité du schéma à prendre en compte efficacement les fortes hétérogénéités et les maillages complexes sur des exemples d’écoulements diphasiques immiscibles et miscibles.
Costa, C. P.; Vilhena, M. T.; Moreira, D. M.; Tirabassi, T.
We present a three-dimensional solution of the steady-state advection-diffusion equation considering a vertically inhomogeneous planetary boundary layer (PBL). We reach this goal applying the generalized integral transform technique (GITT), a hybrid method that had solved a wide class of direct and inverse problems mainly in the area of heat transfer and fluid mechanics. The transformed problem is solved by the advection-diffusion multilayer model (ADMM) method, a semi-analytical solution based on a discretization of the PBL in sub-layers where the advection-diffusion equation is solved by the Laplace transform technique. Numerical simulations are presented and the performances of the solution are compared against field experiments data.
Python tools for rapid development, calibration, and analysis of generalized groundwater-flow models
Starn, J. J.; Belitz, K.
2014-12-01
National-scale water-quality data sets for the United States have been available for several decades; however, groundwater models to interpret these data are available for only a small percentage of the country. Generalized models may be adequate to explain and project groundwater-quality trends at the national scale by using regional scale models (defined as watersheds at or between the HUC-6 and HUC-8 levels). Coast-to-coast data such as the National Hydrologic Dataset Plus (NHD+) make it possible to extract the basic building blocks for a model anywhere in the country. IPython notebooks have been developed to automate the creation of generalized groundwater-flow models from the NHD+. The notebook format allows rapid testing of methods for model creation, calibration, and analysis. Capabilities within the Python ecosystem greatly speed up the development and testing of algorithms. GeoPandas is used for very efficient geospatial processing. Raster processing includes the Geospatial Data Abstraction Library and image processing tools. Model creation is made possible through Flopy, a versatile input and output writer for several MODFLOW-based flow and transport model codes. Interpolation, integration, and map plotting included in the standard Python tool stack also are used, making the notebook a comprehensive platform within on to build and evaluate general models. Models with alternative boundary conditions, number of layers, and cell spacing can be tested against one another and evaluated by using water-quality data. Novel calibration criteria were developed by comparing modeled heads to land-surface and surface-water elevations. Information, such as predicted age distributions, can be extracted from general models and tested for its ability to explain water-quality trends. Groundwater ages then can be correlated with horizontal and vertical hydrologic position, a relation that can be used for statistical assessment of likely groundwater-quality conditions
Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations
Aldoghaither, Abeer
2015-11-12
Fractional calculus has been introduced as an e cient tool for modeling physical phenomena, thanks to its memory and hereditary properties. For example, fractional models have been successfully used to describe anomalous di↵usion processes such as contaminant transport in soil, oil flow in porous media, and groundwater flow. These models capture important features of particle transport such as particles with velocity variations and long-rest periods. Mathematical modeling of physical phenomena requires the identification of pa- rameters and variables from available measurements. This is referred to as an inverse problem. In this work, we are interested in studying theoretically and numerically inverse problems for space Fractional Advection-Dispersion Equation (FADE), which is used to model solute transport in porous media. Identifying parameters for such an equa- tion is important to understand how chemical or biological contaminants are trans- ported throughout surface aquifer systems. For instance, an estimate of the di↵eren- tiation order in groundwater contaminant transport model can provide information about soil properties, such as the heterogeneity of the medium. Our main contribution is to propose a novel e cient algorithm based on modulat-ing functions to estimate the coe cients and the di↵erentiation order for space FADE, which can be extended to general fractional Partial Di↵erential Equation (PDE). We also show how the method can be applied to the source inverse problem. This work is divided into two parts: In part I, the proposed method is described and studied through an extensive numerical analysis. The local convergence of the proposed two-stage algorithm is proven for 1D space FADE. The properties of this method are studied along with its limitations. Then, the algorithm is generalized to the 2D FADE. In part II, we analyze direct and inverse source problems for a space FADE. The problem consists of recovering the source term using final
2.5-dimensional solution of the advective accretion disk:a self-similar approach
Institute of Scientific and Technical Information of China (English)
Shubhrangshu Ghosh; Banibrata Mukhopadhyay
2009-01-01
We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion-induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor f.
Accuracy of spectral and finite difference schemes in 2D advection problems
DEFF Research Database (Denmark)
Naulin, V.; Nielsen, A.H.
2003-01-01
In this paper we investigate the accuracy of two numerical procedures commonly used to solve 2D advection problems: spectral and finite difference (FD) schemes. These schemes are widely used, simulating, e.g., neutral and plasma flows. FD schemes have long been considered fast, relatively easy...... that the accuracy of FD schemes can be significantly improved if one is careful in choosing an appropriate FD scheme that reflects conservation properties of the nonlinear terms and in setting up the grid in accordance with the problem....
Numerical analysis of the advection-diffusion of a solute in random media
Charrier, Julia
2011-01-01
We consider the problem of numerically approximating the solution of the coupling of the flow equation in a random porous medium, with the advection-diffusion equation. More precisely, we present and analyse a numerical method to compute the mean value of the spread of a solute introduced at the initial time, and the mean value of the macro-dispersion, defined at the temporal derivative of the spread. We propose a Monte-Carlo method to deal with the uncertainty, i.e. with the randomness of th...
The role of advection and diffusion in waste disposal by sea urchin embryos
Clark, Aaron; Licata, Nicholas
2014-03-01
We determine the first passage probability for the absorption of waste molecules released from the microvilli of sea urchin embryos. We calculate a perturbative solution of the advection-diffusion equation for a linear shear profile similar to the fluid environment which the embryos inhabit. Rapid rotation of the embryo results in a concentration boundary layer of comparable thickness to the length of the microvilli. A comparison of the results to the regime of diffusion limited transport indicates that fluid flow is advantageous for efficient waste disposal.
Concentration polarization, surface currents, and bulk advection in a microchannel
Nielsen, Christoffer P
2014-01-01
We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behaviour of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk advection and the surface current; without a surface current, bulk advection is strongly suppressed. The numerical simulations are supplemented by analytical models valid in the long channel limit as well as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction.
Directory of Open Access Journals (Sweden)
B. C. Backeberg
2009-02-01
Full Text Available A 4th order advection scheme is applied in a nested eddy-resolving Hybrid Coordinate Ocean Model (HYCOM of the greater Agulhas Current system for the purpose of testing advanced numerics as a means for improving the model simulation for eventual operational implementation. Model validation techniques comparing sea surface height variations, sea level skewness and variogram analyses to satellite altimetry measurements quantify that generally the 4th order advection scheme improves the realism of the model simulation. The most striking improvement over the standard 2nd order momentum advection scheme, is that the Southern Agulhas Current is simulated as a well-defined meandering current, rather than a train of successive eddies. A better vertical structure and stronger poleward transports in the Agulhas Current core contribute toward a better southwestward penetration of the current, and its temperature field, implying a stronger Indo-Atlantic inter-ocean exchange. It is found that the transport, and hence this exchange, is sensitive to the occurrences of mesoscale features originating upstream in the Mozambique Channel and Southern East Madagascar Current, and that the improved HYCOM simulation is well suited for further studies of these inter-actions.
Carbon dioxide seasonality in dynamically ventilated caves: the role of advective fluxes
Lang, Marek; Faimon, Jiří; Godissart, Jean; Ek, Camille
2017-08-01
The seasonality in cave CO2 levels was studied based on (1) a new data set from the dynamically ventilated Comblain-au-Pont Cave (Dinant Karst Basin, Belgium), (2) archive data from Moravian Karst caves, and (3) published data from caves worldwide. A simplified dynamic model was proposed for testing the effect of all conceivable CO2 fluxes on cave CO2 levels. Considering generally accepted fluxes, i.e., the direct diffusive flux from soils/epikarst, the indirect flux derived from dripwater degassing, and the input/output fluxes linked to cave ventilation, gives the cave CO2 level maxima of 1.9 × 10-2 mol m-3 (i.e., ˜ 440 ppmv), which only slightly exceed external values. This indicates that an additional input CO2 flux is necessary for reaching usual cave CO2 level maxima. The modeling indicates that the additional flux could be a convective advective CO2 flux from soil/epikarst driven by airflow (cave ventilation) and enhanced soil/epikarstic CO2 concentrations. Such flux reaching up to 170 mol s-1 is capable of providing the cave CO2 level maxima up to 3 × 10-2 mol m-3 (70,000 ppmv). This value corresponds to the maxima known from caves worldwide. Based on cave geometry, three types of dynamic caves were distinguished: (1) the caves with the advective CO2 flux from soil/epikarst at downward airflow ventilation mode, (2) the caves with the advective soil/epikarstic flux at upward airflow ventilation mode, and (3) the caves without any soil/epikarstic advective flux. In addition to CO2 seasonality, the model explains both the short-term and seasonal variations in δ13C in cave air CO2.
A family of compact high order coupled time-space unconditionally stable vertical advection schemes
Lemarié, Florian; Debreu, Laurent
2016-04-01
Recent papers by Shchepetkin (2015) and Lemarié et al. (2015) have emphasized that the time-step of an oceanic model with an Eulerian vertical coordinate and an explicit time-stepping scheme is very often restricted by vertical advection in a few hot spots (i.e. most of the grid points are integrated with small Courant numbers, compared to the Courant-Friedrichs-Lewy (CFL) condition, except just few spots where numerical instability of the explicit scheme occurs first). The consequence is that the numerics for vertical advection must have good stability properties while being robust to changes in Courant number in terms of accuracy. An other constraint for oceanic models is the strict control of numerical mixing imposed by the highly adiabatic nature of the oceanic interior (i.e. mixing must be very small in the vertical direction below the boundary layer). We examine in this talk the possibility of mitigating vertical Courant-Friedrichs-Lewy (CFL) restriction, while avoiding numerical inaccuracies associated with standard implicit advection schemes (i.e. large sensitivity of the solution on Courant number, large phase delay, and possibly excess of numerical damping with unphysical orientation). Most regional oceanic models have been successfully using fourth order compact schemes for vertical advection. In this talk we present a new general framework to derive generic expressions for (one-step) coupled time and space high order compact schemes (see Daru & Tenaud (2004) for a thorough description of coupled time and space schemes). Among other properties, we show that those schemes are unconditionally stable and have very good accuracy properties even for large Courant numbers while having a very reasonable computational cost.
Manneville, Paul
2014-01-01
The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane Couette flow, the flow generated between counter-translating parallel planes. Subcritical here means discontinuous and direct, with strong hysteresis. This is due to the existence of nontrivial flow regimes between the global stability threshold Re_g, the upper bound for unconditional return to the base flow, and the linear instability threshold Re_c characterized by unconditional departure from the base flow. The transitional range around Re_g is first discussed from an empirical viewpoint ({\\S}1). The recent determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane Couette flow is next examined. In laboratory conditions, its transitional range displays an oblique pattern made of alternately laminar and turbulent bands, up to a third threshold Re_t beyo...
Forced convection analysis for generalized Burgers nanofluid flow over a stretching sheet
Khan, Masood; Khan, Waqar Azeem
2015-10-01
This article reports the two-dimensional forced convective flow of a generalized Burgers fluid over a linearly stretched sheet under the impacts of nano-sized material particles. Utilizing appropriate similarity transformations the coupled nonlinear partial differential equations are converted into a set of coupled nonlinear ordinary differential equations. The analytic results are carried out through the homotopy analysis method (HAM) to investigate the impact of various pertinent parameters for the velocity, temperature and concentration fields. The obtained results are presented in tabular form as well as graphically and discussed in detail. The presented results show that the rate of heat transfer at the wall and rate of nanoparticle volume fraction diminish with each increment of the thermophoresis parameter. While incremented values of the Brownian motion parameter lead to a quite opposite effect on the rates of heat transfer and nanoparticle volume fraction at the wall.
Makinde, O. D.
2014-12-01
In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton's law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.
Sadowski, A; Narayan, R; Abarca, D; McKinney, J C
2016-01-01
We present a numerical method which evolves a two-temperature, magnetized, radiative, accretion flow around a black hole, within the framework of general relativistic radiation magnetohydrodynamics. As implemented in the code KORAL, the gas consists of two sub-components -- ions and electrons -- which share the same dynamics but experience independent, relativistically consistent, thermodynamical evolution. The electrons and ions are heated independently according to a standard prescription from the literature for magnetohydrodynamical turbulent dissipation. Energy exchange between the particle species via Coulomb collisions is included. In addition, electrons gain and lose energy and momentum by absorbing and emitting synchrotron and bremsstrahlung radiation, and through Compton scattering. All evolution equations are handled within a fully covariant framework in the relativistic fixed-metric spacetime of the black hole. Numerical results are presented for five models of low luminosity black hole accretion. ...
TOUGH2: A general-purpose numerical simulator for multiphase nonisothermal flows
Energy Technology Data Exchange (ETDEWEB)
Pruess, K. [Lawrence Berkeley Lab., CA (United States)
1991-06-01
Numerical simulators for multiphase fluid and heat flows in permeable media have been under development at Lawrence Berkeley Laboratory for more than 10 yr. Real geofluids contain noncondensible gases and dissolved solids in addition to water, and the desire to model such `compositional` systems led to the development of a flexible multicomponent, multiphase simulation architecture known as MULKOM. The design of MULKOM was based on the recognition that the mass-and energy-balance equations for multiphase fluid and heat flows in multicomponent systems have the same mathematical form, regardless of the number and nature of fluid components and phases present. Application of MULKOM to different fluid mixtures, such as water and air, or water, oil, and gas, is possible by means of appropriate `equation-of-state` (EOS) modules, which provide all thermophysical and transport parameters of the fluid mixture and the permeable medium as a function of a suitable set of primary thermodynamic variables. Investigations of thermal and hydrologic effects from emplacement of heat-generating nuclear wastes into partially water-saturated formations prompted the development and release of a specialized version of MULKOM for nonisothermal flow of water and air, named TOUGH. TOUGH is an acronym for `transport of unsaturated groundwater and heat` and is also an allusion to the tuff formations at Yucca Mountain, Nevada. The TOUGH2 code is intended to supersede TOUGH. It offers all the capabilities of TOUGH and includes a considerably more general subset of MULKOM modules with added capabilities. The paper briefly describes the simulation methodology and user features.
A generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect
Chen, Li; Kang, Qinjun; Hyman, Jeffrey De'Haven; Viswanathan, Hari S; Tao, Wen-Quan
2014-01-01
Gas slippage occurs when the mean free path of the gas molecules is in the order of the characteristic pore size of a porous medium. This phenomenon leads to the Klinkenberg's effect where the measured permeability of a gas (apparent permeability) is higher than that of the liquid (intrinsic permeability). A generalized lattice Boltzmann model is proposed for flow through porous media that includes Klinkenberg's effect, which is based on the model of Guo et al. (Z.L. Guo et al., Phys.Rev.E 65, 046308 (2002)). The second-order Beskok and Karniadakis-Civan's correlation (A. Beskok and G. Karniadakis, Microscale Thermophysical Engineering 3, 43-47 (1999), F. Civan, Transp Porous Med 82, 375-384 (2010)) is adopted to calculate the apparent permeability based on intrinsic permeability and Knudsen number. Fluid flow between two parallel plates filled with porous media is simulated to validate model. Simulations performed in a heterogeneous porous medium with components of different porosity and permeability indicat...
Sądowski, Aleksander; Wielgus, Maciek; Narayan, Ramesh; Abarca, David; McKinney, Jonathan C.; Chael, Andrew
2017-04-01
We present a numerical method that evolves a two-temperature, magnetized, radiative, accretion flow around a black hole, within the framework of general relativistic radiation magnetohydrodynamics. As implemented in the code KORAL, the gas consists of two sub-components - ions and electrons - which share the same dynamics but experience independent, relativistically consistent, thermodynamical evolution. The electrons and ions are heated independently according to a prescription from the literature for magnetohydrodynamical turbulent dissipation. Energy exchange between the particle species via Coulomb collisions is included. In addition, electrons gain and lose energy and momentum by absorbing and emitting synchrotron and bremsstrahlung radiation and through Compton scattering. All evolution equations are handled within a fully covariant framework in the relativistic fixed-metric space-time of the black hole. Numerical results are presented for five models of low-luminosity black hole accretion. In the case of a model with a mass accretion rate dot{M}˜ 4× 10^{-8} dot{M}_Edd, we find that radiation has a negligible effect on either the dynamics or the thermodynamics of the accreting gas. In contrast, a model with a larger dot{M}˜ 4× 10^{-4} dot{M}_Edd behaves very differently. The accreting gas is much cooler and the flow is geometrically less thick, though it is not quite a thin accretion disc.
Measurements on, and modelling of diffusive and advective radon transport in soil
DEFF Research Database (Denmark)
Graff, E.R. van der; Witteman, G.A.A.; Spoel, W.H. van der;
1994-01-01
Results are presented of measurements on radon transport in soil under controlled conditions with a laboratory facility consisting of a stainless steel vessel (height and diameter 2 m) filled with a uniform column of sand. At several depths under the sand surface, probes are radially inserted...... into the vessel to measure the radon concentration in the soil gas. To study advective radon transport a perforated circular box is placed in the sand close to the bottom of the vessel. By pressurising this box, an air flow through the sand column is induced. Radon concentration profiles were measured without...... an air flow as a function of time, and for several values of the air flow, equilibrium radon concentration profiles were measured....
Efendiev, Yalchin R.
2015-06-05
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on generalized multiscale finite element method (GMsFEM), where we represent the fracture effects on a coarse grid via multiscale basis functions. These multiscale basis functions are constructed in the offline stage via local spectral problems following GMsFEM. To represent the fractures on the fine grid, we consider two approaches (1) discrete fracture model (DFM) (2) embedded fracture model (EFM) and their combination. In DFM, the fractures are resolved via the fine grid, while in EFM the fracture and the fine grid block interaction is represented as a source term. In the proposed multiscale method, additional multiscale basis functions are used to represent the long fractures, while short-size fractures are collectively represented by a single basis functions. The procedure is automatically done via local spectral problems. In this regard, our approach shares common concepts with several approaches proposed in the literature as we discuss. We would like to emphasize that our goal is not to compare DFM with EFM, but rather to develop GMsFEM framework which uses these (DFM or EFM) fine-grid discretization techniques. Numerical results are presented, where we demonstrate how one can adaptively add basis functions in the regions of interest based on error indicators. We also discuss the use of randomized snapshots (Calo et al. Randomized oversampling for generalized multiscale finite element methods, 2014), which reduces the offline computational cost.
Time Periodic Electroosmotic Flow of The Generalized Maxwell Fluids in a Semicircular Microchannel
Institute of Scientific and Technical Information of China (English)
BAO Li-Ping; JIAN Yong-Jun; CHANG Long; SU Jie; ZHANG Hai-Yan; LIU Quan-Sheng
2013-01-01
Analytical solutions are presented using method of separation of variables for the time periodic electroosmotic flow (EOF) of linear viscoelastic fluids in semicircular microchannel.The linear viscoelastic fluids used here are described by the general Maxwell model.The solution involves analytically solving the linearized Poisson-Boltzmann (P-B) equation,together with the Cauchy momentum equation and the general Maxwell constitutive equation.By numerical computations,the influences of electric oscillating Reynolds number Re and Deborah number De on velocity amplitude are presented.For small Re,results show that the larger velocity amplitudeis confined to the region near the charged wall when De is small.With the increase of the Deborah number De,the velocity far away the charged wall becomes larger for large Deborah number De.However,for larger Re,the oscillating characteristic of the velocity amplitude occurs and becomes significant with the increase of De,especially for larger Deborah number.
Consistency Problem with Tracer Advection in the Atmospheric Model GAMIL
Institute of Scientific and Technical Information of China (English)
ZHANG Kai; WAN Hui; WANG Bin; ZHANG Meigen
2008-01-01
The radon transport test,which is a widely used test case for atmospheric transport models,is carried out to evaluate the tracer advection schemes in the Grid-Point Atmospheric Model of IAP-LASG (GAMIL).TWO of the three available schemes in the model are found to be associated with significant biases in the polar regions and in the upper part of the atmosphere,which implies potentially large errors in the simulation of ozone-like tracers.Theoretical analyses show that inconsistency exists between the advection schemes and the discrete continuity equation in the dynamical core of GAMIL and consequently leads to spurious sources and sinks in the tracer transport equation.The impact of this type of inconsistency is demonstrated by idealized tests and identified as the cause of the aforementioned biases.Other potential effects of this inconsistency are also discussed.Results of this study provide some hints for choosing suitable advection schemes in the GAMIL model.At least for the polar-region-concentrated atmospheric components and the closely correlated chemical species,the Flux-Form Semi-Lagrangian advection scheme produces more reasonable simulations of the large-scale transport processes without significantly increasing the computational expense.
Simulating magnetised plasma with the versatile advection code
Keppens, R.; Toth, G.; Palma, J. M. L.; Dongarra, J.; Hernandez, V.
1999-01-01
Matter in the universe mainly consists of plasma. The dynamics of plasmas is controlled by magnetic fields. To simulate the evolution of magnetised plasma, we solve the equations of magnetohydrodynamics using the Versatile Advection Code (VAC). To demonstrate the versatility of VAC, we present calcu
Simulating magnetised plasma with the versatile advection code
Keppens, R.; Toth, G.; Palma, J. M. L.; Dongarra, J.; Hernandez, V.
1999-01-01
Matter in the universe mainly consists of plasma. The dynamics of plasmas is controlled by magnetic fields. To simulate the evolution of magnetised plasma, we solve the equations of magnetohydrodynamics using the Versatile Advection Code (VAC). To demonstrate the versatility of VAC, we present
Roedig, C.; Zanotti, O.; Alic, D.
2012-10-01
We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic (GR) hydrodynamics coupled to an optically thick radiation field in two existing GR-(magneto)hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in most astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several simple 1D tests, we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in one spatial dimension, we compute a luminosity versus accretion rate diagram for the set-up of spherical accretion on to a Schwarzschild black hole and find good agreement with previous work which included more radiation processes than we currently have available. Lastly, we revisit the supersonic Bondi-Hoyle-Lyttleton (BHL) accretion in two dimensions where we can now present simulations of realistic temperatures, down to T ˜ 106 K or less. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicability. The main features of radiation hydrodynamics BHL flows manifest as (i) an effective adiabatic index approaching γeff ˜ 4/3; (ii) accretion rates two orders of magnitude lower than without radiation pressure, but still super-Eddington; (iii) luminosity estimates around the Eddington limit, hence with an overall radiative efficiency as small as ηBHL˜10-2; (iv) strong departures from thermal equilibrium in shocked regions; (v) no appearance of the flip-flop instability. We conclude that the current optically thick approximation to the radiation transfer does give physically substantial improvements over the pure hydro also in set-ups departing from equilibrium, and, once accompanied by an optically thin treatment, is likely to provide a fundamental tool for investigating accretion flows in a large variety of
Geographically weighted regression as a generalized Wombling to detect barriers to gene flow.
Diniz-Filho, José Alexandre Felizola; Soares, Thannya Nascimento; de Campos Telles, Mariana Pires
2016-08-01
Barriers to gene flow play an important role in structuring populations, especially in human-modified landscapes, and several methods have been proposed to detect such barriers. However, most applications of these methods require a relative large number of individuals or populations distributed in space, connected by vertices from Delaunay or Gabriel networks. Here we show, using both simulated and empirical data, a new application of geographically weighted regression (GWR) to detect such barriers, modeling the genetic variation as a "local" linear function of geographic coordinates (latitude and longitude). In the GWR, standard regression statistics, such as R(2) and slopes, are estimated for each sampling unit and thus are mapped. Peaks in these local statistics are then expected close to the barriers if genetic discontinuities exist, capturing a higher rate of population differentiation among neighboring populations. Isolation-by-Distance simulations on a longitudinally warped lattice revealed that higher local slopes from GWR coincide with the barrier detected with Monmonier algorithm. Even with a relatively small effect of the barrier, the power of local GWR in detecting the east-west barriers was higher than 95 %. We also analyzed empirical data of genetic differentiation among tree populations of Dipteryx alata and Eugenia dysenterica Brazilian Cerrado. GWR was applied to the principal coordinate of the pairwise FST matrix based on microsatellite loci. In both simulated and empirical data, the GWR results were consistent with discontinuities detected by Monmonier algorithm, as well as with previous explanations for the spatial patterns of genetic differentiation for the two species. Our analyses reveal how this new application of GWR can viewed as a generalized Wombling in a continuous space and be a useful approach to detect barriers and discontinuities to gene flow.
White, Jeffrey A.; Baurle, Robert A.; Fisher, Travis C.; Quinlan, Jesse R.; Black, William S.
2012-01-01
The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation was accomplished through a hybridization of non-dissipative and dissipative discontinuity-capturing advection schemes that reduces numerical dissipation while maintaining the ability to capture shocks. A methodology for constructing hybrid-advection schemes that blends nondissipative fluxes consisting of linear combinations of divergence and product rule forms discretized using 4th-order symmetric operators, with dissipative, 3rd or 4th-order reconstruction based upwind flux schemes was developed and implemented. A series of benchmark problems with increasing spatial and fluid dynamical complexity were utilized to examine the ability of the candidate schemes to resolve and propagate structures typical of turbulent flow, their discontinuity capturing capability and their robustness. A realistic geometry typical of a high-speed propulsion system flowpath was computed using the most promising of the examined schemes and was compared with available experimental data to demonstrate simulation fidelity.
Rossby Wave Instability in the Accretion Flows around Black Holes
Gholipour, Mahmoud
2017-01-01
The roles of the Rossby wave instability (RWI) have been significantly developed in some important processes, such as planet formation and angular momentum transport through thin accretion disks. However, their development on accretion flows with advection is insignificant. In this paper, we investigate the effect of advection in the occurrence of RWI through accretion flows around black holes (BHs). In the absence of advection, the occurrence of RWI is extremely low because of high viscosity in the accretion flows around BHs. The results of this paper show that there is a significant chance for the occurrence of RWI in some wavelengths if we consider advection even in low amounts. Therefore, the RWI can be a suitable candidate for angular momentum transport in the accretion flows around BHs. Also, the results show that the advection parameter and the ratio of heat capacity, which are special characters of advection flows, play important roles in the occurrence of RWI.
Energy Technology Data Exchange (ETDEWEB)
McKinney, Jonathan C.; Tchekhovskoy, Alexander; Blandford, Roger D.
2012-04-26
Black hole (BH) accretion flows and jets are qualitatively affected by the presence of ordered magnetic fields. We study fully three-dimensional global general relativistic magnetohydrodynamic (MHD) simulations of radially extended and thick (height H to cylindrical radius R ratio of |H/R| {approx} 0.2-1) accretion flows around BHs with various dimensionless spins (a/M, with BH mass M) and with initially toroidally-dominated ({phi}-directed) and poloidally-dominated (R-z directed) magnetic fields. Firstly, for toroidal field models and BHs with high enough |a/M|, coherent large-scale (i.e. >> H) dipolar poloidal magnetic flux patches emerge, thread the BH, and generate transient relativistic jets. Secondly, for poloidal field models, poloidal magnetic flux readily accretes through the disk from large radii and builds-up to a natural saturation point near the BH. While models with |H/R| {approx} 1 and |a/M| {le} 0.5 do not launch jets due to quenching by mass infall, for sufficiently high |a/M| or low |H/R| the polar magnetic field compresses the inflow into a geometrically thin highly non-axisymmetric 'magnetically choked accretion flow' (MCAF) within which the standard linear magneto-rotational instability is suppressed. The condition of a highly-magnetized state over most of the horizon is optimal for the Blandford-Znajek mechanism that generates persistent relativistic jets with and 100% efficiency for |a/M| {approx}> 0.9. A magnetic Rayleigh-Taylor and Kelvin-Helmholtz unstable magnetospheric interface forms between the compressed inflow and bulging jet magnetosphere, which drives a new jet-disk oscillation (JDO) type of quasi-periodic oscillation (QPO) mechanism. The high-frequency QPO has spherical harmonic |m| = 1 mode period of {tau} {approx} 70GM/c{sup 3} for a/M {approx} 0.9 with coherence quality factors Q {approx}> 10. Overall, our models are qualitatively distinct from most prior MHD simulations (typically, |H/R| << 1 and poloidal flux is
Gaubert, Stéphane
2012-01-01
We give a formula for the Lipschitz constant in Thompson's part metric of any order-preserving flow on the interior of a (possibly infinite dimensional) closed convex pointed cone. This provides an explicit form of a characterization of Nussbaum concerning non order-preserving flows. As an application of this formula, we show that the flow of the generalized Riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its Lipschitz constant by a matrix inequality. We also show that the same flow is no longer a contraction in other natural Finsler metrics on this cone, including the standard invariant Riemannian metric. This is motivated by a series of contraction properties concerning the standard Riccati equation, established by Bougerol, Liverani, Wojtowski, Lawson, Lee and Lim: we show that some of these properties do, and that some other do not, carry over to the generalized Riccati equation.
Institute of Scientific and Technical Information of China (English)
HUANG Rui Xin
2014-01-01
Gravitational potential energy (GPE) source and sink due to stirring and cabbeling associated with sigma dif-fusion/advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography;the exces-sive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advec-tion diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffu-sion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.
Advective transport observations with MODPATH-OBS--documentation of the MODPATH observation process
Hanson, R.T.; Kauffman, L.K.; Hill, M.C.; Dickinson, J.E.; Mehl, S.W.
2013-01-01
The MODPATH-OBS computer program described in this report is designed to calculate simulated equivalents for observations related to advective groundwater transport that can be represented in a quantitative way by using simulated particle-tracking data. The simulated equivalents supported by MODPATH-OBS are (1) distance from a source location at a defined time, or proximity to an observed location; (2) time of travel from an initial location to defined locations, areas, or volumes of the simulated system; (3) concentrations used to simulate groundwater age; and (4) percentages of water derived from contributing source areas. Although particle tracking only simulates the advective component of conservative transport, effects of non-conservative processes such as retardation can be approximated through manipulation of the effective-porosity value used to calculate velocity based on the properties of selected conservative tracers. This program can also account for simple decay or production, but it cannot account for diffusion. Dispersion can be represented through direct simulation of subsurface heterogeneity and the use of many particles. MODPATH-OBS acts as a postprocessor to MODPATH, so that the sequence of model runs generally required is MODFLOW, MODPATH, and MODPATH-OBS. The version of MODFLOW and MODPATH that support the version of MODPATH-OBS presented in this report are MODFLOW-2005 or MODFLOW-LGR, and MODPATH-LGR. MODFLOW-LGR is derived from MODFLOW-2005, MODPATH 5, and MODPATH 6 and supports local grid refinement. MODPATH-LGR is derived from MODPATH 5. It supports the forward and backward tracking of particles through locally refined grids and provides the output needed for MODPATH_OBS. For a single grid and no observations, MODPATH-LGR results are equivalent to MODPATH 5. MODPATH-LGR and MODPATH-OBS simulations can use nearly all of the capabilities of MODFLOW-2005 and MODFLOW-LGR; for example, simulations may be steady-state, transient, or a combination
Existence and uniqueness of solutions in general multisolute renal flow problems.
Garner, J B; Kellogg, R B
1988-01-01
This paper considers systems of differential equations that describe flows in renal networks. The flow geometry is of the type that occurs in modelling the renal medulla. The unknowns in the system include the flow rate, the hydrostatic pressure, and the concentrations of the various solutes. Existence and uniqueness of solutions of the appropriate boundary value problems are established, in the case of small permeability coefficients and transport rates, or large diffusion coefficients and small resistance to flow constants.
Institute of Scientific and Technical Information of China (English)
Bai Jing-Song; Zhang Zhan-Ji; Li Ping; Zhong Min
2006-01-01
Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional (2D) multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.
Generalized function of the parameters in the storage-discharge relation for low flows
Fujimura, Kazumasa; Iseri, Yoshihiko; Kanae, Shinjiro; Murakami, Masahiro
2015-04-01
The accurate estimation of low flows can contribute to better water resource management and more reliable evaluation of the impact of climate change on water resources. For the case of low flows, the nonlinearity of the discharge Q associated with the storage S was originally proposed by Horton (1936) as the power function Q=KSN, where K is a constant and N is the exponent. Although the Q(S) relations for groundwater runoff from unconfined aquifers have been treated as second-order polynomial functions on the basis of the hydraulic investigation by Ding (1966), the general power function Q = KNSN was introduced into the unit hydrograph model for overland flow and the parameters K and N were calibrated by Ding (2011). According to recent studies, the value of the exponent N is varied between 1 and 3 or higher by calibration (e.g., Wittenberg, 1994 and Ding, 2011); however, it is currently unclear whether the optimum value of N has the rule. Fujimura et al. (2014) applied the general power function Q = KNSN for low flows in mountainous basins over a period spanning more than 10 years using hourly data, and carried out sensitivity analysis using a hydrological model for 19 900 sets of the two parameters K and N, in which the exponent N was varied between 1 and 100 in steps of 0.5. The results showed that the optimum relation between N and K could be characterized by the exponential function K=1/(α Nβ), where α and β are constants. Moreover, the lowest error in the sensitivity analysis was obtained by using an exponent N of 100. The aim of this study is to extend the previous study of Fujimura et al. to clarify the properties of the K(N) relations. A sensitivity analysis is performed efficiently using a hydrological model, in which the exponent N is varied between 1 and 100 000 along the neighborhood of the exponential function K=1/(α Nβ). The hourly hydrological model used in this study comprises the Diskin-Nazimov infiltration model, groundwater recharge and
Generalized adjoint consistent treatment of wall boundary conditions for compressible flows
Hartmann, Ralf; Leicht, Tobias
2015-11-01
In this article, we revisit the adjoint consistency analysis of Discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations with application to the Reynolds-averaged Navier-Stokes and k- ω turbulence equations. Here, particular emphasis is laid on the discretization of wall boundary conditions. While previously only one specific combination of discretizations of wall boundary conditions and of aerodynamic force coefficients has been shown to give an adjoint consistent discretization, in this article we generalize this analysis and provide a discretization of the force coefficients for any consistent discretization of wall boundary conditions. Furthermore, we demonstrate that a related evaluation of the cp- and cf-distributions is required. The freedom gained in choosing the discretization of boundary conditions without loosing adjoint consistency is used to devise a new adjoint consistent discretization including numerical fluxes on the wall boundary which is more robust than the adjoint consistent discretization known up to now. While this work is presented in the framework of Discontinuous Galerkin discretizations, the insight gained is also applicable to (and thus valuable for) other discretization schemes. In particular, the discretization of integral quantities, like the drag, lift and moment coefficients, as well as the discretization of local quantities at the wall like surface pressure and skin friction should follow as closely as possible the discretization of the flow equations and boundary conditions at the wall boundary.
Gooya, Ali; Liao, Hongen; Sakuma, Ichiro
2012-09-01
Geometric flux maximizing flow (FLUX) is an active contour based method which evolves an initial surface to maximize the flux of a vector field on the surface. For blood vessel segmentation, the vector field is defined as the vectors specified by vascular edge strengths and orientations. Hence, the segmentation performance depends on the quality of the detected edge vector field. In this paper, we propose a new method for level set based segmentation of blood vessels by generalizing the FLUX on a Riemannian manifold (R-FLUX). We consider a 3D scalar image I(x) as a manifold embedded in the 4D space (x, I(x)) and compute the image metric by pullback from the 4D space, whose metric tensor depends on the vessel enhancing diffusion (VED) tensor. This allows us to devise a non-linear filter which both projects and normalizes the original image gradient vectors under the inverse of local VED tensors. The filtered gradient vectors pertaining to the vessels are less sensitive to the local image contrast and more coherent with the local vessel orientation. The method has been applied to both synthetic and real TOF MRA data sets. Comparisons are made with the FLUX and vesselsness response based segmentations, indicating that the R-FLUX outperforms both methods in terms of leakage minimization and thiner vessel delineation.
Institute of Scientific and Technical Information of China (English)
TAN Wenchang; XU Mingyu
2004-01-01
The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced. Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus. The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates. In addition, the solutions of the shear stresses at the plates are also determined.
On High-Order Upwind Methods for Advection
Huynh, H. T.
2017-01-01
In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom ?? per cell, in spite of the different piecewise polynomial degrees, share the same
Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence
Schekochihin, A. A.; Parker, J. T.; Highcock, E. G.; Dellar, P. J.; Dorland, W.; Hammett, G. W.
2016-04-01
> A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g. drift-wave turbulence driven by ion temperature gradients) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. It is found that it is possible to construct a consistent theory in which very little free energy leaks into high velocity moments of the distribution function, rendering the turbulent cascade in the energetically relevant part of the wavenumber space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also in contrast with the linear problem, in which it occurs at the finite rate equal to the Landau damping rate). The ability of the free energy to stay in the low velocity moments of the distribution function is facilitated by the `anti-phase-mixing' effect, whose presence in the nonlinear system is due to the stochastic version of the plasma echo (the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wavenumber space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins its competition with nonlinear advection is governed by the `critical balance' between linear and nonlinear time scales (which for high Hermite moments splits into two thresholds, one demarcating the wavenumber region where phase mixing predominates, the other where plasma echo does).
A tracer-based inversion method for diagnosing eddy-induced diffusivity and advection
Bachman, S. D.; Fox-Kemper, B.; Bryan, F. O.
2015-02-01
A diagnosis method is presented which inverts a set of tracer flux statistics into an eddy-induced transport intended to apply for all tracers. The underlying assumption is that a linear flux-gradient relationship describes eddy-induced tracer transport, but a full tensor coefficient is assumed rather than a scalar coefficient which allows for down-gradient and skew transports. Thus, Lagrangian advection and anisotropic diffusion not necessarily aligned with the tracer gradient can be diagnosed. In this method, multiple passive tracers are initialized in an eddy-resolving flow simulation. Their spatially-averaged gradients form a matrix, where the gradient of each tracer is assumed to satisfy an identical flux-gradient relationship. The resulting linear system, which is overdetermined when using more than three tracers, is then solved to obtain an eddy transport tensor R which describes the eddy advection (antisymmetric part of R) and potentially anisotropic diffusion (symmetric part of R) in terms of coarse-grained variables. The mathematical basis for this inversion method is presented here, along with practical guidelines for its implementation. We present recommendations for initialization of the passive tracers, maintaining the required misalignment of the tracer gradients, correcting for nonconservative effects, and quantifying the error in the diagnosed transport tensor. A method is proposed to find unique, tracer-independent, distinct rotational and divergent Lagrangian transport operators, but the results indicate that these operators are not meaningfully relatable to tracer-independent eddy advection or diffusion. With the optimal method of diagnosis, the diagnosed transport tensor is capable of predicting the fluxes of other tracers that are withheld from the diagnosis, including even active tracers such as buoyancy, such that relative errors of 14% or less are found.
Influences of tidal energy advection on the surface energy balance in a mangrove forest
Directory of Open Access Journals (Sweden)
J. G. Barr
2012-08-01
Full Text Available Mangrove forests are ecosystems susceptible to changing water levels and temperatures due to climate change as well as perturbations resulting from tropical storms. Numerical models can be used to project mangrove forest responses to regional and global environmental changes, and the reliability of these models depends on surface energy balance closure. However, for tidal ecosystems, the surface energy balance is complex because the energy transport associated with tidal activity remains poorly understood. This study aimed to quantify impacts of tidal flows on energy dynamics within a mangrove ecosystem. To address the research objective, an intensive study was conducted in a mangrove forest located along the Shark River in the Everglades National Park, FL. Forest-atmosphere energy exchanges were quantified with an eddy covariance system deployed on a flux tower. The lateral energy transport associated with tidal activity was calculated based on a coupled mass and energy balance approach. The mass balance included tidal flows and accumulation of water on the forest floor. The energy balance included temporal changes in enthalpy, resulting from tidal flows and temperature changes in the water column. By serving as a net sink or a source of available energy, tidal flows reduced the impact of high radiational loads on the mangrove forest. Including tidal energy advection in the surface energy balance improved the 30-min daytime energy closure from 73% to 82% over the study period. Also, the cumulative sum of energy output improved from 79% to 91% of energy input during the study period. Results indicated that tidal inundation provides an important mechanism for heat removal and that tidal exchange should be considered in surface energy budgets of coastal ecosystems. Results also demonstrated the importance of including tidal energy advection in mangrove biophysical models that are used for predicting ecosystem response to changing climate and
Features of a rare advection-radiation event
Institute of Scientific and Technical Information of China (English)
PU MeiJuan; ZHANG GuoZheng; YAN WenLian; LI ZiHua
2008-01-01
To investigate effects of atmospheric pollutants on fog nature,a comprehensive in situ observation project was implemented in the northern suburb of Nanjing,in December of 2006. For December 24-27 there occurred a heavy fog lasting 4 d in succession. This event is of rare characteristics,namely long persistence,high concentration,tall fog top,acid fog water and explosive growth. Detailed analysis along with the causes of the fog was presented. The evidence suggests that the fog was generated by nighttime radiative cooling,maintained and developed under effects of warm,wet advection. As a result,it is an advection-radiation fog event.
Lattice Boltzmann method for the fractional advection-diffusion equation.
Zhou, J G; Haygarth, P M; Withers, P J A; Macleod, C J A; Falloon, P D; Beven, K J; Ockenden, M C; Forber, K J; Hollaway, M J; Evans, R; Collins, A L; Hiscock, K M; Wearing, C; Kahana, R; Villamizar Velez, M L
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β, the fractional order α, and the single relaxation time τ, the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
Spectral Theory of Advective Diffusion in the Ocean
2013-09-19
to study this enhancement of sea ice thermal conductivity and better understand temperature data collected during a 2007 Antarctic expedition. 15...conductivity and better understand temperature data collected during a 2007 Antarctic expedition. Activities and Findings: 1. Advection-enhanced...critically on the properties of this Hilbert space. More specifically, it is only on a special subset of this space that the random operator is Hermitian
Lattice Boltzmann method for the fractional advection-diffusion equation
Zhou, J. G.; Haygarth, P. M.; Withers, P. J. A.; Macleod, C. J. A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R.; Collins, A. L.; Hiscock, K. M.; Wearing, C.; Kahana, R.; Villamizar Velez, M. L.
2016-04-01
Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractional advection-diffusion equation (FADE). The FADE finds a wide range of applications in various areas with great potential for studying complex mass transport in real hydrological systems. However, solution to the FADE is difficult, and the existing numerical methods are complicated and inefficient. In this study, a fresh lattice Boltzmann method is developed for solving the fractional advection-diffusion equation (LabFADE). The FADE is transformed into an equation similar to an advection-diffusion equation and solved using the lattice Boltzmann method. The LabFADE has all the advantages of the conventional lattice Boltzmann method and avoids a complex solution procedure, unlike other existing numerical methods. The method has been validated through simulations of several benchmark tests: a point-source diffusion, a boundary-value problem of steady diffusion, and an initial-boundary-value problem of unsteady diffusion with the coexistence of source and sink terms. In addition, by including the effects of the skewness β , the fractional order α , and the single relaxation time τ , the accuracy and convergence of the method have been assessed. The numerical predictions are compared with the analytical solutions, and they indicate that the method is second-order accurate. The method presented will allow the FADE to be more widely applied to complex mass transport problems in science and engineering.
NUMERICAL SIMULATIONS OF SEA ICE WITH DIFFERENT ADVECTION SCHEMES
Institute of Scientific and Technical Information of China (English)
LIU Xi-ying
2011-01-01
Numerical simulations are carried out for sea ice with four different advection schemes to study their effects on the simulation results.The sea ice model employed here is the Sea Ice Simulator (SIS) of the Geophysical Fluid Dynamics Laboratory (GFDL) Modular Ocean Model version 4b (MOM4b) and the four advection schemes are, the upwind scheme originally used in the SIS, the Multi-Dimensional Positive Advection (MDPA) scheme, the Incremental Remapping Scheme (IRS) and the Two Step Shape Preserving (TSSP) scheme.The latter three schemes are newly introduced.To consider the interactions between sea ice and ocean, a mixed layer ocean model is introduced and coupled to the SIS.The coupled model uses a tri-polar coordinate with 120×65 grids,covering the whole earth globe, in the horizontal plane.Simulation results in the northern high latitudes are analyzed.In all simulations, the model reproduces the seasonal variation of sea ice in the northern high latitudes well.Compared with the results from the observation, the sea ice model produces some extra sea ice coverage in the Greenland Sea and Barents Sea in winter due to the exclusion of ocean current effects and the smaller simulated sea ice thickness in the Arctic basin.There are similar features among the results obtained with the introduced three advection schemes.The simulated sea ice thickness with the three newly introduced schemes are all smaller than that of the upwind scheme and the simulated sea ice velocities of movement are all smaller than that of the upwind scheme.There are more similarities shared in the results obtained with the MPDA and TSSP schemes.
A New Generalized Thermal Wind Equation and its Application to Zonal Flows on the Gas Giant Planets
Marcus, Philip; Tollefson, Joshua; de Pater, Imke
2015-11-01
For baroclinic, rapidly-rotating flows, the Thermal Wind Equation (TWE) describes how the flow varies along the rotation axis as a function of temperature gradients. The TWE works well for many laboratory and atmospheric flows on Earth. We show that the TWE also works well for the zonal (west-to-east) flows u on Jupiter. However, our recent observations of Neptune's zonal flows not only do not fit the TWE, but also have the incorrect ``sign.'' When an atmosphere's longitudinally-averaged temperature is warmer at the equator than at the mid-latitudes, the TWE indicates that u increases with height in the atmosphere. The change in u as a function of height on Neptune has the opposite sign. Here, we show that the high-velocities of u on Neptune make the cyclostrophic terms (i.e., some of the nonlinear terms proportional to u2) large, and these terms are dropped in the standard derivation of the TWE. When the cyclostrophic terms are retained, a more generalized TWE is obtained that both qualitatively and quantitatively agrees with the observations of the change in u as a function of height in Neptune's atmosphere. We show that both the standard and generalized TWE for zonal flows can be extended to the equator despite the fact that the Coriolis force vanishes there.
Hoormann, Janie Katherine
2016-06-01
While Albert Einstein's theory of General Relativity (GR) has been tested extensively in our solar system, it is just beginning to be tested in the strong gravitational fields that surround black holes. As a way to study the behavior of gravity in these extreme environments, I have used and added to a ray-tracing code that simulates the X-ray emission from the accretion disks surrounding black holes. In particular, the observational channels which can be simulated include the thermal and reflected spectra, polarization, and reverberation signatures. These calculations can be performed assuming GR as well as four alternative spacetimes. These results can be used to see if it is possible to determine if observations can test the No-Hair theorem of GR which states that stationary, astrophysical black holes are only described by their mass and spin. Although it proves difficult to distinguish between theories of gravity, it is possible to exclude a large portion of the possible deviations from GR using observations of rapidly spinning stellar mass black holes such as Cygnus X-1. The ray-tracing simulations can furthermore be used to study the inner regions of black hole accretion flows. I examined the dependence of X-ray reverberation observations on the ionization of the disk photosphere. My results show that X-ray reverberation and X-ray polarization provides a powerful tool to constrain the geometry of accretion disks which are too small to be imaged directly. The second part of my thesis describes the work on the balloon-borne X-Calibur hard X-ray polarimetry mission and on the space-borne PolSTAR polarimeter concept.
Cerebral Blood Flow during Rest Associates with General Intelligence and Creativity
Takeuchi, Hikaru; Taki, Yasuyuki; Hashizume, Hiroshi; Sassa, Yuko; Nagase, Tomomi; Nouchi, Rui; Kawashima, Ryuta
2011-01-01
Recently, much scientific attention has been focused on resting brain activity and its investigation through such methods as the analysis of functional connectivity during rest (the temporal correlation of brain activities in different regions). However, investigation of the magnitude of brain activity during rest has focused on the relative decrease of brain activity during a task, rather than on the absolute resting brain activity. It is thus necessary to investigate the association between cognitive factors and measures of absolute resting brain activity, such as cerebral blood flow (CBF), during rest (rest-CBF). In this study, we examined this association using multiple regression analyses. Rest-CBF was the dependent variable and the independent variables included two essential components of cognitive functions, psychometric general intelligence and creativity. CBF was measured using arterial spin labeling and there were three analyses for rest-CBF; namely mean gray matter rest-CBF, mean white matter rest-CBF, and regional rest-CBF. The results showed that mean gray and white matter rest-CBF were significantly and positively correlated with individual psychometric intelligence. Furthermore, mean white matter rest-CBF was significantly and positively correlated with creativity. After correcting the effect of mean gray matter rest-CBF the significant and positive correlation between regional rest-CBF in the perisylvian anatomical cluster that includes the left superior temporal gyrus and insula and individual psychometric intelligence was found. Also, regional rest-CBF in the precuneus was significantly and negatively correlated with individual creativity. Significance of these results of regional rest-CBF did not change when the effect of regional gray matter density was corrected. The findings showed mean and regional rest-CBF in healthy young subjects to be correlated with cognitive functions. The findings also suggest that, even in young cognitively intact
Yan, Jian; Yang, Cheng-Zhang; Zhang, Qiang; Liu, Xiao-Ping; Kong, Fan-Zhi; Cao, Cheng-Xi; Jin, Xin-Qiao
2014-12-01
With a given free-flow electrophoresis device, reasonable conditions (electric field strength, carrier buffer conductivity, and flow rate) are crucial for an optimized separation. However, there has been no experimental study on how to choose reasonable general conditions for a free-flow electrophoresis device with a thermoelectric cooler in view of Joule heat generation. Herein, comparative experiments were carried out to propose the selection procedure of general conditions in this study. The experimental results demonstrated that appropriate conditions were (i) electrophoresis separation would be destroyed by bubbles caused by more Joule heating. Additionally, a series of applications under the appropriate conditions were performed with samples of model dyes, proteins (bovine serum albumin, myoglobin, and cytochrome c), and cells (Escherichia coli, Streptococcus thermophilus, and Saccharomyces cerevisiae). The separation results showed that under the appropriate conditions, separation efficiency was obviously better than that in the previous experiments with randomly or empirically selected conditions.
Pérez Guerrero, J. S.; Skaggs, T. H.
2010-08-01
SummaryMathematical models describing contaminant transport in heterogeneous porous media are often formulated as an advection-dispersion transport equation with distance-dependent transport coefficients. In this work, a general analytical solution is presented for the linear, one-dimensional advection-dispersion equation with distance-dependent coefficients. An integrating factor is employed to obtain a transport equation that has a self-adjoint differential operator, and a solution is found using the generalized integral transform technique (GITT). It is demonstrated that an analytical expression for the integrating factor exists for several transport equation formulations of practical importance in groundwater transport modeling. Unlike nearly all solutions available in the literature, the current solution is developed for a finite spatial domain. As an illustration, solutions for the particular case of a linearly increasing dispersivity are developed in detail and results are compared with solutions from the literature. Among other applications, the current analytical solution will be particularly useful for testing or benchmarking numerical transport codes because of the incorporation of a finite spatial domain.
Spielhagen, Robert F.; Bauch, Henning A.; Maudrich, Martin; Not, Christelle; Telesinski, Maciej M.; Werner, Kirstin
2015-04-01
The Arctic Gateway between Greenland and Svalbard is the main passage for the advection of Atlantic Water to the Arctic Ocean. Water temperature and intensity of this advection largely determine the degree of ice coverage which is fed by sea ice export from the north. Supported by a maximum in insolation, the Early Holocene was a period of extraordinarily strong advection and relatively high near-surface water temperatures in the eastern Nordic Seas (cf. Risebrobakken et al., 2011, Paleoceanography v. 26). Here we present a synthesis of radiocarbon-dated records from the northern and western part of this area, reaching from the SW Greenland Sea (73°N) to the Yermak Plateau (81°N) and revealing temporal and spatial differences in the development of the so-called Holocene Thermal Maximum (HTM). In the northern part of this region, the HTM started ca. 11-10.5 ka as indicated by rapidly increasing amounts of subpolar planktic foraminifers in the sediments. In the eastern Fram Strait and on the Yermak Plateau, our records of (sub)millennial scale resolution show that the maximum influx terminated already 2,000 years later (9-8 ka). Most likely, this development went along with a N-S relocation of the sea ice margin. According to the current stratigraphic model for a core with submillennial-scale resolution from Vesterisbanken seamount (73°N) in the Greenland Sea, the timing was different there. Increasing total amounts of planktic foraminifers in the sediment indicate an early (11-10 ka) reduction in sea ice coverage also in this region. However, evidence from subpolar planktic foraminifers for maximum Atlantic Water advection is younger (9-6 ka) than in the north. Apparently, the site in the SW Greenland Sea was affected by Atlantic Water in the Greenland Gyre that decoupled from the northward flowing Norwegian Atlantic Current/Westspitsbergen Current south of the Fram Strait. Thus, in a suite of events, strong Atlantic Water advection first affected the
Comparison of advection and steam fogs: From direct observation over the sea
Heo, Ki-Young; Ha, Kyung-Ja; Mahrt, Larry; Shim, Jae-Seol
2010-11-01
Sea fog occurs frequently over the Yellow Sea in spring and summer, which causes costly or even catastrophic events including property damage, marine accidents, public health and financial losses. Case studies of advection and steam fogs using direct observation over the sea are constructed to better understand their formation, evolution and dissipation. A southerly wind supplies moisture to initiate advection fog events (AFs). Approximately -100 to -200 W m-2 of latent heat flux and -70 W m-2 of sensible heat flux during mature AFs are characterized with stable stratification which maintains dense fog by limiting downward mixing of dryer air. Steam fogs (SFs) develop from flow of cold air over warmer water, but are normally of limited persistence. During the SFs, a northerly wind decreases the air temperature below the sea surface temperature, which increases the relative humidity through evaporation from the warmer ocean. During mature SF, 360 W m-2 of latent heat flux and 150 W m-2 of sensible heat flux are characterized with neutral and unstable atmospheric conditions. The increase in wind speed and wind shear mixes dry air downward to the surface and limits the duration of the SF.
A high order characteristic discontinuous Galerkin scheme for advection on unstructured meshes
Lee, D.; Lowrie, R.; Petersen, M.; Ringler, T.; Hecht, M.
2016-11-01
A new characteristic discontinuous Galerkin (CDG) advection scheme is presented. In contrast to standard discontinuous Galerkin schemes, the test functions themselves follow characteristics in order to ensure conservation and the edges of each element are also traced backwards along characteristics in order to create a swept region, which is integrated in order to determine the mass flux across the edge. Both the accuracy and performance of the scheme are greatly improved by the use of large Courant-Friedrichs-Lewy numbers for a shear flow test case and the scheme is shown to scale sublinearly with the number of tracers being advected, outperforming a standard flux corrected transport scheme for 10 or more tracers with a linear basis. Moreover the CDG scheme may be run to arbitrarily high order spatial accuracy and on unstructured grids, and is shown to give the correct order of error convergence for piecewise linear and quadratic bases on regular quadrilateral and hexahedral planar grids. Using a modal Taylor series basis, the scheme may be made monotone while preserving conservation with the use of a standard slope limiter, although this reduces the formal accuracy of the scheme to first order. The second order scheme is roughly as accurate as the incremental remap scheme with nonlocal gradient reconstruction at half the horizontal resolution. The scheme is being developed for implementation within the Model for Prediction Across Scales (MPAS) Ocean model, an unstructured grid finite volume ocean model.
Ancey, Christophe; Bohorquez, Patricio; Heyman, Joris
2016-04-01
The advection-diffusion equation arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Stochastic models can also be used to derive this equation, with the significant advantage that they provide information on the statistical properties of particle activity. Stochastic models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. We develop an approach based on birth-death Markov processes, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received little attention. We show that particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.
Kommajosyula, Ravikishore; Mazzocco, Thomas; Ambrosini, Walter; Baglietto, Emilio
2016-11-01
Accurate prediction of Bubble Departure and Lift-off Diameters is key for development of closures in two-phase Eulerian CFD simulation of Flow Boiling, owing to its sensitivity in the Heat Flux partitioning approach. Several models ranging from simple correlations to solving complex force balance models have been proposed in literature; however, they rely on data-fitting for specific databases, and have shown to be inapplicable for general flow applications. The aim of this study is to extend the approach by proposing a more consistent and general formulation that accounts for relevant forces acting on the Bubble at the point of Departure and Lift-off. Among the key features of the model, the Bubble Inclination angle is treated as an unknown to be inferred along with the Departure Diameter, and the relative velocity of the bubble sliding on the surface, is modeled to determine the Lift-off Diameter. A novel expression is developed for the bubble growth force in terms of flow quantities, based on extensive data analysis. The model has been validated using 6 different experimental databases with varying flow conditions and 3 fluids. Results show high accuracy of predictions over a broad range, outperforming existing models both in terms of accuracy and generality. CASL - The Consortium for Advanced Simulation of LWRs.
Ginzburg, Irina
2017-01-01
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (kT) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in kT, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is
Numerical Modeling of Deep Mantle Convection: Advection and Diffusion Schemes for Marker Methods
Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard
2013-04-01
Thermal and chemical evolution of Earth's deep mantle can be studied by modeling vigorous convection in a chemically heterogeneous fluid. Numerical modeling of such a system poses several computational challenges. Dominance of heat advection over the diffusive heat transport, and a negligible amount of chemical diffusion results in sharp gradients of thermal and chemical fields. The exponential dependence of the viscosity of mantle materials on temperature also leads to high gradients of the velocity field. The accuracy of many numerical advection schemes degrades quickly with increasing gradient of the solution, while the computational effort, in terms of the scheme complexity and required resolution, grows. Additional numerical challenges arise due to a large range of length-scales characteristic of a thermochemical convection system with highly variable viscosity. To examplify, the thickness of the stem of a rising thermal plume may be a few percent of the mantle thickness. An even thinner filament of an anomalous material that is entrained by that plume may consitute less than a tenth of a percent of the mantle thickness. We have developed a two-dimensional FEM code to model thermochemical convection in a hollow cylinder domain, with a depth- and temperature-dependent viscosity representative of the mantle (Steinberger and Calderwood, 2006). We use marker-in-cell method for advection of chemical and thermal fields. The main advantage of perfoming advection using markers is absence of numerical diffusion during the advection step, as opposed to the more diffusive field-methods. However, in the common implementation of the marker-methods, the solution of the momentum and energy equations takes place on a computational grid, and nodes do not generally coincide with the positions of the markers. Transferring velocity-, temperature-, and chemistry- information between nodes and markers introduces errors inherent to inter- and extrapolation. In the numerical scheme
Directory of Open Access Journals (Sweden)
Khan Ilyas
2015-01-01
Full Text Available The present paper is concerned with the magnetohydrodynamic unsteady rotating flows of generalized Burgers' fluid with a porous medium. The flows are created by the plate oscillations. Modified Darcy's law has been employed to model the governing problem. Closed-form solutions corresponding to cosine and sine oscillations are obtained by the Laplace transform method. The performed calculations disclose that Hartmann number, porosity of the medium, angular frequency, and oscillating frequency have strong influence on the velocity. The graphs are presented for such influence and examined carefully.
National Research Council Canada - National Science Library
Hiltebrand, Luzius B; Krejci, Vladimir; tenHoevel, Marcus E; Banic, Andrej; Sigurdsson, Gisli H
2003-01-01
.... Impairment of the autoregulation of microcirculatory blood flow in the intestinal tract has been suggested to play an important role in the development of multiple organ failure during sepsis and surgery...
ALGEBRAIC GENERALIZATION OF THE CASH FLOW STATEMENT: REFLECTIONS BY MEANS OF AN ALGEBRAIC ALGORITHM
National Research Council Canada - National Science Library
José Roberto Kassai; Antonio Geloneze Neto
2012-01-01
... (about one million dollars as of this writing) to publish a cash flow statement (CFS) as part of their financial statements, making this statement another important source of information for investors...
Cyclic and heteroclinic flows near general static spherically symmetric black holes
Energy Technology Data Exchange (ETDEWEB)
Ahmed, Ayyesha K.; Jamil, Mubasher [National University of Sciences and Technology(NUST), Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan); Azreg-Ainou, Mustapha [Baskent University, Engineering Faculty, Ankara (Turkey); Faizal, Mir [University of Lethbridge, Department of Physics and Astronomy, Alberta (Canada); University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada)
2016-05-15
We investigate the Michel-type accretion onto a static spherically symmetric black hole. Using a Hamiltonian dynamical approach, we show that the standard method employed for tackling the accretion problem has masked some properties of the fluid flow. We determine new analytical solutions that are neither transonic nor supersonic as the fluid approaches the horizon(s); rather, they remain subsonic for all values of the radial coordinate. Moreover, the three-velocity vanishes and the pressure diverges on the horizon(s), resulting in a flow-out of the fluid under the effect of its own pressure. This is in favor of the earlier prediction that pressure-dominant regions form near the horizon. This result does not depend on the form of the metric and it applies to a neighborhood of any horizon where the time coordinate is timelike. For anti-de Sitter-like f(R) black holes we discuss the stability of the critical flow and determine separatrix heteroclinic orbits. For de Sitter-like f(R) black holes, we construct polytropic cyclic, non-homoclinic, physical flows connecting the two horizons. These flows become non-relativistic for Hamiltonian values higher than the critical value, allowing for a good estimate of the proper period of the flow. (orig.)
Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative
Directory of Open Access Journals (Sweden)
José Francisco Gómez Aguilar
2014-01-01
Full Text Available An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as 0<β, γ≤1 for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters σx and σt are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.
Gustavsson, K
2013-01-01
We calculate the Lyapunov exponents describing spatial clustering of particles advected in one- and two-dimensional random velocity fields at finite Kubo number Ku (a dimensionless parameter characterising the correlation time of the velocity field). In one dimension we obtain accurate results up to Ku ~ 1 by resummation of a perturbation expansion in Ku. At large Kubo numbers we compute the Lyapunov exponent by taking into account the fact that the particles follow the minima of the potential function corresponding to the velocity field. In two dimensions we compute the first four non-vanishing terms in the small-Ku expansion of the Lyapunov exponents. For large Kubo numbers we estimate the Lyapunov exponents by assuming that the particles sample stagnation points of the velocity field with det A > 0 and Tr A < 0 where A is the matrix of flow-velocity gradients.
A high-order discontinuous Galerkin method for unsteady advection-diffusion problems
Borker, Raunak; Farhat, Charbel; Tezaur, Radek
2017-03-01
A high-order discontinuous Galerkin method with Lagrange multipliers is presented for the solution of unsteady advection-diffusion problems in the high Péclet number regime. It operates directly on the second-order form of the governing equation and does not require any stabilization. Its spatial basis functions are chosen among the free-space solutions of the homogeneous form of the partial differential equation obtained after time-discretization. It also features Lagrange multipliers for enforcing a weak continuity of the approximated solution across the element interface boundaries. This leads to a system of differential-algebraic equations which are time-integrated by an implicit family of schemes. The numerical stability of these schemes and the well-posedness of the overall discretization method are supported by a theoretical analysis. The performance of this method is demonstrated for various high Péclet number constant-coefficient model flow problems.
Modeling size segregation of granular materials: the roles of segregation, advection and diffusion
Fan, Yi; Umbanhowar, Paul B; Ottino, Julio M; Lueptow, Richard M
2014-01-01
Predicting segregation of granular materials composed of different-sized particles is a challenging problem. In this paper, we develop and implement a theoretical model that captures the interplay between advection, segregation, and diffusion in size bidisperse granular materials. The fluxes associated with these three driving factors depend on the underlying kinematics, whose characteristics play key roles in determining particle segregation configurations. Unlike previous models for segregation, our model uses parameters based on kinematic measures from discrete element method simulations instead of arbitrarily adjustable fitting parameters, and it achieves excellent quantitative agreement with both experimental and simulation results when applied to quasi-two-dimensional bounded heaps. The model yields two dimensionless control parameters, both of which are only functions of physically control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing l...
Yi, Chuixiang; Anderson, Dean E; Turnipseed, Andrew A; Burns, Sean P; Sparks, Jed P; Stannard, David I; Monson, Russell K
2008-09-01
The eddy covariance technique, which is used in the determination of net ecosystem CO2 exchange (NEE), is subject to significant errors when advection that carries CO2 in the mean flow is ignored. We measured horizontal and vertical advective CO2 fluxes at the Niwot Ridge AmeriFlux site (Colorado, USA) using a measurement approach consisting of multiple towers. We observed relatively high rates of both horizontal (F(hadv)) and vertical (F(vadv)) advective fluxes at low surface friction velocities (u(*)) which were associated with downslope katabatic flows. We observed that F(hadv) was confined to a relatively thin layer (0-6 m thick) of subcanopy air that flowed beneath the eddy covariance sensors principally at night, carrying with it respired CO2 from the soil and lower parts of the canopy. The observed F(vadv) came from above the canopy and was presumably due to the convergence of drainage flows at the tower site. The magnitudes of both F(hadv) and F(vadv) were similar, of opposite sign, and increased with decreasing u(*), meaning that they most affected estimates of the total CO2 flux on calm nights with low wind speeds. The mathematical sign, temporal variation and dependence on u(*) of both F(hadv) and F(vadv) were determined by the unique terrain of the Niwot Ridge site. Therefore, the patterns we observed may not be broadly applicable to other sites. We evaluated the influence of advection on the cumulative annual and monthly estimates of the total CO2 flux (F(c)), which is often used as an estimate of NEE, over six years using the dependence of F(hadv) and F(vadv) on u(*). When the sum of F(hadv) and F(vadv) was used to correct monthly F(c), we observed values that were different from the monthly F(c) calculated using the traditional u(*)-filter correction by--16 to 20 g C x m(-2) x mo(-1); the mean percentage difference in monthly Fc for these two methods over the six-year period was 10%. When the sum of F(hadv) and F(vadv) was used to correct annual Fc
Advection and diffusion in random media implications for sea surface temperature anomalies
Piterbarg, Leonid I
1997-01-01
The book presents the foundations of the theory of turbulent transport within the context of stochastic partial differential equations. It serves to establish a firm connection between rigorous and non-rigorous results concerning turbulent diffusion. Mathematically all of the issues addressed in this book are concentrated around a single linear equation: stochastic advection-diffusion (transport) equation. There is no attempt made to derive universal statistics for turbulent flow. Instead emphasis is placed on a statistical description of a passive scalar (tracer) under given velocity statistics. An application concerning transport of sea surface temperature anomalies reconciles the developed theory and a highly practical issue of modern physical oceanography by using the newly designed inversion techniques which take advantage of powerful maximum likelihood and autoregressive estimators. Audience: Graduate students and researchers in mathematics, fluid dynamics, and physical oceanography.
Linear stability of plane Poiseuille flow over a generalized Stokes layer
Energy Technology Data Exchange (ETDEWEB)
Quadrio, Maurizio [Dip. Ing. Aerospaziale, Politecnico di Milano, Campus Bovisa, I-20156 Milano (Italy); Martinelli, Fulvio; Schmid, Peter J, E-mail: maurizio.quadrio@polimi.it [Laboratoire d' Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique, F-91128 Palaiseau (France)
2011-12-22
Linear stability of plane Poiseuille flow subject to spanwise velocity forcing applied at the wall is studied. The forcing is stationary and sinusoidally distributed along the streamwise direction. The long-term aim of the study is to explore a possible relationship between the modification induced by the wall forcing to the stability characteristic of the unforced Poiseuille flow and the signifcant capabilities demonstrated by the same forcing in reducing turbulent friction drag. We present in this paper the statement of the mathematical problem, which is considerably more complex that the classic Orr-Sommerfeld-Squire approach, owing to the streamwise-varying boundary condition. We also report some preliminary results which, although not yet conclusive, describe the effects of the wall forcing on modal and non-modal characteristics of the flow stability.
Kang, Jianhong; Xu, Mingyu
2009-04-01
The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
Institute of Scientific and Technical Information of China (English)
Jianhong Kang; Mingyu Xu
2009-01-01
The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
Geophysical flows under location uncertainty, Part I Random transport and general models
Resseguier, Valentin; Chapron, Bertrand
2016-01-01
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time. Subsequently, the material derivative is modified and leads to a stochastic version of the material derivative to include a drift correction, an inhomogeneous and anisotropic diffusion, and a multiplicative noise. As derived, this stochastic transport exhibits a remarkable energy conservation property for any realizations. As demonstrated, this pivotal operator further provides elegant means to derive stochastic formulations of classical representations of geophysical flow dynamics.
Analysis of general second-order fluid flow in double cylinder rheometer
Institute of Scientific and Technical Information of China (English)
黄军旗; 何光渝; 刘慈群
1997-01-01
The fractional calculus approach in the constitutive relationship model of second-order fluid is introduced and the flow characteristics of the viscoelastic fluid in double cylinder rheometer are studied. First, the analytical solution of which the derivative order is 1/2 is derived with the analytical solution and the reliability of Laplace numerical inversion based on Crump algorithm for the problem is verified, then the characteristics of second-order fluid flow in the rheometer by using Crump method is analyzed. The results indicate that the more obvious the viscoelastic properties of fluid are, the more sensitive the dependence of velocity and stress on fractional derivative order is.
Directory of Open Access Journals (Sweden)
Baoyan Li
2003-09-01
Full Text Available We study the hp version of three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE methods for the numerical solution of advection-diffusion problems. These methods are based on a space-time mixed formulation of the advection-diffusion problems. In space, they use discontinuous finite elements, and in time they approximately follow the Lagrangian flow paths (i.e., the hyperbolic part of the problems. Boundary conditions are incorporated in a natural and mass conservative manner. In fact, these methods are locally conservative. The analysis of this paper focuses on advection-diffusion problems in one space dimension. Error estimates are explicitly obtained in the grid size h, the polynomial degree p, and the solution regularity; arbitrary space grids and polynomial degree are allowed. These estimates are asymptotically optimal in both h and p for some of these methods. Numerical results to show convergence rates in h and p of the Eulerian-Lagrangian MDFE methods are presented. They are in a good agreement with the theory.
Lubrication of textured surfaces: a general theory for flow and shear stress factors.
Scaraggi, Michele
2012-08-01
We report on a mean field theory of textured surface lubrication. We study the fluid flow dynamics occurring at the interface as a function of the texture characteristics, e.g. texture area density, shape and distribution of microstructures, and local slip lengths. The present results may be very important for the investigation of tailored microtextured surfaces for low-friction hydrodynamic applications.
Zero area singularities in general relativity and inverse mean curvature flow
Robbins, Nicholas P
2010-01-01
First we restate the definition of a Zero Area Singularity, recently introduced by H. Bray. We then consider several definitions of mass for these singularities. We use the Inverse Mean Curvature Flow to prove some new results about the mass of a singularity, the ADM mass of the manifold, and the capacity of the singularity.
Horizontal advection, diffusion and plankton spectra at the sea surface.
Bracco, A.; Clayton, S.; Pasquero, C.
2009-04-01
Plankton patchiness is ubiquitous in the oceans, and various physical and biological processes have been proposed as its generating mechanisms. However, a coherent statement on the problem is missing, due to both a small number of suitable observations and to an incomplete understanding of the properties of reactive tracers in turbulent media. Abraham (1998) suggested that horizontal advection may be the dominant process behind the observed distributions of phytoplankton and zooplankton, acting to mix tracers with longer reaction times (Rt) down to smaller scales. Conversely, Mahadevan and Campbell (2002) attributed the relative distributions of sea surface temperature and phytoplankton to small scale upwelling, where tracers with longer Rt are able to homogenize more than those with shorter reaction times. Neither of the above mechanisms can explain simultaneously the (relative) spectral slopes of temperature, phytoplankton and zooplankton. Here, with a simple advection model and a large suite of numerical experiments, we concentrate on some of the physical processes influencing the relative distributions of tracers at the ocean surface, and we investigate: 1) the impact of the spatial scale of tracer supply; 2) the role played by coherent eddies on the distribution of tracers with different Rt; 3) the role of diffusion (so far neglected). We show that diffusion determines the distribution of temperature, regardless of the nature of the forcing. We also find that coherent structures together with differential diffusion of tracers with different Rt impact the tracer distributions. This may help in understanding the highly variable nature of observed plankton spectra.
Neutrino-driven convection versus advection in core collapse supernovae
Foglizzo, T; Janka, H T
2005-01-01
A toy model is analyzed in order to evaluate the linear stability of the gain region immediately behind a stalled accretion shock, after core bounce. This model demonstrates that a negative entropy gradient is not sufficient to warrant linear instability. The stability criterion is governed by the ratio "chi" of the advection time through the gain region divided by the local timescale of buoyancy. The gain region is linearly stable if chi>3. For chi>3, perturbations are unstable in a limited range of horizontal wavelengths centered around twice the vertical size H of the gain region. The threshold horizontal wavenumbers k_{min} and k_{max} follow simple scaling laws such that Hk_{min}\\propto 1/chi and Hk_{max}\\propto chi. These scaling laws are understood as the consequence of a vortical-acoustic cycle within the gain region, fed by the Rayleigh-Taylor growth of vorticity perturbations during advection. The stability of short wavelength perturbations is compared to the "ablative stabilization" of accelerated ...
The interaction of tidal advection, diffusion and mussel filtration in a tidal channel
Simpson, John H.; Berx, Barbara; Gascoigne, Joanna; Saurel, Camille
2007-12-01
Time series measurements of flow and pigment concentrations (Chl) in the Menai Strait have revealed that the strong residual flow in a tidal channel (˜ 500 m 3 s - 1 ) transports phytoplankton from the open sea into the channel where much of it is consumed by suspension feeders, mainly in commercial beds of Mytilus edulis. The progressive depletion of phytoplankton along the channel results in a strong horizontal gradient of plankton and hence Chl. Tidal displacement of this gradient causes large (± 50% of mean) oscillations of Chl in the vicinity of the mussel beds. Vertical mixing by the strong tidal flows is sufficiently vigorous for most of the tidal cycle to ensure that downward diffusion can resupply the near-bed layer although there are indications of some transient depletion around slack water. This paradigm of the interaction of advection, diffusion and filtration determining the distribution of plankton and its supply to mussels has been encapsulated in a series of simple models forced only by boundary values. In the first, a 1-D model of tidal flow in the channel reproduces the principal features of the observed currents including the unusually large spatial change in phase of the currents and the variation of the residual transport with tidal range. The flow field from this physical model is used to drive a second model based on the advection diffusion equation for Chl with a source at the Irish Sea boundary and a sink over the mussel bed. This model illustrates the formation of a strong Chl gradient along the channel and simulates the amplitude and phase of the M 2 oscillations of Chl and the development of the M 4 variation apparent in the observations. This second model has been extended to 2-D over the mussel beds to allow investigation of the effects of water column mixing. The model indicates that only for a short period (˜ 30 min), close to slack water, is mixing sufficiently reduced to permit the development of a depletion boundary layer and
MPDATA: A positive definite solver for geophysical flows
Energy Technology Data Exchange (ETDEWEB)
Smolarkiewicz, P.K.; Margolin, L.G. [Los Alamos National Lab., NM (United States)
1997-12-31
This paper is a review of MPDATA, a class of methods for the numerical simulation of advection based on the sign-preserving properties of upstream differencing. MPDATA was designed originally as an inexpensive alternative to flux-limited schemes for evaluating the transport of nonnegative thermodynamic variables (such as liquid water or water vapor) in atmospheric models. During the last decade, MPDATA has evolved from a simple advection scheme to a general approach for integrating the conservation laws of geophysical fluids on micro-to-planetary scales. The purpose of this paper is to summarize the basic concepts leading to a family of MPDATA schemes, review the existing MPDATA options, as well as to demonstrate the efficacy of the approach using diverse examples of complex geophysical flows.
Two-dimensional circulation and mixing in the far field of a surface-advected river plume
Mazzini, Piero L. F.; Chant, Robert J.
2016-06-01
Field observations of the Hudson River plume are presented to discuss circulation and mixing in the far field of this coastally trapped buoyant flow. The plume was surface advected and propagated downshelf near the internal wave speed. The plume outflow was characterized by a two-layer bulge-like feature but became continuously stratified and vertically sheared in the far field, where Richardson numbers are generally below 0.5. High-frequency velocity and backscatter data from a moored ADCP revealed strong vertical and horizontal oscillatory motions at the front with a wavelength approximately 7-8 times the plume thickness, consistent with Kelvin-Helmholtz instabilities. These motions quickly died out after 2-3 cycles. The combination of vertical shear and stratification in the plume leads to a buoyancy flux toward the nose of the plume, which competes with mixing. However, the continued salinity increase of the plume as it propagated downshelf indicates that mixing overcomes this delivery of freshwater to the plume front. A simple 2-D model is developed, which relates the time rate-of-change of the plume salinity to: (1) salt entrainment due to vertical mixing, and (2) freshwater flux and salt removal due to the vertical shear of the stratified plume. Estimates of an entrainment coefficient from this model are consistent with previous estimates from the near field of a river outflow. A scaling of the plume width is obtained by assuming that vertical shears are controlled by both thermal wind and a critical Richardson number. This scaling yields plume widths that are consistent with previous laboratory studies.
Pawaskar, Sainath Shrikant; Fisher, John; Jin, Zhongmin
2010-03-01
Contact detection in cartilage contact mechanics is an important feature of any analytical or computational modeling investigation when the biphasic nature of cartilage and the corresponding tribology are taken into account. The fluid flow boundary conditions will change based on whether the surface is in contact or not, which will affect the interstitial fluid pressurization. This in turn will increase or decrease the load sustained by the fluid phase, with a direct effect on friction, wear, and lubrication. In laboratory experiments or clinical hemiarthroplasty, when a rigid indenter or metallic prosthesis is used to apply load to the cartilage, there will not be any fluid flow normal to the surface in the contact region due to the impermeable nature of the indenter/prosthesis. In the natural joint, on the other hand, where two cartilage surfaces interact, flow will depend on the pressure difference across the interface. Furthermore, in both these cases, the fluid would flow freely in non-contacting regions. However, it should be pointed out that the contact area is generally unknown in advance in both cases and can only be determined as part of the solution. In the present finite element study, a general and robust algorithm was proposed to decide nodes in contact on the cartilage surface and, accordingly, impose the fluid flow boundary conditions. The algorithm was first tested for a rigid indenter against cartilage model. The algorithm worked well for two-dimensional four-noded and eight-noded axisymmetric element models as well as three-dimensional models. It was then extended to include two cartilages in contact. The results were in excellent agreement with the previous studies reported in the literature.
General Relativistic Hydrodynamic Simulation of Accretion Flow from a Stellar Tidal Disruption
Shiokawa, Hotaka; Cheng, Roseanne M; Piran, Tsvi; Noble, Scott C
2015-01-01
We study how the matter dispersed when a supermassive black hole tidally disrupts a star joins an accretion flow. Combining a relativistic hydrodynamic simulation of the stellar disruption with a relativistic hydrodynamics simulation of the tidal debris motion, we track such a system until ~80% of the stellar mass bound to the black hole has settled into an accretion flow. Shocks near the stellar pericenter and also near the apocenter of the most tightly-bound debris dissipate orbital energy, but only enough to make the characteristic radius comparable to the semi-major axis of the most-bound material, not the tidal radius as previously thought. The outer shocks are caused by post-Newtonian effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is non-monotonic and slow, requiring ~3--10x the orbital period of the most tightly-bound tidal streams, while the inflow time for most of the mass may be comparable to or longer than the mass accu...
General Reynolds Analogy for Blunt-nosed Bodies in Hypersonic Flows
Chen, Xing-Xing; Yu, Yong-Liang
2015-01-01
In this paper, the relation between skin friction and heat transfer along windward sides of blunt-nosed bodies in hypersonic flows is investigated. The self-similar boundary layer analysis is accepted to figure out the distribution of the ratio of skin friction to heat transfer coefficients along the wall. It is theoretically obtained that the ratio depends linearly on the local slope angle of the wall surface, and an explicit analogy expression is presented for circular cylinders, although the linear distribution is also found for other nose shapes and even in gas flows with chemical reactions. Furthermore, based on the theoretical modelling of the second order shear and heat transfer terms in Burnett equations, a modified analogy is derived in the near continuum regime by considering the rarefied gas effects. And a bridge function is also constructed to describe the nonlinear analogy in the transition flow regime. At last, the direct simulation Monte Carlo method is used to validate the theoretical results....
Eigenmode analysis of advective-diffusive transport in micromixers by the diffusive mapping method
Anderson, Patrick; Speetjens, Michel; Gorodetskyi, Oleksandr; Giona, Max; Mixing Collaboration
2013-11-01
Advective-diffusive transport in microflows is studied by means of the diffusive map- ping method, a recent extension of the mapping method by Gorodetskyi et al. (Phys. Fluids 24, 2012) that includes molecular diffusion. This greatly expands the application area of the mapping technique and makes the powerful concepts of eigenmode decompo- sition and spectral analysis of scalar transport accessible to an important class of flows: inline micromixers with diffusion. The staggered herringbone micro-mixer is adopted as a prototypical three-dimensional micro mixer. Simulations with the diffusive mapping method are in close agreement with experimental observations in literature and expose a strong impact of diffusion on the transport. Diffusion enables crossing of Lagrangian trans- port barriers and thus smoothens concentration gradients and accelerates homogenization. Spectral analysis of the mapping matrix reveals this already occurs on a modal level in that individual eigenmodes progressively smoothen and spread out across transport bar- riers with stronger diffusion. Concurrently, the corresponding eigenvalues diminish and thus fundamentally alter the mixing process by invariably causing homogenization, irre- spective of the Lagrangian flow structure. This happens faster and exhibits an earlier emergence of the dominant eigenmode the stronger the diffusion. Lagrangian structures may still affect the spectral properties in that flows comprising both islands and chaotic seas typically result in a richer set of eigenmodes compared to cases with global chaos.
Advection from the North Atlantic as the Forcing of Winter Greenhouse Effect Over Europe
Otterman, J.; Angell, J.; Atlas, R.; Bungato, D.; Shubert, S.; Starr, David OC.; Susskind, J.; Wu, M.-L. C.
2002-01-01
In winter, large interannual fluctuations in the surface temperature are observed over central Europe. Comparing warm February 1990 with cold February 1996, a satellite-retrieved surface (skin) temperature difference of 9.8 K is observed for the region 50-60 degrees N; 5-35 degrees E. Previous studies show that advection from the North Atlantic constitutes the forcing to such fluctuations. The advection is quantified by Index I(sub na), the average of the ocean-surface wind speed over the eastern North Atlantic when the direction is from the southwest (when the wind is from another direction, it counts as a zero speed to the average). Average I(sub na) for February 1990 was 10.6 m/s, but for February 1996 I(sub na) was only 2.4 m/s. A large value of I(sub na) means a strong southwesterly flow which brings warm and moist air into central Europe at low level, producing a steeper tropospheric lapse rate. Strong ascending motions at 700 mb are observed in association with the occurrence of enhanced warm, moist advection from the ocean in February 1990 producing clouds and precipitation. Total precipitable water and cloud-cover fraction have larger values in February 1990 than in 1996. The difference in the greenhouse effect between these two scenarios, this reduction in heat loss to space, can be translated into a virtual radiative heating of 2.6 W/square m above the February 1990 surface/atmosphere system, which contributes to a warming of the surface on the order of 2.6 K. Accepting this estimate as quantitatively meaningful, we evaluate the direct effect, the rise in the surface temperature in Europe as a result of maritime-air inflow, as 7.2 K (9.8 K-2.6 K). Thus, fractional reinforcement by the greenhouse effect is 2.6/7.2, or 36%, a substantial positive feedback.
Preconditioned time-difference methods for advection-diffusion-reaction equations
Energy Technology Data Exchange (ETDEWEB)
Aro, C.; Rodrigue, G. [Lawrence Livermore National Lab., CA (United States); Wolitzer, D. [California State Univ., Hayward, CA (United States)
1994-12-31
Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions placed on stepsize due to stability. Stability bounds for explicit time differencing methods on advection-diffusion-reaction problems are generally quite severe and implicit methods are used instead. The linear systems arising from these implicit methods are large and sparse so that iterative methods must be used to solve them. In this paper the authors develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods.
Fluid-particle dynamics for passive tracers advected by a thermally fluctuating viscoelastic medium
Hohenegger, Christel; McKinley, Scott A.
2017-07-01
Many biological fluids, like mucus and cytoplasm, have prominent viscoelastic properties. As a consequence, immersed particles exhibit subdiffusive behavior, which is to say, the variance of the particle displacement grows sublinearly with time. In this work, we propose a viscoelastic generalization of the Landau-Lifschitz Navier-Stokes fluid model and investigate the properties of particles that are passively advected by such a medium. We exploit certain exact formulations that arise from the Gaussian nature of the fluid model and introduce analysis of memory in the fluid statistics, marking an important step toward capturing fluctuating hydrodynamics among subdiffusive particles. The proposed method is spectral, meshless and is based on the numerical evaluation of the covariance matrix associated with individual fluid modes. With this method, we probe a central hypothesis of passive microrheology, a field premised on the idea that the statistics of particle trajectories can reveal fundamental information about their surrounding fluid environment.
Bieliński, Henryk
2016-09-01
The current paper presents the experimental validation of the generalized model of the two-phase thermosyphon loop. The generalized model is based on mass, momentum, and energy balances in the evaporators, rising tube, condensers and the falling tube. The theoretical analysis and the experimental data have been obtained for a new designed variant. The variant refers to a thermosyphon loop with both minichannels and conventional tubes. The thermosyphon loop consists of an evaporator on the lower vertical section and a condenser on the upper vertical section. The one-dimensional homogeneous and separated two-phase flow models were used in calculations. The latest minichannel heat transfer correlations available in literature were applied. A numerical analysis of the volumetric flow rate in the steady-state has been done. The experiment was conducted on a specially designed test apparatus. Ultrapure water was used as a working fluid. The results show that the theoretical predictions are in good agreement with the measured volumetric flow rate at steady-state.
Liu, G.; Knobbe, S.; Butler, J. J., Jr.
2015-12-01
Direct measurement of groundwater flux is difficult to obtain in the field so hydrogeologists often use easily-detectable environmental tracers, such as heat or chemicals, as an indirect way to characterize flux. Previously, we developed a groundwater flux characterization (GFC) probe by using distributed temperature sensing (DTS) to monitor the temperature responses to active heating in a well. The temperature responses were consistent with the hydraulic conductivity profiles determined at the same location, and provided high-resolution information (approx. 1.5 cm) about vertical variations in horizontal flux through the screen. One of the key assumptions in the previous GFC approach was that the vertical variations in the thermal conductivity of the aquifer materials near the well are negligible, so that the temperature differences with depth are primarily a result of groundwater flux instead of thermal conduction. Although this assumption is likely valid for wells constructed with an artificial filter pack, it might become questionable for wells with natural filter packs (such as the wells constructed by direct push where the sediments are allowed to directly collapse onto the well screen). In this work, we develop a new procedure for separating advection from thermal conduction during GFC measurement. In addition to the normal open-screen GFC profiling, an impermeable sleeve was used so that heating tests could be performed without advective flow entering the well. The heating tests under sleeved conditions were primarily controlled by the thermal conduction around the well, and therefore could be used to remove the impact of thermal conduction from the normal GFC results obtained under open-screen conditions. This new procedure was tested in a laboratory sandbox, where a series of open-screen and sleeved GFC tests were performed under different flow rates. Results indicated that for the tested range of rates (Darcy velocity 0 - 0.78 m/d), the relation between
Tomography-based monitoring of isothermal snow metamorphism under advective conditions
P. P. Ebner; M. Schneebeli; A. Steinfeld
2015-01-01
Time-lapse X-ray micro-tomography was used to investigate the structural dynamics of isothermal snow metamorphism exposed to an advective airflow. Diffusion and advection across the snow pores were analysed in controlled laboratory experiments. The 3-D digital geometry obtained by tomographic scans was used in direct pore-level numerical simulations to determine the effective transport properties. The results showed that isothermal advection with saturated air have no influence...
von Kameke, A.; Huhn, F.; Muñuzuri, A. P.; Pérez-Muñuzuri, V.
2013-02-01
In the absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present that can be parametrized in terms of effective or turbulent diffusion D*, these patterns should be attainable on a much greater, boosted length scale. However, so far, experimental evidence of these boosted patterns in a turbulent flow was lacking. Here, we report the first experimental observation of boosted target and spiral patterns in an excitable chemical reaction in a quasi-two-dimensional turbulent flow. The wave patterns observed are ˜50 times larger than in the case of molecular diffusion only. We vary the turbulent diffusion coefficient D* of the flow and find that the fundamental Fisher-Kolmogorov-Petrovsky-Piskunov equation, vf∝D*, for the asymptotic speed of a reactive wave remains valid. However, not all measures of the boosted wave scale with D* as expected from molecular diffusion, since the wave fronts turn out to be highly filamentous.
Generalizing J2 flow theory: Fundamental issues in strain gradient plasticity
Institute of Scientific and Technical Information of China (English)
John W. Hutchinson
2012-01-01
It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale.Two classes of basic extensions of classical J2 theory have been proposed:one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhaus and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class,and,as formulated,these do not always satisfy thermodynamic requirements on plastic dissipation.On the other hand,theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes.The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J2 flow theory of plasticity to include a dependence on gradients of plastic strain.A modification of the Fleck-Hutchinson formulation that ensures its thermo dynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher order stresses are expressed in terms of the plastic strain rate.Both versions are constructed to reduce to the classical J2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.
Institute of Scientific and Technical Information of China (English)
HUANG; Guanhua; HUANG; Quanzhong; ZHAN; Hongbin
2005-01-01
The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.
Gillibrand, P. A.; Herzfeld, M.
2016-05-01
We present a flux-form semi-Lagrangian (FFSL) advection scheme designed for offline scalar transport simulation with coastal ocean models using curvilinear horizontal coordinates. The scheme conserves mass, overcoming problems of mass conservation typically experienced with offline transport models, and permits long time steps (relative to the Courant number) to be used by the offline model. These attributes make the method attractive for offline simulation of tracers in biogeochemical or sediment transport models using archived flow fields from hydrodynamic models. We describe the FFSL scheme, and test it on two idealised domains and one real domain, the Great Barrier Reef in Australia. For comparison, we also include simulations using a traditional semi-Lagrangian advection scheme for the offline simulations. We compare tracer distributions predicted by the offline FFSL transport scheme with those predicted by the original hydrodynamic model, assess the conservation of mass in all cases and contrast the computational efficiency of the schemes. We find that the FFSL scheme produced very good agreement with the distributions of tracer predicted by the hydrodynamic model, and conserved mass with an error of a fraction of one percent. In terms of computational speed, the FFSL scheme was comparable with the semi-Lagrangian method and an order of magnitude faster than the full hydrodynamic model, even when the latter ran in parallel on multiple cores. The FFSL scheme presented here therefore offers a viable mass-conserving and computationally-efficient alternative to traditional semi-Lagrangian schemes for offline scalar transport simulation in coastal models.
Sochi, Taha
2015-01-01
We investigate the possibility that the spatial dependency of stress in generalized Newtonian flow systems is a function of the applied pressure field and the conduit geometry but not of the fluid rheology. This possibility is well established for the case of a one-dimensional flow through simply connected regions, specifically tubes of circular uniform cross sections and plane thin slits. If it can also be established for the more general case of generalized Newtonian flow through non-circular or multiply connected geometries, such as the two-dimensional flow through conduits of rectangular or elliptical cross sections or the flow through annular circular pipes, then analytical or semi-analytical or highly accurate numerical solutions; regarding stress, rate of strain, velocity profile and volumetric flow rate; for these geometries can be obtained from the stress function, which can be easily obtained from the Newtonian case, in combination with the constitutive rheological relation for the particular non-Ne...
A high-order splitting scheme for the advection-diffusion equation of pollutants
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A high-order splitting scheme for the advection-diffusion equation of pollutants is proposed in this paper. The multidimensional advection-diffusion equation is splitted into several one-dimensional equations that are solved by the scheme. Only three spatial grid points are needed in each direction and the scheme has fourth-order spatial accuracy. Several typically pure advection and advection-diffusion problems are simulated. Numerical results show that the accuracy of the scheme is much higher than that of the classical schemes and the scheme can be efficiently solved with little programming effort.
Generalized moist potential vorticity and its application in the analysis of atmospheric flows
Institute of Scientific and Technical Information of China (English)
Linus A.Mofor; Chungu Lu
2009-01-01
Potential vorticity(PV)serves as an important dynamic tracer for large-scale motions in the atmosphere and oceans.Significant pro-gress has been made on the understanding and application of PV since the work of Hoskins et al,who introduced an"IPV thinking"of a dynamical system in a purely dry atmosphere.In particular,there has been a substantial amount of work done on the PV in a general moist atmosphere.In this paper,the generalized moist potential vorticity(GMPV)and its application in the mesoscale meteorological fields are reviewed.The GMPV is derived for a real atmosphere(neither completely dry nor saturated)by introducing a generalized potential temperature instead of the potential temperature or equivalent potential temperature.Such a generalization can depict the moist effect on PV anomaly in the non-uniformly saturated atmosphere.The effect of mass forcing induced by rainfall on the anomaly of GMPV is also reviewed and a new dynamic variable,the convective vorticity vector(CVV),is introduced in connection with GMPV.2008 National Natural Science Foundation of China and Chinese Academy of Sciences.Published by Elsevier Limited and Science in China Press.All rights reserved.
Lagrangian viscoelastic flow computations using a generalized molecular stress function model
DEFF Research Database (Denmark)
Rasmussen, Henrik K.
2002-01-01
–Sawyers fluid to a fluid described by a generalized molecular stress function (MSF) model allowing the use of dissipative convective constraint release in the constitutive equation. The convergence of the method is demonstrated on the axis-symmetric problem of the inflation of a polymeric membrane only...
General Observations of the Time-Dependent Flow Field Around Flat Plates in Free Fall
DEFF Research Database (Denmark)
Hærvig, Jakob; Jensen, Anna Lyhne; Pedersen, Marie Cecilie
2015-01-01
The free fall trajectories of flat plates are investigated in order to improve understanding of the forces acting on falling blunt objects. The long term goal is to develop a general applicable model to predict free fall trajectories. Numerically the free fall of a flat plate is investigated usin...
Energy Technology Data Exchange (ETDEWEB)
Lister, D. [University of New Brunswick, Fredericton, NB (Canada). Dept. of Chemical Engineering; Lang, L.C. [Atomic Energy of Canada Ltd., Chalk River Lab., ON (Canada)
2002-07-01
Flow-assisted corrosion (FAC) of carbon steel in high-temperature lithiated water can be described with a model that invokes dissolution of the protective oxide film and erosion of oxide particles that are loosened as a result. General corrosion under coolant conditions where oxide is not dissolved is described as well. In the model, the electrochemistry of magnetite dissolution and precipitation and the effect of particle size on solubility move the dependence on film thickness of the diffusion processes (and therefore the corrosion rate) away from reciprocal. Particle erosion under dissolving conditions is treated stochastically and depends upon the fluid shear stress at the surface. The corrosion rate dependence on coolant flow under FAC conditions then becomes somewhat less than that arising purely from fluid shear (proportional to the velocity squared). Under non-dissolving conditions, particle erosion occurs infrequently and general corrosion is almost unaffected by flow For application to a CANDU primary circuit and its feeders, the model was bench-marked against the outlet feeder S08 removed from the Point Lepreau reactor, which furnished one value of film thickness and one of corrosion rate for a computed average coolant velocity. Several constants and parameters in the model had to be assumed or were optimised, since values for them were not available. These uncertainties are no doubt responsible for the rather high values of potential that evolved as steps in the computation. The model predicts film thickness development and corrosion rate for the whole range of coolant velocities in outlet feeders very well. In particular, the detailed modelling of FAC in the complex geometry of one outlet feeder (F11) is in good agreement with measurements. When the particle erosion computations are inserted in the balance equations for the circuit, realistic values of crud level are obtained. The model also predicts low corrosion rates and thick oxide films for inlet
DEFF Research Database (Denmark)
Rolle, Massimo
2015-01-01
Diffusion and compound-specific mixing significantly affect conservative and reactive transport in groundwater. The variability of diffusion coefficients for different solutes has a relevant impact on their displacement at different scales, not only under diffusion-dominated regimes but also under...... advection-dominated flow through conditions. When the solutes are charged species, besides the magnitude of their aqueous diffusion coefficients also their electrostatic interactions play a significant role in the displacement of the different species. Under flow-through conditions this leads...... to multicomponent ionic dispersion: the dispersive fluxes of the different ions are cross-coupled due to the effects of Coulombic interactions. Such effects are illustrated in flow-through experiments in saturated porous media. Simple strong electrolytes were selected as tracers and their transport was studied...
DEFF Research Database (Denmark)
Jørgensen, Bo Hoffmann
2003-01-01
equations on a general form which accommodate curvilinear coordinates. Strong conservation form is obtained by formulating the equations so that the flow variables, velocity and pressure, are expressed in thephysical coordinate system while the location of evaluation is expressed within the transformed...... coordinate system. The tensor formulation allows both a finite difference and a pseudo-spectral description of the model equations. The intention is for thefinite difference formulation to achieve the same robustness and conservation properties as a finite volume discretization. Furthermore, an invariant...
J Ledent
1980-01-01
First, it is shown that Alonso's general theory of movement relies on a standard doubly-constrained spatial interaction model which subsumes the usual gravity and entropy-derived formulations. Such a finding then suggests the use of a biproportional adjustment method (RAS method) to adequately estimate the systemic variables specified in the underlying model. This eventually leads to the development of a complete and precise methodology for calibrating the Alonso model. This methodology is il...
Generalized breakup and coalescence models for population balance modelling of liquid-liquid flows
Traczyk, Marcin; Thompson, Chris
2015-01-01
Population balance framework is a useful tool that can be used to describe size distribution of droplets in a liquid-liquid dispersion. Breakup and coalescence models provide closures for mathematical formulation of the population balance equation (PBE) and are crucial for accu- rate predictions of the mean droplet size in the flow. Number of closures for both breakup and coalescence can be identified in the literature and most of them need an estimation of model parameters that can differ even by several orders of magnitude on a case to case basis. In this paper we review the fundamental assumptions and derivation of breakup and coalescence ker- nels. Subsequently, we rigorously apply two-stage optimization over several independent sets of experiments in order to identify model parameters. Two-stage identification allows us to estab- lish new parametric dependencies valid for experiments that vary over large ranges of important non-dimensional groups. This be adopted for optimization of parameters in breakup...
Testing General Relativity with Accretion-Flow Imaging of Sgr A^{*}.
Johannsen, Tim; Wang, Carlos; Broderick, Avery E; Doeleman, Sheperd S; Fish, Vincent L; Loeb, Abraham; Psaltis, Dimitrios
2016-08-26
The Event Horizon Telescope is a global, very long baseline interferometer capable of probing potential deviations from the Kerr metric, which is believed to provide the unique description of astrophysical black holes. Here, we report an updated constraint on the quadrupolar deviation of Sagittarius A^{*} within the context of a radiatively inefficient accretion flow model in a quasi-Kerr background. We also simulate near-future constraints obtainable by the forthcoming eight-station array and show that in this model already a one-day observation can measure the spin magnitude to within 0.005, the inclination to within 0.09°, the position angle to within 0.04°, and the quadrupolar deviation to within 0.005 at 3σ confidence. Thus, we are entering an era of high-precision strong gravity measurements.
Testing General Relativity with Accretion-Flow Imaging of Sgr A*
Johannsen, Tim; Broderick, Avery E; Doeleman, Sheperd S; Fish, Vincent L; Loeb, Abraham; Psaltis, Dimitrios
2016-01-01
The Event Horizon Telescope is a global very-long baseline interferometer capable of probing potential deviations from the Kerr metric, which is believed to provide the unique description of astrophysical black holes. Here we report an updated constraint on the quadrupolar deviation of Sagittarius A* within the context of a radiatively inefficient accretion flow model in a quasi-Kerr background. We also simulate near-future constraints obtainable by the forthcoming eight-station array and show that in this model already a one-day observation can measure the spin magnitude to within 0.005, the inclination to within 0.09{\\deg}, the position angle to within 0.04{\\deg}, and the quadrupolar deviation to within 0.005 at 3{\\sigma} confidence. Thus, we are entering an era of high-precision strong gravity measurements.
Migration_USER, IPDS; Wiley, Michael J.; Wilcox, Douglas A.
2016-01-01
The use of diurnal water-table fluctuation methods to calculate evapotranspiration (ET) and groundwater flow is of increasing interest in ecohydrological studies. Most studies of this type, however, have been located in riparian wetlands of semi-arid regions where groundwater levels are consistently below topographic surface elevations and precipitation events are infrequent. Current methodologies preclude application to a wider variety of wetland systems. In this study, we extended a method for estimating sub-daily ET and groundwater flow rates from water-level fluctuations to fit highly dynamic, non-riparian wetland scenarios. Modifications included (1) varying the specific yield to account for periodic flooded conditions and (2) relating empirically derived ET to estimated potential ET for days when precipitation events masked the diurnal signal. To demonstrate the utility of this method, we estimated ET and groundwater fluxes over two growing seasons (2006–2007) in 15 wetlands within a ridge-and-swale wetland complex of the Laurentian Great Lakes under flooded and non-flooded conditions. Mean daily ET rates for the sites ranged from 4.0 mm d−1 to 6.6 mm d−1. Shallow groundwater discharge rates resulting from evaporative demand ranged from 2.5 mm d−1 to 4.3 mm d−1. This study helps to expand our understanding of the evapotranspirative demand of plants under various hydrologic and climate conditions. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.
Helical turbulent Prandtl number in the A model of passive vector advection
Hnatič, M.; Zalom, P.
2016-11-01
Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general A model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via the continuous parameter ρ ranging from ρ =0 (no violation of spatial parity) to |ρ |=1 (maximum violation of spatial parity). Values of A represent a continuously adjustable parameter which governs the interaction structure of the model. In nonhelical environments, we demonstrate that A is restricted to the interval -1.723 ≤A ≤2.800 (rounded to 3 decimal places) in the two-loop order of the field theoretic model. However, when ρ >0.749 (rounded to 3 decimal places), the restrictions may be removed, which means that presence of helicity exerts a stabilizing effect onto the possible stationary regimes of the system. Furthermore, three physically important cases A ∈{-1 ,0 ,1 } are shown to lie deep within the allowed interval of A for all values of ρ . For the model of the linearized Navier-Stokes equations (A =-1 ) up to date unknown helical values of the turbulent Prandtl number have been shown to equal 1 regardless of parity violation. Furthermore, we have shown that interaction parameter A exerts strong influence on advection-diffusion processes in turbulent environments with broken spatial parity. By varying A continuously, we explain high stability of the kinematic MHD model (A =1 ) against helical effects as a result of its proximity to the A =0.912 (rounded to 3 decimal places) case where helical effects are completely suppressed. Contrary, for the physically important A =0 model, we show that it lies deep within the interval of models where helical effects cause the turbulent Prandtl number to decrease with |ρ | . We thus identify internal structure of interactions given by the parameter A , and not the vector character of the admixture itself being the dominant factor influencing
Hernandez-Santana, V.; Asbjornsen, H.; Sauer, T.; Isenhart, T.; Schilling, K.; Schultz, Ronald
2011-01-01
Riparian buffers are designed as management practices to increase infiltration and reduce surface runoff and transport of sediment and nonpoint source pollutants from crop fields to adjacent streams. Achieving these ecosystem service goals depends, in part, on their ability to remove water from the soil via transpiration. In these systems, edges between crop fields and trees of the buffer systems can create advection processes, which could influence water use by trees. We conducted a field study in a riparian buffer system established in 1994 under a humid temperate climate, located in the Corn Belt region of the Midwestern U.S. (Iowa). The goals were to estimate stand level transpiration by the riparian buffer, quantify the controls on water use by the buffer system, and determine to what extent advective energy and tree position within the buffer system influence individual tree transpiration rates. We primarily focused on the water use response (determined with the Heat Ratio Method) of one of the dominant species (Acer saccharinum) and a subdominant (Juglans nigra). A few individuals of three additional species (Quercus bicolor, Betula nigra, Platanus occidentalis) were monitored over a shorter time period to assess the generality of responses. Meteorological stations were installed along a transect across the riparian buffer to determine the microclimate conditions. The differences found among individuals were attributed to differences in species sap velocities and sapwood depths, location relative to the forest edge and prevailing winds and canopy exposure and dominance. Sapflow rates for A. saccharinum trees growing at the SE edge (prevailing winds) were 39% greater than SE interior trees and 30% and 69% greater than NW interior and edge trees, respectively. No transpiration enhancement due to edge effect was detected in the subdominant J. nigra. The results were interpreted as indicative of advection effects from the surrounding crops. Further, significant
Helical turbulent Prandtl number in the A model of passive vector advection.
Hnatič, M; Zalom, P
2016-11-01
Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general A model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via the continuous parameter ρ ranging from ρ=0 (no violation of spatial parity) to |ρ|=1 (maximum violation of spatial parity). Values of A represent a continuously adjustable parameter which governs the interaction structure of the model. In nonhelical environments, we demonstrate that A is restricted to the interval -1.723≤A≤2.800 (rounded to 3 decimal places) in the two-loop order of the field theoretic model. However, when ρ>0.749 (rounded to 3 decimal places), the restrictions may be removed, which means that presence of helicity exerts a stabilizing effect onto the possible stationary regimes of the system. Furthermore, three physically important cases A∈{-1,0,1} are shown to lie deep within the allowed interval of A for all values of ρ. For the model of the linearized Navier-Stokes equations (A=-1) up to date unknown helical values of the turbulent Prandtl number have been shown to equal 1 regardless of parity violation. Furthermore, we have shown that interaction parameter A exerts strong influence on advection-diffusion processes in turbulent environments with broken spatial parity. By varying A continuously, we explain high stability of the kinematic MHD model (A=1) against helical effects as a result of its proximity to the A=0.912 (rounded to 3 decimal places) case where helical effects are completely suppressed. Contrary, for the physically important A=0 model, we show that it lies deep within the interval of models where helical effects cause the turbulent Prandtl number to decrease with |ρ|. We thus identify internal structure of interactions given by the parameter A, and not the vector character of the admixture itself being the dominant factor influencing diffusion-advection
Energy Technology Data Exchange (ETDEWEB)
Bachand, P.A.M., E-mail: Philip.Bachand@Tetratech.com [Tetra Tech, Davis, CA (United States); Bachand, S. [Tetra Tech, Davis, CA (United States); Fleck, J.; Anderson, F. [U.S. Geological Survey, California Water Science Center, Sacramento, CA (United States); Windham-Myers, L. [U.S. Geological Survey, National Research Program, Menlo Park, CA (United States)
2014-06-01
The current state of science and engineering related to analyzing wetlands overlooks the importance of transpiration and risks data misinterpretation. In response, we developed hydrologic and mass budgets for agricultural wetlands using electrical conductivity (EC) as a natural conservative tracer. We developed simple differential equations that quantify evaporation and transpiration rates using flow rates and tracer concentrations at wetland inflows and outflows. We used two ideal reactor model solutions, a continuous flow stirred tank reactor (CFSTR) and a plug flow reactor (PFR), to bracket real non-ideal systems. From those models, estimated transpiration ranged from 55% (CFSTR) to 74% (PFR) of total evapotranspiration (ET) rates, consistent with published values using standard methods and direct measurements. The PFR model more appropriately represents these non-ideal agricultural wetlands in which check ponds are in series. Using a flux model, we also developed an equation delineating the root zone depth at which diffusive dominated fluxes transition to advective dominated fluxes. This relationship is similar to the Peclet number that identifies the dominance of advective or diffusive fluxes in surface and groundwater transport. Using diffusion coefficients for inorganic mercury (Hg) and methylmercury (MeHg) we calculated that during high ET periods typical of summer, advective fluxes dominate root zone transport except in the top millimeters below the sediment–water interface. The transition depth has diel and seasonal trends, tracking those of ET. Neglecting this pathway has profound implications: misallocating loads along different hydrologic pathways; misinterpreting seasonal and diel water quality trends; confounding Fick's First Law calculations when determining diffusion fluxes using pore water concentration data; and misinterpreting biogeochemical mechanisms affecting dissolved constituent cycling in the root zone. In addition, our
Directory of Open Access Journals (Sweden)
Stefano L. Russo
2010-01-01
Full Text Available Problem statement: The increasing diffusion of low-enthalpy geothermal open-loop Groundwater Heat Pumps (GWHP providing buildings air conditioning requires a careful assessment of the overall effects on groundwater system, especially in the urban areas. The impact on the groundwater temperature in the surrounding area of the re-injection well is directly linked to the aquifer properties. Physical processes affecting heat transport within an aquifer include advection (or convection and hydrodynamic thermodispersion (diffusion and mechanical dispersion. If the groundwater flows, the advective components tend to dominate the heat transfer process within the aquifer and the diffusion can be considered negligible. This study illustrates the experimental results derived from the groundwater monitoring in the surrounding area of an injection well connected to an open-loop GWHP plant which has been installed in the "Politecnico di Torino" (NW Italy for cooling some of the university buildings. Groundwater pumping and injection interfere only with the upper unconfined aquifer. Approach: After the description of the hydrogeological setting the authors examined the data deriving from multiparameter probes installed inside the pumping well (P2, the injection well (P4 and a downgradient piezometer (S2. Data refers to the summer 2009. To control the aquifer thermal stratification some multi-temporal temperature logs have been performed in the S2. Results: After the injection of warm water in P4 the plume arrived after 30 days in the S2. That delay is compatible with the calculated plume migration velocity (1.27 m d-1 and their respective distance (35 m. The natural temperature in the aquifer due to the switching-off of the GWHP plant has been reached after two month. The Electrical Conductivity (EC values tend to vary out of phase with the temperature. The temperature logs in the S2 highlighted a thermal stratification in the aquifer due to a low vertical
Dong, Suchuan
2014-01-01
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary conditions, which all ensure the energy stability of the system, even in situations where strong vortices or backflows occur at the open/outflow boundaries. Our numerical algorithm for treating these open boundary conditions is based on a rotational pressure correction-type strategy, with a formulation suitable for $C^0$ spectral-element spatial discretizations. We have introduced a discrete equation and associated boundary conditions for an auxiliary variable. The algorithm contains constructions that prevent a numerical locking at the open/outflow boundary. In addition, we have also developed a scheme with a provable unconditional stability for a sub-class of the open boundary conditions. Extensive numerical experiments have been presented to demonstrate the performance of our meth...
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Sauty, Christophe; Cayatte, Véronique; Celnikier, Ludwik M.
2014-06-01
We present a model for the spine of relativistic Magnetohydrodynamics outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semianalytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Cayatte, Véronique; Celnikier, Ludwik M
2014-01-01
We present a model for the spine of relativistic MHD outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semi-analytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
Energy Technology Data Exchange (ETDEWEB)
McGraw R.
2012-03-01
Moment methods are finding increasing usage for simulations of particle population balance in box models and in more complex flows including two-phase flows. These highly efficient methods have nevertheless had little impact to date for multi-moment representation of aerosols and clouds in atmospheric models. There are evidently two reasons for this: First, atmospheric models, especially if the goal is to simulate climate, tend to be extremely complex and take many man-years to develop. Thus there is considerable inertia to the implementation of novel approaches. Second, and more fundamental, the nonlinear transport algorithms designed to reduce numerical diffusion during advection of various species (tracers) from cell to cell, in the typically coarse grid arrays of these models, can and occasionally do fail to preserve correlations between the moments. Other correlated tracers such as isotopic abundances, composition of aerosol mixtures, hydrometeor phase, etc., are subject to this same fate. In the case of moments, this loss of correlation can and occasionally does give rise to unphysical moment sets. When this happens the simulation can come to a halt. Following a brief description and review of moment methods, the goal of this paper is to present two new approaches that both test moment sequences for validity and correct them when they fail. The new approaches work on individual grid cells without requiring stored information from previous time-steps or neighboring cells.
Lichtenberg, Mads; Nørregaard, Rasmus Dyrmose; Kühl, Michael
2017-03-01
The role of hyaline hairs on the thallus of brown algae in the genus Fucus is long debated and several functions have been proposed. We used a novel motorized set-up for two-dimensional and three-dimensional mapping with O2 microsensors to investigate the spatial heterogeneity of the diffusive boundary layer (DBL) and O2 flux around single and multiple tufts of hyaline hairs on the thallus of Fucus vesiculosus. Flow was a major determinant of DBL thickness, where higher flow decreased DBL thickness and increased O2 flux between the algal thallus and the surrounding seawater. However, the topography of the DBL varied and did not directly follow the contour of the underlying thallus. Areas around single tufts of hyaline hairs exhibited a more complex mass-transfer boundary layer, showing both increased and decreased thickness when compared with areas over smooth thallus surfaces. Over thallus areas with several hyaline hair tufts, the overall effect was an apparent increase in the boundary layer thickness. We also found indications for advective O2 transport driven by pressure gradients or vortex shedding downstream from dense tufts of hyaline hairs that could alleviate local mass-transfer resistances. Mass-transfer dynamics around hyaline hair tufts are thus more complex than hitherto assumed and may have important implications for algal physiology and plant-microbe interactions.
Shen, Xiaoteng; Maa, Jerome P.-Y.
2017-09-01
In estuaries and coastal waters, floc size and its statistical distributions of cohesive sediments are of primary importance, due to their effects on the settling velocity and thus deposition rates of cohesive aggregates. The development of a robust flocculation model that includes the predictions of floc size distributions (FSDs), however, is still in a research stage. In this study, a one-dimensional longitudinal (1-DL) flocculation model along a streamtube is developed. This model is based on solving the population balance equation to find the FSDs by using the quadrature method of moments. To validate this model, a laboratory experiment is carried out to produce an advection transport-dominant environment in a cylindrical tank. The flow field is generated by a marine pump mounted at the bottom center, with its outlet facing upward. This setup generates an axially symmetric flow which is measured by an acoustic Doppler velocimeter (ADV). The measurement results provide the hydrodynamic input data required for this 1-DL model. The other measurement results, the FSDs, are acquired by using an automatic underwater camera system and the resulting images are analyzed to validate the predicted FSDs. This study shows that the FSDs as well as their representative sizes can be efficiently and reasonably simulated by this 1-DL model.
Institute of Scientific and Technical Information of China (English)
ABBAS Zaheer; MASOOD Tahmina; OLANREWAJU Philip Oladapo
2015-01-01
An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.
Institute of Scientific and Technical Information of China (English)
LIN Zhenhua; ZHAO Dongliang; SONG Jinbao
2011-01-01
Different advection schemes and two-equation turbulence closure models based on eddy viscosity concept are used to compute the drag coefficient around a circular cylinder at high Reynolds number (106).The numerical results from these simulations are compared with each other and with experimental data in order to evaluate the performance of different combinations of advection scheme and two-equation turbulence model.The separate contributions from form drag and friction drag are also analyzed.The computational results show that the widely used standard k-ε turbulence closure is not suitable for such kind of study,while the other two-equation turbulence closure models produce acceptable results.The influence of the different advection schemes on the final results are small compared to that produced by the choice of turbulence closure method.The present study serves as a reference for the choice of advection schemes and turbulence closure models for more complex numerical simulation of the flow around a circular cylinder at high Reynolds number.
Interpretation of Isopycnal Layer Thickness Advection in Terms of Eddy-Topography Interaction
Liu, Chuanyu; Koehl, Armin; Stammer, Detlef
2013-04-01
Spatially varying amplitude of the eddy isopycnal layer thickness diffusivity Kgm and the layer thickness advection Kgmskew of the modified Gent and McWilliams parameterization are estimated using two different approaches: the adjoint estimation from a global data assimilation system and the inversion calculation according to divergent buoyancy eddy flux-mean buoyancy gradient relation using results from idealized eddy resolving numerical models with various bottom topographies. This work focuses on the properties of Kgmskew. From the adjoint estimation, large Kgmskew values are found along meandering currents and predominantly positive (negative) over the deep ocean and negative (positive) over seamounts in the southern (northern) hemisphere, implying close relation to the 'Neptune effect" parameterization by Holloway in which the eddy induced mean velocity stream function is represented by -fHL, where H is the bottom depth, f the Coriolis parameter and L a length scale. In the inversion calculation, divergent buoyancy eddy fluxes are obtained by removing the rotational components from the total buoyancy eddy fluxes through Helmholtz-Hodge decomposition. Though subject to topographic length scale, the inversed Kgmskew reveals characteristics of both f and H, and interactions with the mean current, inter-confirming the adjoint estimation results. Applying this parameterization for Kgmskew in the general circulation model produces cold domes and anti-cyclonic circulations over seamounts, which reduces common model biases there. By construction, the original thickness advection Kgmskew redistributes potential energy and the original "Neptune effect" parameterization improves potential vorticity conservation, applying the latter into the former as suggested in the present study thus more correctly reproduces the potential vorticity structure over a sloping topography while conserving the total potential energy.
Directory of Open Access Journals (Sweden)
M. N. Juckes
2006-01-01
Full Text Available A new data assimilation algorithm, using the isentropic advection equation, is applied to MIPAS and SBUV measurements of stratospheric ozone. The system is solved separately on each isentropic level, with neither vertical advection nor chemical reactions represented. The results are validated against HALOE, POAM III, SAGE II & III, OSIRIS and ozone sonde data. The new assimilation algorithm has the accuracy of the Kalman smoother but is, for the systems studied here with up to 200 000 variables per time step and 61 million control variables in total, many orders of magnitude less computationally expensive. The analysis produced minimises a single penalty function evaluated over an analysis window of over one month. The cost of the analysis is found to increase nearly linearly with the number of control variables. Compared with over 800 profiles from Electrochemical Concentration Cell sondes at 29 sites the analysis is found to be merely 0.1% high at 420 K, rising to 0.4% at 650 K. Comparison against the other satellites imply that the bias remains small up to 1250 K (38 km and then increases to around −10% at 1650 K (44 km. Between 20 and 35 km the root-mean-square difference relative to HALOE, SAGE II & III, and POAM is in the 5 to 10% range, with larger discrepancies relative to other instruments. Outside this height range rms differences are generally larger, though agreement with HALOE remains good up to 50 km. The assimilation has closer agreement to independent observations than found in direct near-neighbour comparisons between profiles, demonstrating that the assimilation can add value to the observations.
Analysis of impact of general-purpose graphics processor units in supersonic flow modeling
Emelyanov, V. N.; Karpenko, A. G.; Kozelkov, A. S.; Teterina, I. V.; Volkov, K. N.; Yalozo, A. V.
2017-06-01
Computational methods are widely used in prediction of complex flowfields associated with off-normal situations in aerospace engineering. Modern graphics processing units (GPU) provide architectures and new programming models that enable to harness their large processing power and to design computational fluid dynamics (CFD) simulations at both high performance and low cost. Possibilities of the use of GPUs for the simulation of external and internal flows on unstructured meshes are discussed. The finite volume method is applied to solve three-dimensional unsteady compressible Euler and Navier-Stokes equations on unstructured meshes with high resolution numerical schemes. CUDA technology is used for programming implementation of parallel computational algorithms. Solutions of some benchmark test cases on GPUs are reported, and the results computed are compared with experimental and computational data. Approaches to optimization of the CFD code related to the use of different types of memory are considered. Speedup of solution on GPUs with respect to the solution on central processor unit (CPU) is compared. Performance measurements show that numerical schemes developed achieve 20-50 speedup on GPU hardware compared to CPU reference implementation. The results obtained provide promising perspective for designing a GPU-based software framework for applications in CFD.
Generalization of Martinelli-Nelson method of pressure drop calculation in two-phase flows
Directory of Open Access Journals (Sweden)
Trela Marian
2017-01-01
Full Text Available A simple method of pressure drop calculation for two-phase flows of different fluids during convective boiling in channels is presented. It is based on experimental data of pressure drop multiplier R and void fraction φ obtained by Martinelli and Nelson for boiling of water in vertical tubes. The data cover the whole two-phase domain from ambient to critical pressure. Unfortunately, they have been presented in graphical forms. The first step in the procedure proposed in the paper was a transformation of the graphical data into analytical formulas which contain such dimensionless quantities as steam quality x, Martinelli parameter X, multiplier Φl2 and dimensionless coefficients D, m, E and k. In the second step, simple analytical formulas were determined to express the dimensionless coefficients as a function of physical property parameter K. In this way two simple analytical expressions for the multiplier R and void fraction φ were obtained. They are in analytical dimensionless form so they may be used directly for different fluids, not only for water. This is the main advantage of the proposed method.
Directory of Open Access Journals (Sweden)
Ezad Hafidzuddin
2016-01-01
Full Text Available In this paper, the steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is studied. The flow and heat transfer induced by stretching/shrinking sheets are important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual (upper and lower branch solutions are found for a certain range of the suction and stretching/shrinking parameters. Stability analysis is performed to determine which solutions are stable and physically realizable and which are not stable. The effects of suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed in detail. It is found that the introduction of the generalized slip boundary condition resulted in the reduction of the local skin friction coefficient and local Nusselt number. Finally, it is concluded from the stability analysis that the first (upper branch solution is stable while the second (lower branch solution is not stable.
Anco, Stephen C.; Myrzakulov, R.
2010-10-01
A moving frame formulation of non-stretching geometric curve flows in Euclidean space is used to derive a 1+1 dimensional hierarchy of integrable SO(3)-invariant vector models containing the Heisenberg ferromagnetic spin model as well as a model given by a spin vector version of the mKdV equation. These models describe a geometric realization of the NLS hierarchy of soliton equations whose bi-Hamiltonian structure is shown to be encoded in the Frenet equations of the moving frame. This derivation yields an explicit bi-Hamiltonian structure, recursion operator, and constants of motion for each model in the hierarchy. A generalization of these results to geometric surface flows is presented, where the surfaces are non-stretching in one direction while stretching in all transverse directions. Through the Frenet equations of a moving frame, such surface flows are shown to encode a hierarchy of 2+1 dimensional integrable SO(3)-invariant vector models, along with their bi-Hamiltonian structure, recursion operator, and constants of motion, describing a geometric realization of 2+1 dimensional bi-Hamiltonian NLS and mKdV soliton equations. Based on the well-known equivalence between the Heisenberg model and the Schrödinger map equation in 1+1 dimensions, a geometrical formulation of these hierarchies of 1+1 and 2+1 vector models is given in terms of dynamical maps into the 2-sphere. In particular, this formulation yields a new integrable generalization of the Schrödinger map equation in 2+1 dimensions as well as a mKdV analog of this map equation corresponding to the mKdV spin model in 1+1 and 2+1 dimensions.
Deev, V. I.; Kharitonov, V. S.; Churkin, A. N.
2017-02-01
Experimental data on heat transfer to supercritical pressure water presented at ISSCWR-5, 6, and 7 international symposiums—which took place in 2011-2015 in Canada, China, and Finland—and data printed in recent periodical scientific publications were analyzed. Results of experiments with annular channels and three- and four-rod bundles of heating elements positioned in square or triangular grids were examined. Methodology used for round pipes was applied at generalization of experimental data and establishing of correlations suitable for engineering analysis of heat exchange coefficient in conditions of strongly changing water properties in the near-critical pressure region. Empiric formulas describing normal heat transfer to supercritical pressure water mowing in annular channels and rod bundles were obtained. As compared to existing recommendations, suggested correlations are distinguished by specified dependency of heat exchange coefficient on density of heat flux and mass flow velocity of water near pseudo-critical temperature. Differences between computed values of heat exchange coefficient and experimental data usually do not exceed ±25%. Detailed statistical analysis of deviations between computed and experimental results at different states of supercritical pressure water flow was carried out. Peculiarities of deteriorated heat exchange were considered and their existence boundaries were defined. Experimental results obtained for these regimes were generalized using criteria by J.D. Jackson that take the influence of thermal acceleration and Archimedes forces on heat exchange processes into account. Satisfactory agreement between experimental data on heat exchange at flowing of water in annular channels and rod bundles and data for round pipes was shown.
Advection in polar and sub-polar environments: Impacts on high latitude marine ecosystems
Hunt, George L.; Drinkwater, Kenneth F.; Arrigo, Kevin; Berge, Jørgen; Daly, Kendra L.; Danielson, Seth; Daase, Malin; Hop, Haakon; Isla, Enrique; Karnovsky, Nina; Laidre, Kristin; Mueter, Franz J.; Murphy, Eugene J.; Renaud, Paul E.; Smith, Walker O.; Trathan, Philip; Turner, John; Wolf-Gladrow, Dieter
2016-12-01
We compare and contrast the ecological impacts of atmospheric and oceanic circulation patterns on polar and sub-polar marine ecosystems. Circulation patterns differ strikingly between the north and south. Meridional circulation in the north provides connections between the sub-Arctic and Arctic despite the presence of encircling continental landmasses, whereas annular circulation patterns in the south tend to isolate Antarctic surface waters from those in the north. These differences influence fundamental aspects of the polar ecosystems from the amount, thickness and duration of sea ice, to the types of organisms, and the ecology of zooplankton, fish, seabirds and marine mammals. Meridional flows in both the North Pacific and the North Atlantic oceans transport heat, nutrients, and plankton northward into the Chukchi Sea, the Barents Sea, and the seas off the west coast of Greenland. In the North Atlantic, the advected heat warms the waters of the southern Barents Sea and, with advected nutrients and plankton, supports immense biomasses of fish, seabirds and marine mammals. On the Pacific side of the Arctic, cold waters flowing northward across the northern Bering and Chukchi seas during winter and spring limit the ability of boreal fish species to take advantage of high seasonal production there. Southward flow of cold Arctic waters into sub-Arctic regions of the North Atlantic occurs mainly through Fram Strait with less through the Barents Sea and the Canadian Archipelago. In the Pacific, the transport of Arctic waters and plankton southward through Bering Strait is minimal. In the Southern Ocean, the Antarctic Circumpolar Current and its associated fronts are barriers to the southward dispersal of plankton and pelagic fishes from sub-Antarctic waters, with the consequent evolution of Antarctic zooplankton and fish species largely occurring in isolation from those to the north. The Antarctic Circumpolar Current also disperses biota throughout the Southern Ocean
Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations are applied to the nonlinear advection equa-tion. The results show that the approach is effective for the exact analytical solu-tion and the algorithm has higher precision than other existing algorithms in nu-merical computation for the nonlinear advection equation.
Lenhard, R. J.; Oostrom, M.; Simmons, C. S.; White, M. D.
1995-07-01
An experiment was conducted to evaluate whether vapor-density effects are significant in transporting volatile organic compounds (VOC's) with high vapor pressure and molecular mass through the subsurface. Trichloroethylene (TCE) was chosen for the investigation because it is a common VOC contaminant with high vapor pressure and molecular mass. For the investigation, a 2-m-long by 1-m-high by 7.5-cm-thick flow cell was constructed with a network of sampling ports. The flow cell was packed with sand, and a water table was established near the lower boundary. Liquid TCE was placed near the upper boundary of the flow cell in a chamber from which vapors could enter and migrate through the sand. TCE concentrations in the gas phase were measured by extracting 25-μl gas samples with an air-tight syringe and analyzing them with a gas chromatograph. The evolution of the TCE gas plume in the sand was investigated by examining plots of TCE concentrations over the domain for specific times and for particular locations as a function of time. To help in this analysis, a numerical model was developed that can predict the simultaneous movements of a gas, a nonaqueous liquid and water in porous media. The model also considers interphase mass transfer by employing the phase equilibrium assumption. The model was tested with one- and two-dimensional analytical solutions of fluid flow before it was used to simulate the experiment. Comparisons between experimental data and simulation results when vapor-density effects are considered were very good. When vapor-density effects were ignored, agreement was poor. These analyses suggest that vapor-density effects should be considered and that density-driven vapor advection may be an important mechanism for moving VOC's with high vapor pressures and molecular mass through the subsurface.
A general methodology and applications for conduction-like flow-channel design.
Energy Technology Data Exchange (ETDEWEB)
Cummings, Eric B.; Fiechtner, Gregory J.
2004-02-01
A novel design methodology is developed for creating conduction devices in which fields are piecewise uniform. This methodology allows the normally analytically intractable problem of Lagrangian transport to be solved using algebraic and trigonometric equations. Low-dispersion turns, manifolds, and expansions are developed. In this methodology, regions of piece-wise constant specific permeability (permeability per unit width) border each other with straight, generally tilted interfaces. The fields within each region are made uniform by satisfying a simple compatibility relation between the tilt angle and ratio of specific permeability of adjacent regions. This methodology has particular promise in the rational design of quasi-planar devices, in which the specific permeability is proportional to the depth of the channel. For such devices, the methodology can be implemented by connecting channel facets having two or more depths, fabricated, e.g., using a simple two-etch process.
Modeling Two-Phase Flow and Vapor Cycles Using the Generalized Fluid System Simulation Program
Smith, Amanda D.; Majumdar, Alok K.
2017-01-01
This work presents three new applications for the general purpose fluid network solver code GFSSP developed at NASA's Marshall Space Flight Center: (1) cooling tower, (2) vapor-compression refrigeration system, and (3) vapor-expansion power generation system. These systems are widely used across engineering disciplines in a variety of energy systems, and these models expand the capabilities and the use of GFSSP to include fluids and features that are not part of its present set of provided examples. GFSSP provides pressure, temperature, and species concentrations at designated locations, or nodes, within a fluid network based on a finite volume formulation of thermodynamics and conservation laws. This paper describes the theoretical basis for the construction of the models, their implementation in the current GFSSP modeling system, and a brief evaluation of the usefulness of the model results, as well as their applicability toward a broader spectrum of analytical problems in both university teaching and engineering research.
Ebner, Pirmin Philipp; Andreoli, Christian; Schneebeli, Martin; Steinfeld, Aldo
2015-12-01
Snow at or close to the surface commonly undergoes temperature gradient metamorphism under advective flow, which alters its microstructure and physical properties. A functional understanding of this process is essential for many disciplines, from modeling the effects of snow on regional and global climate to assessing avalanche formation. Time-lapse X-ray microtomography was applied to investigate the structural dynamics of temperature gradient snow metamorphism exposed to an advective airflow in controlled laboratory conditions. Experiments specifically analyzed sublimation and deposition of water vapor on the ice structure. In addition, an analysis of the ice-air interface dynamics was carried out using a macroscopic equivalent model of heat and water vapor transport through a snow layer. The results indicate that sublimation of the ice matrix dominated for flow rates surface area and thus suggest a change of the physical and optical properties of the snow. The estimated values of the curvature effect of the ice crystals and the interface kinetic coefficient are in good agreement with previously published values.
Dentzer, Jacques; Violette, Sophie; Lopez, Simon; Bruel, Dominique
2017-06-01
This study is the first quantification of the combined impact of diffusive and advective paleoclimatic phenomena to explain the weak vertical thermal flux anomaly in the upper part of the Anglo-Paris intracratonic sedimentary basin in northern France. The aim of the research is to understand the mechanisms at the origin of the thermal flux anomaly at the level of the Meso-Cenozoic sediment pile. Based on a temperature profile representative of the basin, transient thermo-hydraulic simulations were performed along a representative vertical cross-section of about 400 km within the Lower Cretaceous multi-layer aquifer. Four paleoclimatic scenarios are the combination of two paleotemperature climatic forcings and two hydrodynamic regimes, one of them taking into account the interruption of the recharge linked to permafrost development. The simulation results clearly show the transient nature of the basin's thermal regime. Then, for the reference well, the majority of the thermal flux anomaly can be explained by advective and paleoclimatic mechanisms with a decrease in geothermal flux simulated up to a little over 30 mW/m2, depending on the scenarios. Decrease in heat flux because of basin-scale subsurface flows in the Lower Cretaceous is around 15 mW/m2. There are several ways forward from this first simple model, including simulation of development of permafrost and also the integration of vertical flows in the basin by use of a three-dimensional model to better explain the data.
Llanes, F.; dela Resma, M.; Ferrer, P.; Realino, V.; Aquino, D. T.; Eco, R. C.; Lagmay, A.
2013-12-01
From November 14 to December 3, 2004, Luzon Island was ravaged by 4 successive typhoons: Typhoon Mufia, Tropical Storm Merbok, Tropical Depression Winnie, and Super Typhoon Nanmadol. Tropical Depression Winnie was the most destructive of the four when it triggered landslides on November 29 that devastated the municipalities of Infanta, General Nakar, and Real in Quezon Province, southeast Luzon. Winnie formed east of Central Luzon on November 27 before it moved west-northwestward over southeastern Luzon on November 29. A total of 1,068 lives were lost and more than USD 170 million worth of damages to crops and infrastructure were incurred from the landslides triggered by Typhoon Winnie on November 29 and the flooding caused by the 4 typhoons. FLO-2D, a flood routing software for generating flood and debris flow hazard maps, was utilized to simulate the debris flows that could potentially affect the study area. Based from the rainfall intensity-duration-frequency analysis, the cumulative rainfall from typhoon Winnie on November 29 which was approximately 342 mm over a 9-hour period was classified within a 100-year return period. The Infanta station of the Philippine Atmospheric Geophysical and Astronomical Services Administration (PAGASA) was no longer able to measure the amount of rainfall after this period because the rain gauge in that station was washed away by floods. Rainfall data with a 100-year return period was simulated over the watersheds delineated from a SAR-derived digital elevation model. The resulting debris flow hazard map was compared with results from field investigation and previous studies made on the landslide event. The simulation identified 22 barangays (villages) with a total of 45,155 people at risk of turbulent flow and flooding.
Di Federico, V.; Ciriello, V.
2011-12-01
Non-Newtonian fluid flow in porous media is of considerable interest in hydrology, chemical and petroleum engineering, and biofluid mechanics. We consider an infinite porous domain of plane (d=1), cylindrical (d=2) or semi-spherical geometry (d=3), having uniform permeability k and porosity Φ, initially at uniform pressure and saturated by a weakly compressible non-Newtonian fluid, and analyze the dynamics of the pressure variation generated within the domain by an instantaneous mass injection m0 in its origin. The fluid is described by a rheological power-law model of given consistency index H and flow behavior index n; the flow law is a modified Darcy's law depending on H, Φ, n. Coupling flow law and mass balance equations yields the nonlinear partial differential equation governing the pressure field; an analytical solution is derived in space r and time t as a function of a self-similar variable η=r/tβ(n). We revisit and expand the work in previous papers by providing a dimensionless general formulation and solution to the problem for d=1,2,3. When a shear-thinning fluid (nfluids; the front velocity is proportional to t(n-2)/2 in plane geometry, t(2n-3)/(3-n) in cylindrical geometry, and t(3n-4)/(4-2n) in semi-spherical geometry. The front position is a markedly increasing function of n and is inversely dependent on d; the pressure front advances at a slower rate for larger values of compressibility, higher injected mass and lower porosity. When pressure is considered, it is seen that an increase in d from 1 to 3 brings about an order of magnitude reduction. An increase in compressibility implies a significant decrease in pressure, especially at early times. To reflect the uncertainty inherent in values of the problem parameters, we then consider selected properties of fluid (flow behavior index n) and porous domain (permeability k, porosity Φ, and medium compressibility cp) as independent random variables with uniform probability distribution. The
Arraud, Nicolas; Gounou, Céline; Turpin, Delphine; Brisson, Alain R
2016-02-01
Plasma contains cell-derived extracellular vesicles (EVs) which participate in various physiopathological processes and have potential biomedical applications. Despite intense research activity, knowledge on EVs is limited mainly due to the difficulty of isolating and characterizing sub-micrometer particles like EVs. We have recently reported that a simple flow cytometry (FCM) approach based on triggering the detection on a fluorescence signal enabled the detection of 50× more Annexin-A5 binding EVs (Anx5+ EVs) in plasma than the conventional FCM approach based on light scattering triggering. Here, we present the application of the fluorescence triggering approach to the enumeration and phenotyping of EVs from platelet free plasma (PFP), focusing on CD41+ and CD235a+ EVs, as well as their sub-populations which bind or do not bind Anx5. Higher EV concentrations were detected by fluorescence triggering as compared to light scattering triggering, namely 40× for Anx5+ EVs, 75× for CD41+ EVs, and 15× for CD235a+ EVs. We found that about 30% of Anx5+ EVs were of platelet origin while only 3% of them were of erythrocyte origin. In addition, a majority of EVs from platelet and erythrocyte origin do not expose PS, in contrast to the classical theory of EV formation. Furthermore, the same PFP samples were analyzed fresh and after freeze-thawing, showing that freeze-thawing processes induce an increase, of about 35%, in the amount of Anx5+ EVs, while the other EV phenotypes remain unchanged. The method of EV detection and phenotyping by fluorescence triggering is simple, sensitive and reliable. We foresee that its application to EV studies will improve our understanding on the formation mechanisms and functions of EVs in health and disease and help the development of EV-based biomarkers. © 2015 International Society for Advancement of Cytometry.
Butler, N. L.; Hunt, J. R.; Tompkins, M. R.
2011-12-01
Hyporheic exchange can locally mitigate thermal stress caused by high water temperatures by upwelling water cooler than ambient stream temperatures and thus providing thermal refuge for critical cold water organisms like salmonids. Ten hyporheic exchange locations were identified by dye tracer experiments along a 16 km stretch of Deer Creek near Vina, California. Four months of continuous temperature measurements were made in the late summer of 2005 at each downwelling and upwelling location and revealed upwelled temperatures that were lagged in time and damped in amplitude. Upwelling hyporheic temperatures that could provide thermal refuge were observed in seven of the ten temperature records. This data was modeled by an analytical one-dimensional advection-diffusion equation solution using subsurface water velocity and the hydrodynamic dispersivity fitting parameters. At each location variations in upwelling temperature are explained by changing subsurface water velocities and flow pathways. The lag time in hyporheic heat flow ranged from a few hours to 44 hours over distances of 15 to 76 meters. The daily stream temperature variation was on the order of 10°C, which was reduced to 1 to 8°C in the upwelling hyporheic flow. At four locations, there was evidence that changes in stream flow produced changes in the amplitude and phase of the upwelling hyporheic water temperature by altering both the subsurface water velocity and hydrodynamic dispersivity. At two locations, additional cold water refuge was created by decreases in surface water flow because it reduced the estimated subsurface water velocity increasing the lag time between the peak surface water and subsurface water temperatures. Increases in surface water flow increased the dispersivity at three locations providing more cold water refuge by reducing the amplitude of the upwelling hyporheic temperature. Such changes alter thermal refuge for salmonids placing a new emphasis on managing surface water
Roedig, Constanze; Alic, Daniela
2012-01-01
We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic hydrodynamics coupled to an optically thick radiation field in two existing GR-hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several 1D tests we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in 1D, we compute a luminosity versus accretion rate diagram for the setup of spherical accretion onto a Schwarzschild black hole and find good agreement with previous work. Lastly, we revisit the supersonic Bondi Hoyle Lyttleton (BHL) accretion in 2D where we can now present simulations of realistic temperatures, down to T~10^6 K. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicabil...
Hoormann, Janie K
2016-01-01
While Albert Einstein's theory of General Relativity (GR) has been tested extensively in our solar system, it is just beginning to be tested in the strong gravitational fields that surround black holes. As a way to study the behavior of gravity in these extreme environments I have used and added to a ray-tracing code that simulates the X-ray emission from the accretion disks surrounding black holes. In particular, the observational channels which can be simulated include the thermal and reflected spectra, polarization, and reverberation signatures. These calculations can be performed assuming GR as well as four alternative spacetimes. These results can be used to see if it is possible to determine if observations can test the No-Hair theorem of GR which states that stationary, astrophysical black holes are only described by their mass and spin. Although it proves difficult to distinguish between theories of gravity it is possible to exclude a large portion of the possible deviations from GR using observations...
Energy Technology Data Exchange (ETDEWEB)
Shiokawa, Hotaka; Dolence, Joshua C.; Gammie, Charles F. [Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 West Green Street, Urbana, IL 61801 (United States); Noble, Scott C. [Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623 (United States)
2012-01-10
Global, general relativistic magnetohydrodynamic (GRMHD) simulations of non-radiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of four in linear resolution, from 96 Multiplication-Sign 96 Multiplication-Sign 64 to 384 Multiplication-Sign 384 Multiplication-Sign 256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma {beta}; (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma {beta} decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of two in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model ({sup s}hearing box{sup )} calculations and with the recent non-relativistic global convergence studies of Hawley et al.
Modelling the advection of herring larvae in the North Sea
Bartsch, J.; Brander, K.; Heath, M.; Munk, P.; Richardson, K.; Svendsen, E.
1989-08-01
THE number of fish at the age of first capture in a fishery (recruitment) is dependent on the production of eggs by the parent stock and the survival of early life stages (eggs, larvae and juveniles). In many pelagic fish species the survival of larvae depends on transport from spawning to nursery areas1. To investigate larval transport processes for North Sea herring (Clupea harengus L.) we have modelled in three dimensions the advection of autumn-spawned larvae during the winter of 1987-1988 and compared the results with sequential field data on the actual distribution of larvae. Circulation in the North Sea is pre-dominantly wind-driven during the winter, and in 1987-1988 anomalous atmospheric conditions caused a reduction in cyclonic circulation and unusual transport of larvae from northern North Sea and west of Scotland spawning areas. Predicting variations in recruitment in advance of fishery legislation has always been difficult and the collapse of North Sea herring populations during the mid-1970s is believed to have been due to a period of several years of low recruitment coupled with high fishing activity2. Our results suggest that a better understanding can be achieved with the aid of environmental modelling.
Mass loss from advective accretion disc around rotating black holes
Aktar, Ramiz; Nandi, Anuj
2015-01-01
We examine the properties of the outflowing matter from an advective accretion disc around a spinning black hole. During accretion, rotating matter experiences centrifugal pressure supported shock transition that effectively produces a virtual barrier around the black hole in the form of post-shock corona (hereafter, PSC). Due to shock compression, PSC becomes hot and dense that eventually deflects a part of the inflowing matter as bipolar outflows because of the presence of extra thermal gradient force. In our approach, we study the outflow properties in terms of the inflow parameters, namely specific energy (${\\mathcal E}$) and specific angular momentum ($\\lambda$) considering the realistic outflow geometry around the rotating black holes. We find that spin of the black hole ($a_k$) plays an important role in deciding the outflow rate $R_{\\dot m}$ (ratio of mass flux of outflow and inflow), in particular, $R_{\\dot m}$ is directly correlated with $a_k$ for the same set of inflow parameters. It is found that ...
Population persistence under advection-diffusion in river networks.
Ramirez, Jorge M
2012-11-01
An integro-differential equation on a tree graph is used to model the time evolution and spatial distribution of a population of organisms in a river network. Individual organisms become mobile at a constant rate, and disperse according to an advection-diffusion process with coefficients that are constant on the edges of the graph. Appropriate boundary conditions are imposed at the outlet and upstream nodes of the river network. The local rates of population growth/decay and that by which the organisms become mobile, are assumed constant in time and space. Imminent extinction of the population is understood as the situation whereby the zero solution to the integro-differential equation is stable. Lower and upper bounds for the eigenvalues of the dispersion operator, and related Sturm-Liouville problems are found. The analysis yields sufficient conditions for imminent extinction and/or persistence in terms of the values of water velocity, channel length, cross-sectional area and diffusivity throughout the river network.
Heat flow and ground water flow in the Great Plains of the United States
Gosnold, William D.
1985-12-01
Regional groundwater flow in deep aquifers adds advective components to the surface heat flow over extensive areas within the Great Plains province. The regional groundwater flow is driven by topographically controlled piezometric surfaces for confined aquifers that recharge either at high elevations on the western edge of the province or from subcrop contacts. The aquifers discharge at lower elevations to the east. The assymetrical geometry for the Denver and Kennedy Basins is such that the surface areas of aquifer recharge are small compared to the areas of discharge. Consequently, positive advective heat flow occurs over most of the province. The advective component of heat flow in the Denver Basin is on the order of 15 mW m -2 along a zone about 50 km wide that parallels the structure contours of the Dakota aquifer on the eastern margin of the Basin. The advective component of heat flow in the Kennedy Basin is on the order of 20 mW m -2 and occurs over an extensive area that coincides with the discharge areas of the Madison (Mississippian) and Dakota (Cretaceous) aquifers. Groundwater flow in Paleozoic and Mesozoic aquifers in the Williston Basin causes thermal anomalies that are seen in geothermal gradient data and in oil well temperature data. The pervasive nature of advective heat flow components in the Great Plains tends to mask the heat flow structure of the crust, and only heat flow data from holes drilled into the crystalline basement can be used for tectonic heat flow studies.
Fuller, Nathaniel J
2016-01-01
Obtaining a detailed understanding of the physical interactions between a cell and its environment often requires information about the flow of fluid surrounding the cell. Cells must be able to effectively absorb and discard material in order to survive. Strategies for nutrient acquisition and toxin disposal, which have been evolutionarily selected for their efficacy, should reflect knowledge of the physics underlying this mass transport problem. Motivated by these considerations, in this paper we consider a two-dimensional advection-diffusion problem at small Reynolds number and large P\\'eclet number. We discuss the problem of mass transport for a circular cell in a uniform far-field flow. We approach the problem numerically, and also analytically through a rescaling of the concentration boundary layer. A biophysically motivated first-passage problem for the absorption of material by the cell demonstrates quantitative agreement between the numerical and analytical approaches.
Huang, Bo; Chen, Dehui; Li, Xingliang; Li, Chao
2014-05-01
The Global/Regional Assimilation and PrEdiction System (GRAPES) is the new-generation numerical weather prediction (NWP) system developed by the China Meteorological Administration. It is a fully compressible non-hydrostatical global/regional unified model that uses a traditional semi-Lagrangian advection scheme with cubic Lagrangian interpolation (referred to as the SL_CL scheme). The SL_CL scheme has been used in many operational NWP models, but there are still some deficiencies, such as the damping effects due to the interpolation and the relatively low accuracy. Based on Reich's semi-Lagrangian advection scheme (referred to as the R2007 scheme), the Re_R2007 scheme that uses the low- and high-order B-spline function for interpolation at the departure point, is developed in this paper. One- and two-dimensional idealized tests in the rectangular coordinate system with uniform grid cells were conducted to compare the Re_R2007 scheme and the SL_CL scheme. The numerical results showed that: (1) the damping effects were remarkably reduced with the Re_R2007 scheme; and (2) the normalized errors of the Re_R2007 scheme were about 7.5 and 3 times smaller than those of the SL_CL scheme in one- and two-dimensional tests, respectively, indicating the higher accuracy of the Re_R2007 scheme. Furthermore, two solid-body rotation tests were conducted in the latitude-longitude spherical coordinate system with nonuniform grid cells, which also verified the Re_R2007 scheme's advantages. Finally, in comparison with other global advection schemes, the Re_R2007 scheme was competitive in terms of accuracy and flow independence. An encouraging possibility for the application of the Re_R2007 scheme to the GRAPES model is provided.
Bachand, P.A.M.; S. Bachand,; Fleck, Jacob A.; Anderson, Frank E.; Windham-Myers, Lisamarie
2014-01-01
The current state of science and engineering related to analyzing wetlands overlooks the importance of transpiration and risks data misinterpretation. In response, we developed hydrologic and mass budgets for agricultural wetlands using electrical conductivity (EC) as a natural conservative tracer. We developed simple differential equations that quantify evaporation and transpiration rates using flowrates and tracer concentrations atwetland inflows and outflows. We used two ideal reactormodel solutions, a continuous flowstirred tank reactor (CFSTR) and a plug flow reactor (PFR), to bracket real non-ideal systems. From those models, estimated transpiration ranged from 55% (CFSTR) to 74% (PFR) of total evapotranspiration (ET) rates, consistent with published values using standard methods and direct measurements. The PFR model more appropriately represents these nonideal agricultural wetlands in which check ponds are in series. Using a fluxmodel, we also developed an equation delineating the root zone depth at which diffusive dominated fluxes transition to advective dominated fluxes. This relationship is similar to the Peclet number that identifies the dominance of advective or diffusive fluxes in surface and groundwater transport. Using diffusion coefficients for inorganic mercury (Hg) and methylmercury (MeHg) we calculated that during high ET periods typical of summer, advective fluxes dominate root zone transport except in the top millimeters below the sediment–water interface. The transition depth has diel and seasonal trends, tracking those of ET. Neglecting this pathway has profound implications: misallocating loads along different hydrologic pathways; misinterpreting seasonal and diel water quality trends; confounding Fick's First Law calculations when determining diffusion fluxes using pore water concentration data; and misinterpreting biogeochemicalmechanisms affecting dissolved constituent cycling in the root zone. In addition,our understanding of internal
Mudunuru, M. K.; Nakshatrala, K. B.
2016-01-01
We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balance property. The proposed methodology is valid on general computational grids, can handle heterogeneous anisotropic media, and provides accurate numerical solutions even for very high Péclet numbers. The significant contribution of this paper is to incorporate advection (which makes the spatial part of the differential operator non-self-adjoint) into the non-negative computational framework, and overcome numerical challenges associated with advection. We employ low-order mixed finite element formulations based on least-squares formalism, and enforce explicit constraints on the discrete problem to meet the desired properties. The resulting constrained discrete problem belongs to convex quadratic programming for which a unique solution exists. Maximum principles and the non-negative constraint give rise to bound constraints while element-wise species balance gives rise to equality constraints. The resulting convex quadratic programming problems are solved using an interior-point algorithm. Several numerical results pertaining to advection-dominated problems are presented to illustrate the robustness, convergence, and the overall performance of the proposed computational framework.
Summertime influences of tidal energy advection on the surface energy balance in a mangrove forest
Directory of Open Access Journals (Sweden)
J. G. Barr
2013-01-01
Full Text Available Mangrove forests are ecosystems susceptible to changing water levels and temperatures due to climate change as well as perturbations resulting from tropical storms. Numerical models can be used to project mangrove forest responses to regional and global environmental changes, and the reliability of these models depends on surface energy balance closure. However, for tidal ecosystems, the surface energy balance is complex because the energy transport associated with tidal activity remains poorly understood. This study aimed to quantify impacts of tidal flows on energy dynamics within a mangrove ecosystem. To address the research objective, an intensive 10-day study was conducted in a mangrove forest located along the Shark River in the Everglades National Park, FL, USA. Forest–atmosphere turbulent exchanges of energy were quantified with an eddy covariance system installed on a 30-m-tall flux tower. Energy transport associated with tidal activity was calculated based on a coupled mass and energy balance approach. The mass balance included tidal flows and accumulation of water on the forest floor. The energy balance included temporal changes in enthalpy, resulting from tidal flows and temperature changes in the water column. By serving as a net sink or a source of available energy, flood waters reduced the impact of high radiational loads on the mangrove forest. Also, the regression slope of available energy versus sink terms increased from 0.730 to 0.754 and from 0.798 to 0.857, including total enthalpy change in the water column in the surface energy balance for 30-min periods and daily daytime sums, respectively. Results indicated that tidal inundation provides an important mechanism for heat removal and that tidal exchange should be considered in surface energy budgets of coastal ecosystems. Results also demonstrated the importance of including tidal energy advection in mangrove biophysical models that are used for predicting ecosystem
1987-01-01
Renewed interest in natural laminar flow (NLF) had rekindled designer concern that manufacuring deviations may destroy the effectiveness of NLF for an operational aircraft. Experiments are summarized that attemtped to measure total drag changes associated with three different wing surface conditions on an aircraft typical of current general aviation high performance singles. The speed power technique was first used in an attempt to quantify the changes in total drag. Predicted and measured boundary layer transition locations for three different wing surface conditions were also compared, using two different forms of flow visualization. The three flight test phases included: assessment of an unpainted airframe, flight tests of the same aircraft after painstakingly filling and sanding the wings to design contours, and similar measurement after this aricraft was painted. In each flight phase, transition locations were monitored using with sublimating chemicals or pigmented oil. Two-dimensional drag coefficients were estimated using the Eppler-Somers code and measured with a wake rake in a method very similar to Jones' pitot traverse method. The net change in two-dimensional drag coefficient was approximately 20 counts between the unpainted aircraft and the hand-smoothed aircraft for typical cruise flight conditions.
Icardi, Matteo
2014-09-01
The inhomogeneous generalized population balance equation, which is discretized with the direct quadrature method of moment (DQMOM), is solved to predict the bubble size distribution (BSD) in a vertical pipe flow. The proposed model is compared with a more classical approach where bubbles are characterized with a constant mean size. The turbulent two-phase flow field, which is modeled using a Reynolds-Averaged Navier-Stokes equation approach, is assumed to be in local equilibrium, thus the relative gas and liquid (slip) velocities can be calculated with the algebraic slip model, thereby accounting for the drag, lift, and lubrication forces. The complex relationship between the bubble size distribution and the resulting forces is described accurately by the DQMOM. Each quadrature node and weight represents a class of bubbles with characteristic size and number density, which change dynamically in time and space to preserve the first moments of the BSD. The predictions obtained are validated against previously published experimental data, thereby demonstrating the advantages of this approach for large-scale systems as well as suggesting future extensions to long piping systems and more complex geometries. © 2014 Elsevier Inc.
Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1994-01-01
In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
Unstable mass-outflows in geometrically thick accretion flows around black holes
Okuda, Toru
2015-01-01
Accretion flows around black holes generally result in mass-outflows that exhibit irregular behavior quite often. Using 2D time-dependent hydrodynamical calculations, we show that the mass-outflow is unstable in the cases of thick accretion flows such as the low angular momentum accretion flow and the advection-dominated accretion flow. For the low angular momentum flow, the inward accreting matter on the equatorial plane interacts with the outflowing gas along the rotational axis and the centrifugally supported oblique shock is formed at the interface of both the flows, when the viscosity parameter $\\alpha$ is as small as $\\alpha \\le 10^{-3}$. The hot and rarefied blobs, which result in the eruptive mass-outflow, are generated in the inner shocked region and grow up toward the outer boundary. The advection-dominated accretion flow attains finally in the form of a torus disc with the inner edge of the disc at $3R_{\\rm g} \\le r \\le 6R_{\\rm g}$ and the center at $6R_ {\\rm g} \\le r \\le 10R_{\\rm g}$, and a series...
The contiguous domains of Arctic Ocean advection: Trails of life and death
Wassmann, P.; Kosobokova, K. N.; Slagstad, D.; Drinkwater, K. F.; Hopcroft, R. R.; Moore, S. E.; Ellingsen, I.; Nelson, R. J.; Carmack, E.; Popova, E.; Berge, J.
2015-12-01
The central Arctic Ocean is not isolated, but tightly connected to the northern Pacific and Atlantic Oceans. Advection of nutrient-, detritus- and plankton-rich waters into the Arctic Ocean forms lengthy contiguous domains that connect subarctic with the arctic biota, supporting both primary production and higher trophic level consumers. In turn, the Arctic influences the physical, chemical and biological oceanography of adjacent subarctic waters through southward fluxes. However, exports of biomass out of the Arctic Ocean into both the Pacific and Atlantic Oceans are thought to be far smaller than the northward influx. Thus, Arctic Ocean ecosystems are net biomass beneficiaries through advection. The biotic impact of Atlantic- and Pacific-origin taxa in arctic waters depends on the total supply of allochthonously-produced biomass, their ability to survive as adults and their (unsuccessful) reproduction in the new environment. Thus, advective transport can be thought of as trails of life and death in the Arctic Ocean. Through direct and indirect (mammal stomachs, models) observations this overview presents information about the advection and fate of zooplankton in the Arctic Ocean, now and in the future. The main zooplankton organisms subjected to advection into and inside the Arctic Ocean are (a) oceanic expatriates of boreal Atlantic and Pacific origin, (b) oceanic Arctic residents and (c) neritic Arctic expatriates. As compared to the Pacific gateway the advective supply of zooplankton biomass through the Atlantic gateways is 2-3 times higher. Advection characterises how the main planktonic organisms interact along the contiguous domains and shows how the subarctic production regimes fuel life in the Arctic Ocean. The main differences in the advective regimes through the Pacific and Atlantic gateways are presented. The Arctic Ocean is, at least in some regions, a net heterotrophic ocean that - during the foreseeable global warming trend - will more and more rely
Seirin Lee, Sungrim; Shibata, Tatsuo
2015-10-07
Anterior-Posterior (AP) polarity formation of cell membrane proteins plays a crucial role in determining cell asymmetry, which depends not only on the several genetic process but also biochemical and biophysical interactions. The mechanism of AP formation of Caenorhabditis elegans embryo is characterized into the three processes: (i) membrane association and dissociation of posterior and anterior proteins, (ii) diffusion into the membrane and cytosol, and (iii) active cortical and cytoplasmic flows induced by the contraction of the acto-myosin cortex. We explored the mechanism of symmetry breaking and AP polarity formation using self-recruitment model of posterior proteins. We found that the AP polarity pattern is established over wide range in the total mass of polarity proteins and the diffusion ratio in the cytosol to the membrane. We also showed that the advective transport in both membrane and cytosol during the establishment phase affects optimal time interval of establishment and positioning of the posterior domain, and plays a role to increase the robustness in the AP polarity formation by reducing the number of posterior domains for the sensitivity of initial conditions. We also demonstrated that a proper ratio of the total mass to cell size robustly regulate the length scale of the posterior domain.
The role of a delay time on the spatial structure of chaotically advected reactive scalars
Tzella, Alexandra
2009-01-01
The stationary-state spatial structure of reacting scalar fields, chaotically advected by a two-dimensional large-scale flow, is examined for the case for which the reaction equations contain delay terms. Previous theoretical investigations have shown that, in the absence of delay terms and in a regime where diffusion can be neglected (large P\\'eclet number), the emergent spatial structures are filamental and characterized by a single scaling regime with a H\\"older exponent that depends on the rate of convergence of the reactive processes and the strength of the stirring measured by the average stretching rate. In the presence of delay terms, we show that for sufficiently small scales all interacting fields should share the same spatial structure, as found in the absence of delay terms. Depending on the strength of the stirring and the magnitude of the delay time, two further scaling regimes that are unique to the delay system may appear at intermediate length scales. An expression for the transition length s...
Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence
Schekochihin, A A; Highcock, E G; Dellar, P J; Dorland, W; Hammett, G W
2015-01-01
A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g., drift-wave turbulence driven by temperature gradients) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating ExB flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. A consistent theory is constructed in which very little free energy leaks into high velocity moments of the distribution, rendering the turbulent cascade in the energetically relevant part of the wave-number space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also i...
Tomography-based monitoring of isothermal snow metamorphism under advective conditions
Directory of Open Access Journals (Sweden)
P. P. Ebner
2015-02-01
Full Text Available Time-lapse X-ray micro-tomography was used to investigate the structural dynamics of isothermal snow metamorphism exposed to an advective airflow. Diffusion and advection across the snow pores were analysed in controlled laboratory experiments. The 3-D digital geometry obtained by tomographic scans was used in direct pore-level numerical simulations to determine the effective transport properties. The results showed that isothermal advection with saturated air have no influence on the coarsening rate that is typical for isothermal snow metamorphism. Diffusion originating in the Kelvin effect between snow structures dominates and is the main transport process in isothermal snow packs.
Because the Surface Energy Balance Algorithm for Land (SEBAL) tends to underestimate ET under conditions of advection, the model was modified by incorporating an advection component as part of the energy usable for crop evapotranspiration (ET). The modification involved the estimation of advected en...
Gwo, J. P.; Jardine, P. M.; Wilson, G. V.; Yeh, G. T.
1996-03-01
Waste management problems for shallow land burial facilities in the humid eastern United States are usually complicated by slow but continuous movement of wastes through the soil matrix and discrete but rapid pulses of wastes through macropores and fractures. Multiple-pore-region models employed to describe flow and solute transport in the soils usually consist of multiple mass transfer coefficients that cannot be measured experimentally, and their effects on subsurface mass transport are poorly understood. The objective of this research was to study the individual and concurrent effects of interaggregate advection and diffusion on mass transport in a structured soil. The interactions of these two mass transfer processes and local solute concentration equilibrium are examined for a heterogeneous soil. Pore region water retention, hydraulic conductivity, and dispersivities, obtained from independent measurements and published calibration results, were used to test a novel three-pore-region, one-dimensional numerical model. Advective and diffusive mass transfer coefficients were estimated using mass transfer equations and fracture spacings published in the literature. The mass transfer coefficients were then varied systematically, and the sensitivity of local fluid pressure and solute concentration nonequilibrium to interregion mass transfer were analyzed. Our results indicated that time-dependent interaggregate advection and diffusion were important processes controlling solute mobility in heterogeneous media. Under transient flow conditions, interaggregate advection may reduce the significance of interaggregate diffusion that otherwise dominates interaggregate mass transfer under steady state conditions. Nonetheless, the equilibrium of local solute concentrations was 20 times more sensitive to diffusive mass transfer than to advective mass transfer, which suggests that site characterization efforts should be directed more toward the former process. Unfortunately
Rodríguez-Escales, P.; FernÃ ndez-Garcia, D.; Drechsel, J.; Folch, A.; Sanchez-Vila, X.
2017-05-01
Improving degradation rates of emerging organic compounds (EOCs) in groundwater is still a challenge. Although their degradation is not fully understood, it has been observed that some substances are preferably degraded under specific redox conditions. The coupling of Managed Aquifer Recharge with soil aquifer remediation treatment, by placing a reactive layer containing organic matter at the bottom of the infiltration pond, is a promising technology to improve the rate of degradation of EOCs. Its success is based on assuming that recharged water and groundwater get well mixed, which is not always true. It has been demonstrated that mixing can be enhanced by inducing chaotic advection through extraction-injection-engineering. In this work, we analyze how chaotic advection might enhance the spreading of redox conditions with the final aim of improving degradation of a mix of benzotriazoles: benzotriazole, 5-methyl-benzotriazole, and 5-chloro-benzotriazole. The degradation of the first two compounds was fastest under aerobic conditions whereas the third compound was best degraded under denitrification conditions. We developed a reactive transport model that describes how a recharged water rich in organic matter mixes with groundwater, how this organic matter is oxidized by different electron acceptors, and how the benzotriazoles are degraded attending for the redox state. The model was tested in different scenarios of recharge, both in homogenous and in heterogenous media. It was found that chaotic flow increases the spreading of the plume of recharged water. Consequently, different redox conditions coexist at a given time, facilitating the degradation of EOCs.
Ballester, Joan; Bordoni, Simona; Petrova, Desislava; Rodó, Xavier
2016-06-01
The oscillatory nature of El Niño-Southern Oscillation results from an intricate superposition of near-equilibrium balances and out-of-phase disequilibrium processes between the ocean and the atmosphere. The main objective of the present work is to perform an exhaustive spatiotemporal analysis of the upper ocean heat budget in an ensemble of state-of-the-art ocean assimilation products. We put specific emphasis on the ocean heat advection mechanisms, and their representation in individual ensemble members and in the different stages of the ENSO oscillation leading to EN events. Our analyses consistently show that the initial subsurface warming in the western equatorial Pacific is advected to the central Pacific by the equatorial undercurrent, which, together with the equatorward advection associated with anomalies in both the meridional temperature gradient and circulation at the level of the thermocline, explains the heat buildup in the central Pacific during the recharge phase. We also find that the recharge phase is characterized by an increase of meridional tilting of the thermocline, as well as a southward upper-ocean cross-equatorial mass transport resulting from Ekman-induced anomalous vertical motion in the off-equatorial regions. Although differences between data sets are generally small, and anomalies tend to have the same sign, the differences in the magnitude of the meridional term are seen to be key for explaining the different propagation speed of the subsurface warming tendency along the thermocline. The only exception is GECCO, which does not produce the patterns of meridional surface Ekman divergence (subsurface Sverdrup convergence) in the western and central equatorial Pacific.
Energy Technology Data Exchange (ETDEWEB)
Karniadakis, George Em [Brown University
2014-03-11
The main objective of this project is to develop new computational tools for uncertainty quantifica- tion (UQ) of systems governed by stochastic partial differential equations (SPDEs) with applications to advection-diffusion-reaction systems. We pursue two complementary approaches: (1) generalized polynomial chaos and its extensions and (2) a new theory on deriving PDF equations for systems subject to color noise. The focus of the current work is on high-dimensional systems involving tens or hundreds of uncertain parameters.
Boundary value problemfor multidimensional fractional advection-dispersion equation
Directory of Open Access Journals (Sweden)
Khasambiev Mokhammad Vakhaevich
2015-05-01
authors first considered the boundary value problem for stationary equation for mass transfer in super-diffusion conditions and abnormal advection. Then the solution of the problem is explicitly given. The solution is obtained by the Fourier’s method.The obtained results will be useful in liquid filtration theory in fractal medium and for modeling the temperature variations in the heated bar.
Rigorous upper bounds for fluid and plasma transport due to passive advection
Energy Technology Data Exchange (ETDEWEB)
Krommes, J.A.; Smith, R.A.; Kim, C.B.
1987-07-01
The formulation of variational principles for transport due to passive advection is described. A detailed account of the work has been published elsewhere. In the present paper, the motivations, philosophy, and implications of the method are briefly discussed. 15 refs.
Advective surface velocity in the north west Pacific derived from NOAA AVHRR images
Digital Repository Service at National Institute of Oceanography (India)
Pankajakshan, T.; Akiyama, M.; Okada, Y.; Sugimori, Y.
Using sequential AVHRR images in November 1983, nearsurface advective velocities are derived in the region Kuroshio south of Japan. For deriving the velocities two methods are used. One is the Method of Cross Correlation (MCC), using image pair...
Sanford, Ward E.; Niel Plummer, L.; Casile, Gerolamo; Busenberg, Ed; Nelms, David L.; Schlosser, Peter
2017-06-01
Dual-domain transport is an alternative conceptual and mathematical paradigm to advection-dispersion for describing the movement of dissolved constituents in groundwater. Here we test the use of a dual-domain algorithm combined with advective pathline tracking to help reconcile environmental tracer concentrations measured in springs within the Shenandoah Valley, USA. The approach also allows for the estimation of the three dual-domain parameters: mobile porosity, immobile porosity, and a domain exchange rate constant. Concentrations of CFC-113, SF6, 3H, and 3He were measured at 28 springs emanating from carbonate rocks. The different tracers give three different mean composite piston-flow ages for all the springs that vary from 5 to 18 years. Here we compare four algorithms that interpret the tracer concentrations in terms of groundwater age: piston flow, old-fraction mixing, advective-flow path modeling, and dual-domain modeling. Whereas the second two algorithms made slight improvements over piston flow at reconciling the disparate piston-flow age estimates, the dual-domain algorithm gave a very marked improvement. Optimal values for the three transport parameters were also obtained, although the immobile porosity value was not well constrained. Parameter correlation and sensitivities were calculated to help quantify the uncertainty. Although some correlation exists between the three parameters being estimated, a watershed simulation of a pollutant breakthrough to a local stream illustrates that the estimated transport parameters can still substantially help to constrain and predict the nature and timing of solute transport. The combined use of multiple environmental tracers with this dual-domain approach could be applicable in a wide variety of fractured-rock settings.
D'Ovidio, Mirko
2012-01-01
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular we obtain solutions written in terms of Wright functions by exploiting operational rules involving the shift operator. We also consider fractional advection diffusion equations involving fractional powers of the negative Laplace operator and directional derivatives of fractional order and discuss the probabilistic interpretations of solutions.
Tomography-based monitoring of isothermal snow metamorphism under advective conditions
P. P. Ebner; M. Schneebeli; A. Steinfeld
2015-01-01
Time-lapse X-ray microtomography was used to investigate the structural dynamics of isothermal snow metamorphism exposed to an advective airflow. The effect of diffusion and advection across the snow pores on the snow microstructure were analysed in controlled laboratory experiments and possible effects on natural snowpacks discussed. The 3-D digital geometry obtained by tomographic scans was used in direct pore-level numerical simulations to determine the effective permeabi...
Endeve, Eirik; Xing, Yulong; Mezzacappa, Anthony
2014-01-01
We extend the positivity-preserving method of Zhang & Shu (2010, JCP, 229, 3091-3120) to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stability-preserving, Runge-Kutta (SSP-RK) time integration. Special care in taken to ensure that the method preserves strict bounds for the phase space distribution function $f$; i.e., $f\\in[0,1]$. The combination of suitable CFL conditions and the use of the high-order limiter proposed in Zhang & Shu (2010) is sufficient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergence-free property of ...
Guihéneuf, N.; Boisson, A.; Bour, O.; Le Borgne, T.; Marechal, J.; Nigon, B.; Wajiddudin, M.; Ahmed, S.
2013-12-01
The prediction of transport in weathered and fractured rocks is critical as it represents the primary control of contaminant transfer from the subsurface in many parts of the world. This is the case in Southern India, where the subsurface is composed mainly of weathered and fractured granite and where the overexploitation of the groundwater resource since the 70's has led to high water table depletion and strong groundwater quality deterioration. One key issue for modelling transport in such systems is to quantify the respective role of advective heterogeneities and matrix diffusion, which can both lead to strongly non Fickian transport properties. We investigate this question by analysing tracer test experiments performed under different flow configurations at a fractured granite experimental site located in Andhra Pradesh (India). We performed both convergent and push-pull tracer tests within the same fracture and at different scales. Three convergent tracer tests were performed with a solution of fluorescein for different pumping rate and for different distances between injection and pumping boreholes: 6, 30 and 41 meters. To evaluate diffusive process, we performed two long-duration push-pull tests (push time of 3 hours) with a solution of two conservative tracers of different diffusion coefficient (fluorescein and sodium chloride). We performed also six others push-pull tests with only fluorescein but for a variable push times of 14 min and 55 min with or without resting time of about 60 min. The late-time behaviour on the breakthrough curves (BTCs) obtained for all convergent tracer tests showed a power-law slope of -2. Two of them showed an inflexion in the BTCs suggesting the existence of two independent flow paths and thus a highly channelized flow. The long-duration push-pull tests showed similar late-time behaviour with a power-law slope of -2.2 for both tracers. The six others push-pull tests showed a variation of power-law exponent from -3 to -2
Gutiérrez Vargas, Juan Carlos; Gutiérrez Vargas, Randall; Ureña Bonilla, Pedro
2013-01-01
The purpose of this study was to describe and analyze the relationship between self-efficacy, pre-competitive anxiety and flow feeling in male and female handball team players from the Costa Rica national teams. Participants were 28 players (14 male and 14 female) from both teams. The scales of general self-efficacy, flow feeling and competitive anxiety were used to collect data. The average score in relation to self-efficacy was high (> 8.40). Regarding flow sensation, the average scores we...
Suresh, Chintalapudi V.; Sivanagaraju, Sirigiri; Reddy, P. Umapathi
2016-09-01
In power system restructuring, pricing the electrical power plays a vital role in cost allocation between suppliers and consumers. In optimal power dispatch problem, not only the cost of active power generation but also the costs of reactive power generated by the generators, shunt capacitors, transmission losses and device investment costs should be considered. In this paper, a more realistic multi-fuel total cost objective is formulated by considering all the above mentioned costs. As the characteristics of reactive power cost curve are similar to that of active power cost curve, a non-convex reactive power cost function is formulated. The formulated cost function is optimized by satisfying equality, in-equality and practical constraints and also device limits using the proposed uniform distributed two-stage particle swarm optimization. In this paper, power injection model of generalized unified power flow controller (GUPFC) including converter switching losses is presented. The proposed objective functions are optimized in the presence of UPFC and GUPFC and finally suitable device is identified for the standard IEEE-30 bus test system.
DEFF Research Database (Denmark)
Celia, Michael A.; Binning, Philip John
1992-01-01
. Numerical results also demonstrate the potential importance of air phase advection when considering contaminant transport in unsaturated soils. Comparison to several other numerical algorithms shows that the modified Picard approach offers robust, mass conservative solutions to the general equations......A numerical algorithm for simulation of two-phase flow in porous media is presented. The algorithm is based on a modified Picard linearization of the governing equations of flow, coupled with a lumped finite element approximation in space and dynamic time step control. Numerical results indicate...... that the algorithm produces solutions that are essentially mass conservative and oscillation free, even in the presence of steep infiltrating fronts. When the algorithm is applied to the case of air and water flow in unsaturated soils, numerical results confirm the conditions under which Richards's equation is valid...
Harnik, Nili; Garfinkel, Chaim
2016-04-01
Global warming is expected raise the number of warm spells and lower the number of cold spells, by simply shifting of the near-surface temperature probability distribution to warmer temperatures. However, changes in the shape of distribution strongly affect how the occurrence of temperature extremes will change. Hence, understanding the processes shaping the spatial and statistical distribution of temperature variations and extremes in the present climate is central to understanding how temperature extremes might vary in the future. Using meteorological reanalyses data we show that the distribution of near-surface temperature variability is non-Gaussian, and consistent with this, extreme warm anomalies occur preferentially poleward of the location of extreme cold anomalies. The non-Guassianity evident in reanalysis data is also found in a set of dry General Circulation Model runs in which the jet is forced at different latitudes, and the location of extremes is influenced by the location of the jet stream. Using a simple model of Lagrangian temperature advection, we investigate the role of synoptic dynamics in causing this non Gaussianity. The meridional shifting between cold and warm extremes, and the related non-Gaussianity are traced back to the synoptic evolution leading up to cold and warm extreme events. We find that the meridional movement of synotpic systems, as well as nonlinear temperature advection are both of crucial importance for the warm/cold asymmetry in the latitudinal distribution of the temperature extremes. The possible implications for future changes in extremes will be briefly discussed.
Dal Gesso, Sara; Neggers, Roel
2017-04-01
Boundary-layer clouds remain the major contributor to the inter-model spread in future climate predictions. Although light has been shed on the low-level cloud feedback, much remains to be understood about the physical mechanisms at the basis of the response of these clouds to climate warming. In the present study, EC-EARTH Single Column Model (SCM) is used to explore the boundary-layer cloud-climate feedback by imposing a Radiative-Advective Equilibrium, namely a balance between the radiative cooling and the advection of warm air. 30-year simulations are performed with the SCM forced by high-frequency cfSites outputs of the CMIP5 simulations of the host General Circulation Model (GCM) for both the AMIP and AMIP4K experiments. As this study exclusively focuses on marine low-level cloud regimes, the simulations are performed at the Barbados Cloud Observatory in the so-called "dry period", when the large-scale forcing are representative of subtropical marine trade-wind conditions. A first step is to assess how representative long-term SCM simulations are of their host GCM. Subsequently, the SCM is forced by different GCMs within the same framework. In this way, the contribution of the physical parameterization to the boundary-layer cloud feedback is isolated from the dynamics, and systematically evaluated. Finally, a procedure to integrate Large-Eddy Simulations and observations into this framework is discussed.
Badrot-Nico, Fabiola; Brissaud, François; Guinot, Vincent
2007-09-01
A finite volume upwind numerical scheme for the solution of the linear advection equation in multiple dimensions on Cartesian grids is presented. The small-stencil, Modified Discontinuous Profile Method (MDPM) uses a sub-cell piecewise constant reconstruction and additional information at the cell interfaces, rather than a spatial extension of the stencil as in usual methods. This paper presents the MDPM profile reconstruction method in one dimension and its generalization and algorithm to two- and three-dimensional problems. The method is extended to the advection-diffusion equation in multiple dimensions. The MDPM is tested against the MUSCL scheme on two- and three-dimensional test cases. It is shown to give high-quality results for sharp gradients problems, although some scattering appears. For smooth gradients, extreme values are best preserved with the MDPM than with the MUSCL scheme, while the MDPM does not maintain the smoothness of the original shape as well as the MUSCL scheme. However the MDPM is proved to be more efficient on coarse grids in terms of error and CPU time, while on fine grids the MUSCL scheme provides a better accuracy at a lower CPU.
Scheck, L; Foglizzo, T; Kifonidis, K
2007-01-01
By 2D hydrodynamic simulations including a detailed equation of state and neutrino transport, we investigate the interplay between different non-radial hydrodynamic instabilities that play a role during the postbounce accretion phase of collapsing stellar cores. The convective mode of instability, which is driven by negative entropy gradients caused by neutrino heating or by time variations of the shock strength, can be identified clearly by the development of typical Rayleigh-Taylor mushrooms. However, in cases where the gas in the postshock region is rapidly advected towards the gain radius, the growth of such a buoyancy instability can be suppressed. In such a situation the shocked flow nevertheless can develop non-radial asymmetry with an oscillatory growth of the amplitude. This phenomenon was previously termed ``standing accretion shock instability'' (SASI) by Blondin et al. (2003). It is shown here that the oscillation period of the SASI observed in our simulations agrees well with the one estimated fo...
DEFF Research Database (Denmark)
In this paper, single wake characteristics have been studied both experimentally and numerically. Firstly, the wake is studied experimentally using full-scale measurements from an adapted focused pulsed lidar system, which potentially gives more insight into the wake dynamics as compared to class...... using the EllipSys3D flow solver using Large Eddy Simulation (LES) and Actuator Line Technique (ACL) to model the rotor. Discrepancies due to the uncertainties on the wake advection velocity are observed and discussed....... of the wake, and it is compared to the predictions from the Dynamic Wake Meandering model, for a selected 10 minutes dataset. Secondly, the average wake expansion in the fixed frame of reference is determined from measurements and compared to results from CFD simulations. The CFD simulations were conducted...
DEFF Research Database (Denmark)
Machefaux, Ewan; Larsen, Gunner Chr.; Troldborg, Niels;
2013-01-01
In this paper, single wake characteristics have been studied both experimentally and numerically. Firstly, the wake is studied experimentally using full-scale measurements from an adapted focused pulsed lidar system, which potentially gives more insight into the wake dynamics as compared to class...... using the EllipSys3D flow solver using Large Eddy Simulation (LES) and Actuator Line Technique (ACL) to model the rotor. Discrepancies due to the uncertainties on the wake advection velocity are observed and discussed....... of the wake, and it is compared to the predictions from the Dynamic Wake Meandering model, for a selected 10 minutes dataset. Secondly, the average wake expansion in the fixed frame of reference is determined from measurements and compared to results from CFD simulations. The CFD simulations were conducted...
Otterman, J.; Ardizzone, J.; Atlas, R.; Demaree, G.; Huth, R.; Jaagus, J.; Koslowsky, D.; Przybylak, R.; Wos, A.; Atlas, Robert (Technical Monitor)
1999-01-01
It is well recognized that advection from the North Atlantic has a profound effect on the climatic conditions in central Europe. A new dataset of the ocean-surface winds, derived from the Special Sensor Microwave Imager, SSM/1, is now available. This satellite instrument measures the wind speed, but not the direction. However, variational analysis developed at the Data Assimilation Office, NASA Goddard Space Flight Center, by combining the SSM/I measurements with wind vectors measured from ships, etc., produced global maps of the ocean surface winds suitable for climate analysis. From this SSM/I dataset, a specific index I(sub na) of the North Atlantic surface winds has been developed, which pertinently quantifies the low-level advection into central Europe. For a selected time-period, the index I(sub na) reports the average of the amplitude of the wind, averaging only the speed when the direction is from the southwest (when the wind is from another direction, the contribution counts to the average as zero speed). Strong correlations were found between February I(sub na) and the surface air temperatures in Europe 50-60 deg N. In the present study, we present the correlations between I(sub na) and temperature I(sub s), and also the sensitivity of T(sub s), to an increase in I(sub na), in various seasons and various regions. We specifically analyze the flow of maritime-air from the North Atlantic that produced two extraordinary warm periods: February 1990, and early-winter 2000/2001. The very cold December 2001 was clearly due to a northerly flow. Our conclusion is that the SSM/I dataset is very useful for providing insight to the forcing of climatic fluctuations in Europe.
Theoretical model of blood flow measurement by diffuse correlation spectroscopy
Sakadžić, Sava; Boas, David A.; Carp, Stefan
2017-02-01
Diffuse correlation spectroscopy (DCS) is a noninvasive method to quantify tissue perfusion from measurements of the intensity temporal autocorrelation function of diffusely scattered light. However, DCS autocorrelation function measurements in tissue better match theoretical predictions based on the diffusive motion of the scatterers than those based on a model where the advective nature of blood flow dominates the stochastic properties of the scattered light. We have recently shown using Monte Carlo (MC) simulations and assuming a simplistic vascular geometry and laminar flow profile that the diffusive nature of the DCS autocorrelation function decay is likely a result of the shear-induced diffusion of the red blood cells. Here, we provide theoretical derivations supporting and generalizing the previous MC results. Based on the theory of diffusing-wave spectroscopy, we derive an expression for the autocorrelation function along the photon path through a vessel that takes into account both diffusive and advective scatterer motion, and we provide the solution for the DCS autocorrelation function in a semi-infinite geometry. We also derive the correlation diffusion and correlation transfer equation, which can be applied for an arbitrary sample geometry. Further, we propose a method to take into account realistic vascular morphology and flow profile.
National Research Council Canada - National Science Library
Rex, S; Meyer, P. T; Baumert, J.-H; Rossaint, R; Fries, M; Büll, U; Schaefer, W. M
2008-01-01
Background The effects of xenon on regional cerebral blood flow (rCBF) are controversial. Moreover, the precise sites of action at which xenon exerts its effects in the human brain remain to be established...
Directory of Open Access Journals (Sweden)
M. Sofiev
2015-03-01
Full Text Available The paper presents dynamic cores v.4 and v.5 of the System for Integrated modeLling of Atmospheric coMposition SILAM v.5.5 based on the advection algorithm of Michael Galperin. This advection routine, so far weakly presented in international literature, is non-diffusive, positively defined, stable with regard to Courant number significantly above one, and very efficient computationally. For the first time, we present a rigorous description of its original version, along with several updates that improve its monotonicity and allow applications to long-living species in conditions of complex atmospheric flows. The other extension allows the scheme application to dynamics of aerosol spectra. The scheme is accompanied with the previously developed vertical diffusion algorithm, which encapsulates the dry deposition process as a boundary condition. Connection to chemical transformation modules is outlined, accounting for the specifics of transport scheme. Quality of the advection routine is evaluated using a large set of tests. The original approach has been previously compared with several classic algorithms widely used in operational models. The basic tests were repeated for the updated scheme, along with demanding global 2-D tests recently suggested in literature, which allowed positioning the scheme with regard to sophisticated state-of-the-art approaches. The model performance appeared close to the top of the list with very modest computational costs.
Intraseasonal Variability in an Aquaplanet General Circulation Model
Directory of Open Access Journals (Sweden)
Adam H Sobel
2010-04-01
Full Text Available An aquaplanet atmospheric general circulation model simulation with a robust intraseasonal oscillation is analyzed. The SST boundary condition resembles the observed December-April average with continents omitted, although with the meridional SST gradient reduced to be one-quarter of that observed poleward of 10 ̊ latitude. Slow, regular eastward propagation at 5 m s21 in winds and precipitation with amplitude greater than that in the observed MJO is clearly identified in unfiltered fields. Local precipitation rate is a strongly non-linear and increasing function of column precipitable water, as in observations. The model intraseasonal oscillation resembles a moisture mode that is destabilized by wind-evaporation feedback, and that propagates eastward through advection of anomalous humidity by the sum of perturbation winds and mean westerly flow. A series of sensitivity experiments are conducted to test hypothesized mechanisms. A mechanism denial experiment in which intraseasonal latent heat flux variability is removed largely eliminates intraseasonal wind and precipitation variability. Reducing the lower-troposphere westerly flow in the warm pool by reducing the zonal SST gradient slows eastward propagation, supporting the importance of horizontal advection by the low-level wind to eastward propagation. A zonally symmetric SST basic state produces weak and unrealistic intraseasonal variability between 30 and 90 day timescales, indicating the importance of mean low-level westerly winds and hence a realistic phase relationship between precipitation and surface flux anomalies for producing realistic tropical intraseasonal variability.
Planktonic interactions and chaotic advection in Langmuir circulation
DEFF Research Database (Denmark)
Bees, Martin Alan; Mezic, I.; McGlade, J.
1998-01-01
The role of unsteady laminar flows for planktonic communities is investigated. Langmuir circulation is used, as a typical medium-scale structure, to illustrate mechanisms for the generation of plankton patches. Two behaviours are evident: chaotic regions that help to spread plankton and locally c...... coherent regions that do not mix with the chaotic regions and which persist for long periods of time. The interaction of populations of phytoplankton with zooplankton is discussed, taking into account the variations in plankton buoyancy....
An approximate calculation of advective gas-phase transport of 14C at Yucca Mountain, Nevada
Knapp, R. B.
1990-01-01
A quasilinear partial differential equation, which describes gas-phase transport of a 14C kinematic wave through a porous medium, is derived, its sensitivity to system variables is analyzed and it is applied to one possible release scenarion at the porposed Yucca Mountain, Nevada high-level radioactive waste repository. Advection, isotope exchange between CO 2 in a flowing gas phase and HCO 3- in a static aqueous phase, and radioactive decay are incorporated. The governing equation is solved analytically by the method of characteristics. The mass fraction of 14C in the gas phase,X 14g, is controlled by radioactive decay. The relatively long half-line of 14C, about 5720 years, and the relatively shallow proposed burial depth of the radioactive waste, about 350m, requires significant retardation of the 14C wave velocity for significant reduction in X 14g. 14C wave velocity is most sensitive to temperature and pH which control the distribution of total carbon between gas and liquid phase; the greater the partitioning of carbon into the liquid phase, the greater the retardation of the 14C wave velocity and the greater the ultimate reduction in X 14g from initial conditions. Partitioning of total carbon into the liquid phase is greatest at low temperatures, 8. Increasing water saturation also tends to retard 14C wave velocity but to a lesser extent. The governing equation has been applied using conditions that may possibly occur at the proposed Yucca Mountain repository. Calculations indicate that the 14C wave takes about 5900 years to reach the surface with a X 14g equal to 25 ppm. Diffusion and dispersion are not of major importance for these conditions. These calculations are approximate due to the number of assumptions involved. Discharge of 14C into the gas before the selected time would accelerate wave arrival and increase the amount of 14C reaching the surface.
Phase dependent advection-diffusion in drift wave - zonal flow turbulence
Moradi, Sara
2016-01-01
In plasma turbulence theory, due to the complexity of the system with many non-linearly interacting waves, the dynamics of the phases is often disregarded and the so-called random-phase approximation (RPA) is used assuming the existence of a Chirikov-like criterion for the onset of wave stochasticity. The dynamical amplitudes are represented as complex numbers, $\\psi = \\psi_r + i\\psi_i = ae^{i\\theta}$, with the amplitudes slowly varying whereas the phases are rapidly varying and, in particular, distributed uniformly over the interval $[0;2\\pi)$. However, one could expect that the phase dynamics can play a role in the self-organisation and the formation of coherent structures. In the same manner it is also expected that the RPA falls short to take coherent interaction between phases into account. In this work therefore, we studied the role of phase dynamics and the coupling of phases between different modes on the characteristic time evolution of the turbulent. We assume a simple turbulent system where the so-...
Signatures of Accretion Shocks in Broadband Spectrum of Advective Flows Around Black Holes
Mandal, S; Mandal, Samir; Chakrabarti, Sandip K.
2005-01-01
We compute the effects of the centrifugal pressure supported shock waves on the emitted spectrum from an accretion disk primarily consisting of low angular momentum matter. Electrons are very efficiently accelerated by the accretion shock and acquire power-law distribution. The accelerated particles in turn emit synchrotron radiation in presence of a stochastic magnetic field in equipartition with the gas. Efficient cooling of the electrons by these soft photons reduces its temperature in comparison to the protons. We explore the nature of the broadband spectra by using Comptonization, bremsstrahlung and synchrotron emission. We then show that there could be two crossing points in a broadband spectrum, one near $\\sim 10 keV$ and the other $\\sim 300-400$KeV.
Energy Technology Data Exchange (ETDEWEB)
Hao Wu; Peter Glarborg; Flemming Jappe Frandsen; Kim Dam-Johansen; Peter Arendt Jensen; Bo Sander [Technical University of Denmark, Lyngby (Denmark). Department of Chemical and Biochemical Engineering
2011-05-15
Co-combustion of a bituminous coal and a solid recovered fuel (SRF) was carried out in an entrained flow reactor, and the influence of additives such as NaCl, PVC, ammonium sulphate, and kaolinite was investigated. The experiments were carried out with SRF shares of 7.9 wt.%, 14.8 wt.% and 25 wt.%, respectively. The effect of additives was evaluated by maintaining the share of secondary fuel (mixture of SRF and additive) at 14.8 wt.%. The results showed that fuel burnout, NO and SO{sub 2} emission decreased with increasing share of SRF. The majority of the additives inhibited the burnout, except for NaCl which seemed to have a promoting effect. The impact of additives on NO emission was mostly insignificant, except for ammonium sulphate which greatly reduced NO emission. For SO{sub 2}, it was found that all of the additives increased the S-retention in ash. Analysis of the bulk composition of fly ash from different experiments indicated that the majority of S and Cl in the fuels were released to gas phase during combustion, whereas the K and Na in the fuels were mainly retained in ash in water insoluble form such as aluminosilicates or silicates. The addition of NaCl, PVC, and ammonium sulphate generally promoted the vaporization of Na and K, resulting in increased formation of water soluble alkalis such as alkali chlorides or sulphates. The vaporization degree of Na and K was found to be correlated during the experiments, suggesting an interaction between the vaporization of Na and K during combustion. By collecting deposits on an air-cooled probe, it was found that the ash deposition propensity in co-combustion decreased with increasing share of SRF. The addition of NaCl and PVC significantly increased the ash deposition propensity, whereas the addition of ammonium sulphate or kaolinite showed a slight reducing effect. 46 refs., 13 figs., 2 tabs.
Incompressible laminar flow through hollow fibers: a general study by means of a two-scale approach
Borsi, Iacopo; Farina, Angiolo; Fasano, Antonio
2011-08-01
We study the laminar flow of an incompressible Newtonian fluid in a hollow fiber, whose walls are porous. We write the Navier-Stokes equations for the flow in the inner channel and Darcy's law for the flow in the fiber, coupling them by means of the Beavers-Joseph condition which accounts for the (possible) slip at the membrane surface. Then, we introduce a small parameter {\\varepsilon ≪ 1} (the ratio between the radius and the length of the fiber) and expand all relevant quantities in powers of ɛ. Averaging over the fiber cross section, we find the velocity profiles for the longitudinal flow and for the cross-flow, and eventually, we determine the explicit expression of the permeability of the system. This work is also preliminary to the study of more complex systems comprising a large number of identical fibers (e.g., ultrafiltration modules and dialysis).
Energy Technology Data Exchange (ETDEWEB)
Belucz, Bernadett; Forgács-Dajka, Emese [Eötvös University, Department of Astronomy, 1518 Budapest, Pf. 32 (Hungary); Dikpati, Mausumi, E-mail: bbelucz@astro.elte.hu, E-mail: dikpati@ucar.edu [High Altitude Observatory, National Center for Atmospheric Research, 3080 Center Green, Boulder, CO 80307-3000 (United States)
2015-06-20
Babcock–Leighton type-solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock–Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that the presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in the butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of the butterfly wing to an antisolar type. A butterfly diagram constructed from the middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in latitude behaves distinctly differently in the two regimes, producing solar-like butterfly diagrams with fast cycles in the higher diffusivity regime, and complex branches in butterfly diagrams in the lower diffusivity regime. We also find that dynamo solutions for a four-celled pattern, two in radius and two in latitude, prefer to quickly relax to quadrupolar parity if the bottom flow speed is strong enough, of similar order of magnitude as the surface flow speed.
State Transitions of Black Hole Accretion Flows
Institute of Scientific and Technical Information of China (English)
卢炬甫; 潘刘彬
2001-01-01
We show that the thermal instability-triggered transition from the state of the Shakura-Sunyaev disc to the state of the advection-dominated accretion flow is possible for black hole accretion flows composed of two-temperature plasma with bremsstrahlung and synchrotron radiation and Comptonization.
Ghosh, Shubhrangshu; Banik, Prabir
2015-07-01
In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central
Convection-Dominated Accretion Flows with Radiative Cooling
Institute of Scientific and Technical Information of China (English)
LI Shuang-Liang; XUE Li; LU Ju-Fu
2007-01-01
@@ By numerically solving the set of basic equations describing black hole accretion flows with low accretion rates,we show that although the dynamical structure of these flows is essentially unaffected by radiative processes in comparison with the case in which the radiation is not considered, the radiative cooling can be more important than the advective cooling in the flow's convection-dominated zone, and this result may have implications to distinguish observationally convection-dominated accretion flows from advection-dominated accretion flows.
Evaporative loss from irrigated interrows in a highly advective semi-arid agricultural area
Agam, Nurit; Evett, Steven R.; Tolk, Judy A.; Kustas, William P.; Colaizzi, Paul D.; Alfieri, Joseph G.; McKee, Lynn G.; Copeland, Karen S.; Howell, Terry A.; Chávez, Jose L.
2012-12-01
Agricultural productivity has increased in the Texas High Plains at the cost of declining water tables, putting at risk the sustainability of the Ogallala Aquifer as a principal source of water for irrigated agriculture. This has led area producers to seek alternative practices that can increase water use efficiency (WUE) through more careful management of water. One potential way of improving WUE is by reducing soil evaporation (E), thus reducing overall evapotranspiration (ET). Before searching for ways to reduce E, it is first important to quantify E and understand the factors that determine its magnitude. The objectives of this study were (1) to quantify E throughout part of the growing season for irrigated cotton in a strongly advective semi-arid region; (2) to study the effects of LAI, days after irrigation, and measurement location within the row on the E/ET fraction; and (3) to study the ability of microlysimeter (ML) measures of E combined with sap flow gage measures of transpiration (T) to accurately estimate ET when compared with weighing lysimeter ET data and to assess the E/T ratio. The research was conducted in an irrigated cotton field at the Conservation & Production Research Laboratory of the USDA-ARS, Bushland, TX. ET was measured by a large weighing lysimeter, and E was measured by 10 microlysimeters that were deployed in two sets of 5 across the interrow. In addition, 10 heat balance sap flow gages were used to determine T. A moderately good agreement was found between the sum E + T and ET (SE = 1 mm or ˜10% of ET). It was found that E may account for >50% of ET during early stages of the growing season (LAI < 0.2), significantly decreasing with increase in LAI to values near 20% at peak LAI of three. Measurement location within the north-south interrows had a distinct effect on the diurnal pattern of E, with a shift in time of peak E from west to east, a pattern that was governed by the solar radiation reaching the soil surface. However, total
Coulombic interactions during advection-dominated transport of ions in porous media
Muniruzzaman, Muhammad; Stolze, Lucien; Rolle, Massimo
2017-04-01
Solute transport of charged species in porous media is significantly affected by the electrochemical migration term resulting from the charge-induced interactions among dissolved ions and with solid surfaces. Therefore, the characterization of such Coulombic interactions and their effect on multicomponent ionic transport is of critical importance for assessing the fate of charged solutes in porous media. In this work we present a detailed investigation of the electrochemical effects during conservative multicomponent ionic transport in homogeneous and heterogeneous domains by means of laboratory bench-scale experiments and numerical simulations. The investigation aims at quantifying the key role of small-scale electrostatic interactions in flow-through systems, especially when advection is the dominant mass-transfer process. Considering dilute solutions of strong electrolytes (e.g., MgCl2 and NaBr) we report results showing the important role of Coulombic interactions in the lateral displacement of the different ionic species for steady-state transport scenarios in which the solutions are continuously injected through different portions of the flow-through chamber [1, 2]. Successively, we focus our attention on transient transport and pulse injection of the electrolytes. In these experiments high-resolution spatial and temporal monitoring of the ions' concentrations (600 samples; 1800 concentration measurements), at closely spaced outlet ports (5 mm), allowed us resolving the effects of charge interactions on the temporal breakthrough and spatial profiles of the cations and anions [3]. The interpretation of the experimental results requires a multicomponent modeling approach with an accurate description of local hydrodynamic dispersion, as well as the explicit quantification of the dispersive fluxes' cross-coupling due to the Coulombic interactions between the charged species. A new 2-D simulator [4], coupling the solution of the multicomponent ionic transport
Spurious sea ice formation caused by oscillatory ocean tracer advection schemes
Naughten, Kaitlin A.; Galton-Fenzi, Benjamin K.; Meissner, Katrin J.; England, Matthew H.; Brassington, Gary B.; Colberg, Frank; Hattermann, Tore; Debernard, Jens B.
2017-08-01
Tracer advection schemes used by ocean models are susceptible to artificial oscillations: a form of numerical error whereby the advected field alternates between overshooting and undershooting the exact solution, producing false extrema. Here we show that these oscillations have undesirable interactions with a coupled sea ice model. When oscillations cause the near-surface ocean temperature to fall below the freezing point, sea ice forms for no reason other than numerical error. This spurious sea ice formation has significant and wide-ranging impacts on Southern Ocean simulations, including the disappearance of coastal polynyas, stratification of the water column, erosion of Winter Water, and upwelling of warm Circumpolar Deep Water. This significantly limits the model's suitability for coupled ocean-ice and climate studies. Using the terrain-following-coordinate ocean model ROMS (Regional Ocean Modelling System) coupled to the sea ice model CICE (Community Ice CodE) on a circumpolar Antarctic domain, we compare the performance of three different tracer advection schemes, as well as two levels of parameterised diffusion and the addition of flux limiters to prevent numerical oscillations. The upwind third-order advection scheme performs better than the centered fourth-order and Akima fourth-order advection schemes, with far fewer incidents of spurious sea ice formation. The latter two schemes are less problematic with higher parameterised diffusion, although some supercooling artifacts persist. Spurious supercooling was eliminated by adding flux limiters to the upwind third-order scheme. We present this comparison as evidence of the problematic nature of oscillatory advection schemes in sea ice formation regions, and urge other ocean/sea-ice modellers to exercise caution when using such schemes.
Energy Technology Data Exchange (ETDEWEB)
Chapallaz, J.-M.
2007-02-15
This first part of a final report for the Swiss Federal Office of Energy (SFOE) discusses the use of a pump equipped with variable guide vanes, similar to a Francis turbine. This first part of a four-part article describes the PAT-Francis project in general. The turbine was realised by removing the existing spiral casing from a standard pump and replacing it with a guide vane system with a new spiral. General topics on the use of pumps as turbines are discussed and the characteristic curves and operational limits of a PAT are examined. The proposed concept for a PAT with variable flow, or PAT-Francis, is presented.
Solving Time-Fractional Advection-Dispersion Equation by Variable Weights Particle Tracking Method
Cao, Shaohua; Jiang, Jianguo; Wu, Jichun
2017-09-01
Particle tracking method is an efficient and reliable method to solve time-fractional advection-dispersion equation, which can describe anomalous transport in heterogeneous porous media. However, this method will lead to severe fluctuation or disappearance of solutions if the concentration value is small. A variable weights method is developed to conquer the shortcoming of particle tracking method. Then, one-dimensional and two-dimensional time-fractional advection-dispersion equations are solved by the variable weights particle tracking method. Compared to traditional particle tracking method, the variable weights version may eliminate the fluctuation and improve the accuracy by orders of magnitude without more computational cost.
Advection of NH3 over a pasture field and its effect on gradient flux measurements
Directory of Open Access Journals (Sweden)
M. A. Sutton
2009-07-01
Full Text Available Deposition of atmospheric ammonia (NH3 to semi-natural ecosystems leads to serious adverse effects, such as acidification and eutrophication. A step in quantifying such effects is the measurement of NH3 fluxes over semi-natural and agricultural land. However, measurement of NH3 fluxes over vegetation in the vicinity of strong NH3 sources is challenging, since NH3 emissions are highly heterogeneous. Indeed, under such conditions, local advection errors may alter the measured fluxes. In this study, local advection errors (ΔFz,adv were estimated over a 14 ha grassland field, which was successively cut and fertilised, as part of the GRAMINAE integrated Braunschweig experiment. The magnitude of ΔFz,adv was determined up to 810 m downwind from farm buildings emitting between 6.2 and 9.9 kg NH3 day−1. The GRAMINAE experiment provided a unique opportunity to compare two methods of estimating ΔFz,adv: one inference method based on measurements of horizontal concentration gradients, and one based on inverse dispersion modelling with a two-dimensional model. Two sources of local advection were clearly identified: the farm NH3 emissions leading to positive ΔFz,adv ("bias towards emissions" and field NH3 emissions, which led to a negative ΔFz,adv ("bias towards deposition". The local advection flux from the farm was in the range 0 to 27 ng NH3 m−2 s−1 at 610 m from the farm, whereas ΔFz,adv due to field emission was proportional to the local flux, and ranged between −209 and 13 ng NH3 m−2 s−1. The local advection flux ΔFz,adv was either positive or negative depending on the magnitude of these two contributions. The modelled and inferred advection errors agreed well. The inferred advection errors, relative to the vertical flux at 1 m height, were 52% on average, before the field was cut, and less than 2.1% when the field was fertilised. The variability of the advection errors in response to changes in micrometeorological conditions is also
1983-11-01
element u.-lei is readily applied to such flows. For lully developed flow V = 0, and U and H are functions of y only (i.e., J ■ U(y) and H ■ H(y...included, application of the basic momentum theorem yields T b |£| . / w+ Jb \\ T r ’dx’ I W < s,av where T is the average shear stress
Directory of Open Access Journals (Sweden)
Juan Carlos Gutiérrez Vargas
2013-12-01
Full Text Available The purpose of this study was to describe and analyze the relationship between self-efficacy, pre-competitive anxiety and flow feeling in male and female handball team players from the Costa Rica national teams. Participants were 28 players (14 male and 14 female from both teams. The scales of general self-efficacy, flow feeling and competitive anxiety were used to collect data. The average score in relation to self-efficacy was high (> 8.40. Regarding flow sensation, the average scores were range from 3.41 (autotelic experience to 5,78 (control sense. Somatic anxiety was the lowest in men = 1.59 and women female = 1.98, and self-confidence was the highest score in men = 2.99 and women = 2.70 respectively. No significant changes were observed throughout the game in relation to the flow feeling. The anxiety reported by men was significantly lower than women, and the self-confidence levels were higher in men than in women. No significant correlation was found between self efficacy and sense of flow. Somatic anxiety showed significant correlations with some dimensions of the flow feeling. In conclusion, these data showed that there is a need to incorporate psychological interventions to ensure that athletes can reach optimal psychophysical states in order to perform better.
Mitchell, William H.; Spagnolie, Saverio E.
2017-03-01
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to link the surface tractions on the body to integrals involving the background velocity and stress fields on an imaginary bounding sphere (or hemisphere for wall-bounded flows). The derivation requires the velocity and stress fields associated with numerous fundamental singularity solutions which we provide for free-space and wall-bounded domains. Two sample applications of the method are discussed: we study the tractions on an ellipsoid moving near a plane wall, which provides a more detailed understanding of the well-studied glancing and reversing trajectories in the context of particle sedimentation, and the erosion of bodies by a viscous flow, in which the surface is ablated at a rate proportional to the local viscous shear stress. Simulations and analytical estimates suggest that a spherical body in a uniform flow first reduces nearly but not exactly to the drag minimizing profile and then vanishes in finite time. The shape dynamics of an eroding body in a shear flow and near a wall are also investigated. Stagnation points on the body surface lead generically to the formation of cusps, whose number depends on the flow configuration and/or the presence of nearby boundaries.
A generalization of the Runge-Kutta iteration
Haelterman, R.; Vierendeels, J.; van Heule, D.
2009-02-01
Iterative solvers in combination with multi-grid have been used extensively to solve large algebraic systems. One of the best known is the Runge-Kutta iteration. We show that a generally used formulation [A. Jameson, Numerical solution of the Euler equations for compressible inviscid fluids, in: F. Angrand, A. Dervieux, J.A. Désidéri, R. Glowinski (Eds.), Numerical Methods for the Euler Equations of Fluid Dynamics, SIAM, Philadelphia, 1985, pp. 199-245] does not allow to form all possible polynomial transmittance functions and we propose a new formulation to remedy this, without using an excessive number of coefficients. After having converted the optimal parameters found in previous studies (e.g. [B. Van Leer, C.H. Tai, K.G. Powell, Design of optimally smoothing multi-stage schemes for the Euler equations, AIAA Paper 89-1923, 1989]) we compare them with those that we obtain when we optimize for an integrated 2-grid V-cycle and show that this results in superior performance using a low number of stages. We also propose a variant of our new formulation that roughly follows the idea of the Martinelli-Jameson scheme [A. Jameson, Analysis and design of numerical schemes for gas dynamics 1, artificial diffusion, upwind biasing, limiter and their effect on multigrid convergence, Int. J. Comput. Fluid Dyn. 4 (1995) 171-218; J.V. Lassaline, Optimal multistage relaxation coefficients for multigrid flow solvers. http://www.ryerson.ca/~jvl/papers/cfd2005.pdf] used on the advection-diffusion equation which that can be extended to other types. Gains in the order of 30%-50% have been shown with respect to classical iterative schemes on the advection equation. Better results were also obtained on the advection-diffusion equation than with the Martinelli-Jameson coefficients, but with less than half the number of matrix-vector multiplications.
Ke, Xinyou; Alexander, J Iwan D; Savinell, Robert F
2016-01-01
In this work, a two-dimensional mathematical model is developed to study the flow patterns and volumetric flow penetrations in the flow channel over the porous electrode layered system in vanadium flow battery with serpentine flow field design. The flow distributions at the interface between the flow channel and porous electrode are examined. It is found that the non-linear pressure distributions can distinguish the interface flow distributions under the ideal plug flow and ideal parabolic flow inlet boundary conditions. However, the volumetric flow penetration within the porous electrode beneath the flow channel through the integration of interface flow velocity reveals that this value is identical under both ideal plug flow and ideal parabolic flow inlet boundary conditions. The volumetric flow penetrations under the advection effects of flow channel and landing/rib are estimated. The maximum current density achieved in the flow battery can be predicted based on the 100% amount of electrolyte flow reactant ...
Xingxing, Chen; Zhihui, Wang; Yongliang, Yu
2016-11-01
Hypersonic chemical non-equilibrium gas flows around blunt nosed bodies are studied in the present paper to investigate the Reynolds analogy relation on curved surfaces. With a momentum and energy transfer model being applied through boundary layers, influences of molecular dissociations and recombinations on skin frictions and heat fluxes are separately modeled. Expressions on the ratio of Cf / Ch (skin friction coefficient to heat flux) are presented along the surface of circular cylinders under the ideal dissociation gas model. The analysis indicates that molecular dissociations increase the linear distribution of Cf / Ch, but the nonlinear Reynolds analogy relation could ultimately be obtained in flows with larger Reynolds numbers and Mach numbers, where the decrease of wall heat flux by molecular recombinations signifies. The present modeling and analyses are also verified by the DSMC calculations on nitrogen gas flows.
Shell model for time-correlated random advection of passive scalars
DEFF Research Database (Denmark)
Andersen, Ken Haste; Muratore-Ginanneschi, P.
1999-01-01
We study a minimal shell model for the advection of a passive scalar by a Gaussian time-correlated velocity field. The anomalous scaling properties of the white noise limit are studied analytically. The effect of the time correlations are investigated using perturbation theory around the white...
Effects of upwinding on the solution of a 1-D advection-diffusion problem
Energy Technology Data Exchange (ETDEWEB)
Sahai, V.
1991-12-01
A one-dimensional advection-diffusion problem whose solution is known was solved using TOPAZ2D. Two numerical upwinding techniques were used to damp out the numerical oscillations that occur. Comparisons between the exact and numerical solution were made.
Shen, S.; Liu, F.; Anh, V.; Turner, I.
2008-12-01
In this paper, we consider a Riesz fractional advection-dispersion equation (RFADE), which is derived from the kinetics of chaotic dynamics. The RFADE is obtained from the standard advection-dispersion equation by replacing the first-order and second-order space derivatives by the Riesz fractional derivatives of order{alpha} [isin] (0, 1) and {beta} [isin] (1, 2], respectively. We derive the fundamental solution for the Riesz fractional advection-dispersion equation with an initial condition (RFADE-IC). We investigate a discrete random walk model based on an explicit finite-difference approximation for the RFADE-IC and prove that the random walk model belongs to the domain of attraction of the corresponding stable distribution. We also present explicit and implicit difference approximations for the Riesz fractional advection-dispersion equation with initial and boundary conditions (RFADE-IBC) in a finite domain. Stability and convergence of these numerical methods for the RFADE-IBC are discussed. Some numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.
Rogers, M. A.
2015-12-01
Using satellite observations from GOES-E and GOES-W platforms in concert with GFS-derived cloud-level winds and a standalone radiative transfer model, an advection-derived forecast for surface GHI over the continental United States, with intercomparison between forecasts for four zones over the CONUS and Central Pacific with SURFRAD results. Primary sources for error in advection-based forecasts, primarily driven by false- or mistimed ramp events are discussed, with identification of error sources quantified along with techniques used to improve advection-based forecasts to approximately 10% MAE for designated surface locations. Development of a blended steering wind product utilizing NWP output combined with satellite-derived winds from AMV techniques to improve 0-1 hour advection forecasts will be discussed. Additionally, the use of two years' of solar forecast observations in the development of a prototype probablistic forecast for ramp events will be shown, with the intent of increasing the use of satellite-derived forecasts for grid operators and optimizing integration of renewable resources into the power grid. Elements of the work were developed under the 'Public-Private-Academic Partnership to Advance Solar Power Forecasting' project spearheaded by the National Center for Atmospheric Research.
3D IBFV : Hardware-Accelerated 3D Flow Visualization
Telea, Alexandru; Wijk, Jarke J. van
2003-01-01
We present a hardware-accelerated method for visualizing 3D flow fields. The method is based on insertion, advection, and decay of dye. To this aim, we extend the texture-based IBFV technique for 2D flow visualization in two main directions. First, we decompose the 3D flow visualization problem in a
Advection of magnetic flux by accretion disks around neutron stars
Flores-Tulian, S.; Reisenegger, A.
The aim of our research is to address why millisecond pulsars have relatively weak surface magnetic fields, of about 10^8 G, with a narrow spread. We propose that the accretion of plasma from the companion star fully screens the original neutron star field, but the accretion disk carries additional magnetic flux from the companion star, or itself can generate field by means of dynamo processes. For a strongly magnetized star, the field prevents the disk from approaching the star. The accretion is along the field lines and deposits the matter on the polar cap. Then, the accreted plasma flows, dragging with itself the magnetic field lines, from the pole to the equator (Payne & Melatos 2004). In a following stage, when the star becomes non-magnetic, because the field has been buried, the disk touches the star. We suggest that some effective mechanism of magnetic flux transport such as that proposed by Spruit & Uzdensky 2005 (or Bisnovatyi-Kogan & Lovelace 2007), operates and necessarily leads to a "strongly magnetized disk''. It becomes laminar because the magneto-rotational instability saturates (it is considered to be responsible for turbulence in the disk), and the magnetic difussivity is negligible. Then, the loss of angular momentum allowing the accretion is only caused by the magneto-centrifugal disk-wind (Blandford & Payne 1982). Meanwhile, the wind-driven transport of the magnetic flux by the disk re-magnetizes the star. This process continues until the Lorentz force due to the star's magnetic field forbids any further accretion of matter and magnetic flux, in the Ideal Magneto-Hydro-Dynamics approach. Additional of material can fall onto the star (but at lower rate) if some instability process sets in, allowing the diffusion of mass through the magnetic field lines (e.g the Interchange Instability, Spruit & Taam 1990). All these processes might lead to an asymptotic magnetic field of 10^8 G,as is inferred from observations. We are developing a self
River-flow predictions for the South African mid-summer using a coupled general circulation model
CSIR Research Space (South Africa)
Olivier, C
2013-09-01
Full Text Available There are limited sources of streamflow data available in South Africa. These include simulated streamflow for catchments across South Africa and measured river-flow at specific rivers around the country. Given that a number of studies has been done...
Beijeren, H. van; Dorfman, J.R.
1980-01-01
We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas.
Seo, Bong-Chul; Krajewski, Witold F.
2015-12-01
This study offers a method to correct for the radar temporal sampling error when determining radar-rainfall accumulations. The authors evaluate the correction effect with respect to multiple factors associated with storm advection, rainfall characteristics, and different rainfall accumulation time scales. The advection method presented in this study uses linear interpolation of static rain storm locations observed at two intermittent radar sampling times to correct for the missed rainfall accumulations. The advection correction is applied to the high space (0.5 km) and time (5-min) resolution radar-rainfall products provided by the Iowa Flood Center. We use the ground reference data from a high quality and high density rain gauge network distributed over the Turkey River basin in Iowa to evaluate the advection corrected rain fields. We base our evaluation on six rain events and examine the correction performance/improvement with respect to the advection discretization, spatial grid aggregation, rainfall basin coverage, and conditional average rainfall intensity. The results show that the 1-min advection discretization is sufficient to represent the observed distribution of storm velocities for the presented cases. Grid aggregation that is motivated by the need to expedite the computation may induce errors in estimating advection vectors. The authors found that while the advection correction tends to enhance the QPE accuracy for intense rain storms over small or isolated areas, it has little impact on the improvement of light rain estimation.
Institute of Scientific and Technical Information of China (English)
Xin Wen
2009-01-01
In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, (2008), 1-22] to establish the L1-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the L1-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, (2005), 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, (2008), 2688-2714].
Shah, Anant Pankaj
2005-01-01
Gas turbines for military applications, when operating in harsh environments like deserts often encounter unexpected operation faults. Such performance deterioration of the gas turbine decreases the mission readiness of the Air Force and simultaneously increases the maintenance costs. Some of the major factors responsible for the reduced performance are ingestion of debris during take off and landing, distorted intake flows during low altitude maneuvers, and hot gas ingestion during artillery...
Karimi-Fard, M.; Durlofsky, L. J.
2016-10-01
A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.
Perdigou, C.; Audoly, B.
2016-11-01
The stability of thin viscous sheets has been studied so far in the special case where the base flow possesses a direction of invariance: the linear stability is then governed by an ordinary differential equation. We propose a mathematical formulation and a numerical method of solution that are applicable to the linear stability analysis of viscous sheets possessing no particular symmetry. The linear stability problem is formulated as a non-Hermitian eigenvalue problem in a 2D domain and is solved numerically using the finite-element method. Specifically, we consider the case of a viscous sheet in an open flow, which falls in a bath of fluid; the sheet is mildly stretched by gravity and the flow can become unstable by 'curtain' modes. The growth rates of these modes are calculated as a function of the fluid parameters and of the geometry, and a phase diagram is obtained. A transition is reported between a buckling mode (static bifurcation) and an oscillatory mode (Hopf bifurcation). The effect of surface tension is discussed.
Liu, Hui-Hai
2014-05-01
In clay or other low-permeability media, water flow becomes non-Darcian and characterized by the non-linear relationship between water flux and hydraulic gradient. This work is devoted to addressing a number of key issues related to geological disposal of high-level nuclear waste in clay/shale formations. It is demonstrated that water flow velocity in the damaged zone (often considered as a potential preferential advection paths in a repository) surrounding the tunnel is extremely small, as a result of non-Darcian flow behavior, such that solute transport is dominated by diffusion, rather than advection. The finding is also consistent with the often-observed existence of persistent abnormal pressures in shale formations. While relative permeability is the key parameter for modeling the unsaturated flow process, without incorporating non-Darcian flow behavior, significant errors can occur in the determination of relative permeability values from traditional measurement methods. An approach for dealing with temperature impact on non-Darcian flow and a formulation to calculate non-Darcian water flux in an anisotropic medium are presented, taking into consideration that a geological repository is subject to temperature evolution in the near field as a result of heat generated by nuclear waste, and that shale formations are generally anisotropic.
Moortgat, J.; Amooie, M. A.; Soltanian, M. R.
2016-12-01
Problems in hydrogeology and hydrocarbon reservoirs generally involve the transport of solutes in a single solvent phase (e.g., contaminants or dissolved injection gas), or the flow of multiple phases that may or may not exchange mass (e.g., brine, NAPL, oil, gas). Often, flow is viscously and gravitationally unstable due to mobility and density contrasts within a phase or between phases. Such instabilities have been studied in detail for single-phase incompressible fluids and for two-phase immiscible flow, but to a lesser extent for multiphase multicomponent compressible flow. The latter is the subject of this presentation. Robust phase stability analyses and phase split calculations, based on equations of state, determine the mass exchange between phases and the resulting phase behavior, i.e., phase densities, viscosities, and volumes. Higher-order finite element methods and fine grids are used to capture the small-scale onset of flow instabilities. A full matrix of composition dependent coefficients is considered for each Fickian diffusive phase flux. Formation heterogeneity can have a profound impact and is represented by realistic geostatistical models. Qualitatively, fingering in multiphase compositional flow is different from single-phase problems because 1) phase mobilities depend on rock wettability through relative permeabilities, and 2) the initial density and viscosity ratios between phases may change due to species transfer. To quantify mixing rates in different flow regimes and for varying degrees of miscibility and medium heterogeneities, we define the spatial variance, scalar dissipation rate, dilution index, skewness, and kurtosis of the molar density of introduced species. Molar densities, unlike compositions, include compressibility effects. The temporal evolution of these measures shows that, while transport at the small-scale (cm) is described by the classical advection-diffusion-dispersion relations, scaling at the macro-scale (> 10 m) shows
Moaty Sayed, A A; Hussein, M A; Becker, T
2010-04-01
Lattice Boltzmann models (LBM) are rapidly showing their ability to simulate a lot of fluid dynamics problems that previously required very complex approaches. This study presents a LBM for simulating diffusion-advection transport of substrate in a 2-D laminar flow. The model considers the substrate influx into a set of active cells placed inside the flow field. A new innovative method was used to simulate the cells activity using the LBM by means of Michaelis-Menten kinetics. The model is validated with some numerical benchmark problems and proved highly accurate results. After validation the model was used to simulate the transport of oxygen substrates that diffuse in water to feed a set of active cartilage cells inside a new designed bioreactor.
Particulate export vs lateral advection in the Antarctic Polar Front (Southern Pacific Ocean)
Tesi, T.; Langone, L.; Ravaioli, M.; Capotondi, L.; Giglio, F.
2012-04-01
The overarching goal of our study was to describe and quantify the influence of lateral advection relative to the vertical export in the Antarctic Polar Front (Southern Pacific Ocean). In areas where lateral advection of particulate material is significant, budgets of bioactive elements can be inaccurate if fluxes through the water column and to the seabed are exclusively interpreted as passive sinking of particles. However, detailed information on the influence of lateral advection in the water column in the southern ocean is lacking. With this in mind, our study focused between the twilight zone (i.e. mesopelagic) and the benthic nepheloid layer to understand the relative importance of lateral flux with increasing water depth. Measurements were performed south of the Antarctic Polar Front for 1 year (January 10th 1999-January 3rd 2000) at 900, 1300, 2400, and 3700 m from the sea surface. The study was carried out using a 3.5 km long mooring line instrumented with sediment traps, current meters and sensors of temperature and conductivity. Sediment trap samples were characterized via several parameters including total mass flux, elemental composition (organic carbon, total nitrogen, biogenic silica, and calcium carbonate), concentration of metals (aluminum, iron, barium, and manganese), 210Pb activity, and foraminifera taxonomy. High fluxes of biogenic particles were observed in both summer 1999 and 2000 as a result of seasonal algal blooms associated with sea ice retreat and water column stratification. During no-productive periods, several high energy events occurred and resulted in advecting resuspended biogenic particles from flat-topped summits of the Pacific Antarctic Ridge. Whereas the distance between seabed and uppermost sediment traps was sufficient to avoid lateral advection processes, resuspension was significant in the lowermost sediment traps accounting for ~60 and ~90% of the material caught at 2400 and 3700 m, respectively. Samples collected during
Directory of Open Access Journals (Sweden)
Mcebisi Mkhwanazi
2015-11-01
Full Text Available The Surface Energy Balance Algorithm for Land (SEBAL is one of the remote sensing (RS models that are increasingly being used to determine evapotranspiration (ET. SEBAL is a widely used model, mainly due to the fact that it requires minimum weather data, and also no prior knowledge of surface characteristics is needed. However, it has been observed that it underestimates ET under advective conditions due to its disregard of advection as another source of energy available for evaporation. A modified SEBAL model was therefore developed in this study. An advection component, which is absent in the original SEBAL, was introduced such that the energy available for evapotranspiration was a sum of net radiation and advected heat energy. The improved SEBAL model was termed SEBAL-Advection or SEBAL-A. An important aspect of the improved model is the estimation of advected energy using minimal weather data. While other RS models would require hourly weather data to be able to account for advection (e.g., METRIC, SEBAL-A only requires daily averages of limited weather data, making it appropriate even in areas where weather data at short time steps may not be available. In this study, firstly, the original SEBAL model was evaluated under advective and non-advective conditions near Rocky Ford in southeastern Colorado, a semi-arid area where afternoon advection is common occurrence. The SEBAL model was found to incur large errors when there was advection (which was indicated by higher wind speed and warm and dry air. SEBAL-A was then developed and validated in the same area under standard surface conditions, which were described as healthy alfalfa with height of 40–60 cm, without water-stress. ET values estimated using the original and modified SEBAL were compared to large weighing lysimeter-measured ET values. When the SEBAL ET was compared to SEBAL-A ET values, the latter showed improved performance, with the ET Mean Bias Error (MBE reduced from −17
Yochelis, Arik; Bar-On, Tomer; Gov, Nir S.
2016-04-01
Unconventional myosins belong to a class of molecular motors that walk processively inside cellular protrusions towards the tips, on top of actin filament. Surprisingly, in addition, they also form retrograde moving self-organized aggregates. The qualitative properties of these aggregates are recapitulated by a mass conserving reaction-diffusion-advection model and admit two distinct families of modes: traveling waves and pulse trains. Unlike the traveling waves that are generated by a linear instability, pulses are nonlinear structures that propagate on top of linearly stable uniform backgrounds. Asymptotic analysis of isolated pulses via a simplified reaction-diffusion-advection variant on large periodic domains, allows to draw qualitative trends for pulse properties, such as the amplitude, width, and propagation speed. The results agree well with numerical integrations and are related to available empirical observations.
A balancing domain decomposition method by constraints for advection-diffusion problems
Energy Technology Data Exchange (ETDEWEB)
Tu, Xuemin; Li, Jing
2008-12-10
The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.
An advection-diffusion model for cross-field runaway electron transport in perturbed magnetic fields
Särkimäki, Konsta; Decker, Joan; Varje, Jari; Kurki-Suonio, Taina
2016-01-01
Disruption-generated runaway electrons (RE) present an outstanding issue for ITER. The predictive computational studies of RE generation rely on orbit-averaged computations and, as such, they lack the effects from the magnetic field stochasticity. Since stochasiticity is naturally present in post-disruption plasma, and externally induced stochastization offers a prominent mechanism to mitigate RE avalanche, we present an advection-diffusion model that can be used to couple an orbit-following code to an orbit-averaged tool in order to capture the cross-field transport and to overcome the latter's limitation. The transport coefficients are evaluated via a Monte Carlo method. We show that the diffusion coefficient differs significantly from the well-known Rechester-Rosenbluth result. We also demonstrate the importance of including the advection: it has a two-fold role both in modelling transport barriers created by magnetic islands and in amplifying losses in regions where the islands are not present.
Directory of Open Access Journals (Sweden)
Carlos Humberto Galeano Urueña
2010-05-01
Full Text Available This article describes the streamline upwind Petrov-Galerkin (SUPG method as being a stabilisation technique for resolving the diffusion-advection-reaction equation by finite elements. The first part of this article has a short analysis of the importance of this type of differential equation in modelling physical phenomena in multiple fields. A one-dimensional description of the SUPG me- thod is then given to extend this basis to two and three dimensions. The outcome of a strongly advective and a high numerical complexity experiment is presented. The results show how the version of the implemented SUPG technique allowed stabilised approaches in space, even for high Peclet numbers. Additional graphs of the numerical experiments presented here can be downloaded from www.gnum.unal.edu.co.
A condensed-mass advection based model for the simulation of liquid polar stratospheric clouds
Directory of Open Access Journals (Sweden)
D. Lowe
2002-06-01
Full Text Available We present a condensed-mass advection based model (MADVEC designed to simulate the condensation/evaporation of liquid polar stratospheric cloud (PSC particles. A (Eulerian-in-radius discretization scheme is used, making the model suitable for use in global or mesoscale chemistry and transport models (CTMs. The mass advection equations are solved using an adaption of the weighted average flux (WAF scheme. We validate the numerical scheme using an analytical solution for multicomponent aerosols. The physics of the model are tested using a test case designed by Meilinger et al. (1995. The results from this test corroborate the composition gradients across the size distribution under rapid cooling conditions that were reported in earlier studies.
Directory of Open Access Journals (Sweden)
Gurhan Gurarslan
2013-01-01
Full Text Available This study aims to produce numerical solutions of one-dimensional advection-diffusion equation using a sixth-order compact difference scheme in space and a fourth-order Runge-Kutta scheme in time. The suggested scheme here has been seen to be very accurate and a relatively flexible solution approach in solving the contaminant transport equation for Pe≤5. For the solution of the present equation, the combined technique has been used instead of conventional solution techniques. The accuracy and validity of the numerical model are verified through the presented results and the literature. The computed results showed that the use of the current method in the simulation is very applicable for the solution of the advection-diffusion equation. The present technique is seen to be a very reliable alternative to existing techniques for these kinds of applications.
A convective-advective balance approach for solving some nonlinear evolution equations analytically
Energy Technology Data Exchange (ETDEWEB)
Abdel Hamid, B. [United Arab Emirates Univ. (United Arab Emirates). Dept. of Mathematics and Computer Science
1999-09-01
A symbolic computation-based approach of balancing the convective and advective effects in a nonlinear evolution equation leads to a transformation that maps the nonlinear equation onto either a linear one or to a system of linear and homogeneous equations. The method is demonstrated by mapping Burgers' equation and nonlinear heat equation onto the linear heat equation. It is shown that the transformation obtained by balancing the convective-advective effects are reducible to those obtained by the Cole and Hopf through Backlund transformation. The method is also used to transform the modified KdV equation into a system of linear and homogeneous functions in the partial derivatives which leads to an exact solution. Computations in the presented approach are carried out in a straightforward way.
Improvement of the One-dimensional Vertical Advection-diffusion Model in Seawater
Institute of Scientific and Technical Information of China (English)
王保栋; 单宝田; 战闰; 王修林
2003-01-01
The classical 1-D vertical advection-diffusion model was improved in this work. Themain advantages of the improved model over the previous one are: 1 ) The applicable condition ofthe 1-D model is made clear in the improved model, in that it is substantively applicable only to avertical domain on which two end-member water masses are mixing. 2) The substitution of parame-ter f(z) in the equation of the classical 1-D model with end-member fraction f1 makes the modelmore precisely and easily solved. 3 ) All the terms in the improved model equation have specificphysical meanings, which makes the model easily understood. Practical application of the improvedmodel to predict the vertical profiles of dissolved oxygen and micronutrients in abyssal ocean waterof the North Pacific proved that the improvement of the 1-D advection-diffusion model is successfuland practicable.
Object-oriented implementations of the MPDATA advection equation solver in C++, Python and Fortran
Arabas, Sylwester; Jaruga, Anna; Fijałkowski, Maciej
2013-01-01
Three object-oriented implementations of a prototype solver of the advection equation are introduced. Presented programs are based on Blitz++ (C++), NumPy (Python), and Fortran's built-in array containers. The solvers include an implementation of the Multidimensional Positive-Definite Advective Transport Algorithm (MPDATA). The introduced codes exemplify how the application of object-oriented programming (OOP) techniques allows to reproduce the mathematical notation used in the literature within the program code. The introduced codes serve as a basis for discussion on the tradeoffs of the programming language choice. The main angles of comparison are code brevity and syntax clarity (and hence maintainability and auditability) as well as performance. In case of Python, a significant performance gain is observed when switching from the standard interpreter (CPython) to the PyPy implementation of Python. Entire source code of all three implementations is embedded in the text and is licensed under the terms of th...
Directory of Open Access Journals (Sweden)
Birol İbiş
2014-01-01
Full Text Available This paper aims to obtain the approximate solution of time-fractional advection-dispersion equation (FADE involving Jumarie’s modification of Riemann-Liouville derivative by the fractional variational iteration method (FVIM. FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs.
Noise Prevents Infinite Stretching of the Passive Field in a Stochastic Vector Advection Equation
Flandoli, Franco; Maurelli, Mario; Neklyudov, Mikhail
2014-09-01
A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Hölder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh; Ahmad Abd. Majid; Ahmad Izani Md. Ismail
2012-01-01
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Font, A.; Morguí, J.-A.; Curcoll, R.; Rodó, X.
2009-04-01
A model framework which couples the Lagrangian Particle Dispersion Model FLEXPART (LPDM) with the new global surface flux inversion CarbonTracker from NOAA-ESRL (2007B release) is used to quantify the advected CO2 concentration from outbound surface fluxes to measured vertical profiles carried out during different seasons in 2006 at La Muela site in Spain (LMU; 41.60°N, 1.1°W). The Lagrangian Particle Dispersion Model FLEXPART (LPDM) calculates the influence of surface CO2 fluxes upwind of the study area, allowing us to identify those sources or sink areas that strongly modify the CO2 content of air masses that arrives at different altitudes of measured profiles. CarbonTracker is a new assimilation system that informs of global carbon fluxes at 1°x1° at 3 hours resolution. Coupling LPDM results with surface fluxes allows assessing the net CO2 contribution of identified areas to measured concentrations along the profiles above a reference or background concentration. Furthermore, it allows the quantification of the percentage of each component flux (biospheric, anthropogenic and oceanic) to each vertical layer. At LMU, biospheric fluxes account ~70% of total CO2 advection; fossil fuel ~25%; and ~5% is attributed to the oceanic ones. By far, late spring and summer profiles are largely influence by the biospheric component (~90%). Finally, the CO2 concentration above the background value of profiles measured on 22nd February, 13th October and 30th November 2006 are well explained by the advection of upstream surface fluxes. In other profiles examined, the variation of CO2 along the profile is partially explained by the advection of CO2 outbound fluxes.
Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems
Li, Zhen; Yazdani, Alireza; Tartakovsky, Alexandre; Karniadakis, George Em
2015-01-01
We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic dissipative particle dynamics (DPD) framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux a...
Direct and inverse source problems for a space fractional advection dispersion equation
Aldoghaither, Abeer
2016-05-15
In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic solution to the direct problem which we use to prove the uniqueness and the unstability of the inverse source problem using final measurements. Finally, we illustrate the results with a numerical example.
ADVECTION AND DIFFUSION OF POISONOUS GAS CONTAMINANT RELEASED FROM BOTTOM SLUDGE IN OPEN CHANNEL
Institute of Scientific and Technical Information of China (English)
WU Zhou-hu
2004-01-01
In some cases, poisonous contaminants may be released from bottom sludge in open channels. The equation of advection and diffusion for the related problem was analyzed in this paper. The conditions for the definite solution to the equation were given. The analytic solution of poisonous gas concentration distribution was worked out. The reasonableness of this solution was discussed. The result is also of significance for other similar problems.
Narayan, Ramesh; Penna, Robert F; Kulkarni, Akshay K
2012-01-01
We present results from two long-duration GRMHD simulations of an advection-dominated accretion flow around a non-spinning black hole. The first simulation was designed to avoid significant accumulation of magnetic flux around the black hole. This simulation was run for a time of 200,000GM/c^3 and achieved inflow equilibrium out to a radius \\sim 100GM/c^2. Up to this radius, we do not see significant mass outflow. We estimate that, if at all, only at radii \\gsim 300GM/c^2 does the mass outflow rate (\\dot{M}_{\\rm out}) exceed the net mass inflow rate into the black hole (\\dot{M}_{\\rm BH}). The second simulation was designed to achieve substantial magnetic flux accumulation around the black hole in a magnetically arrested disc. This simulation was run for a time of only 100,000GM/c^3. Nevertheless, because the mean radial velocity was several times larger than in the first simulation, it reached inflow equilibrium out to a radius \\sim 200GM/c^2. The mass outflow rate is larger, though even in this case, $\\dot{M...
X-ray Variability as a Probe of Advection-Dominated Accretion in Low-Luminosity AGN
Ptak, A; Mushotzky, R F; Serlemitsos, P J; Griffiths, R
1998-01-01
As a class, LINERs and Low-Luminosity AGN tend to show little or no significant short-term variability (i.e., with time-scales less than a day). This is a marked break for the trend of increased variability in Seyfert 1 galaxies with decreased luminosity. We propose that this difference is due to the lower accretion rate in LINERs and LLAGN which is probably causing the accretion flow to be advection-dominated. This results in a larger characteristic size for the X-ray producing region than is the case in ``normal'' AGN. Short-term variability may be caused by a localized instability or occultation events, but we note that such events would likely be accompanied by broad-band spectral changes. Since the ADAF is more compact in a Kerr metric, it is possible that the X-ray emission from ADAFs around rotating blackholes would be more variable than X-ray emission from ADAFs in a Schwarzchild metric. Similar variability arguments also apply to other wavelengths, and accordingly multiwavelength monitoring of LLAGN ...
Belucz, Bernadett; Forgacs-Dajka, Emese
2015-01-01
Babcock-Leighton type solar dynamo models with single-celled meridional circulation are successful in reproducing many solar cycle features. Recent observations and theoretical models of meridional circulation do not indicate a single-celled flow pattern. We examine the role of complex multi-cellular circulation patterns in a Babcock-Leighton solar dynamo in advection- and diffusion-dominated regimes. We show from simulations that presence of a weak, second, high-latitude reverse cell speeds up the cycle and slightly enhances the poleward branch in butterfly diagram, whereas the presence of a second cell in depth reverses the tilt of butterfly wing to an anti-solar type. A butterfly diagram constructed from middle of convection zone yields a solar-like pattern, but this may be difficult to realize in the Sun because of magnetic buoyancy effects. Each of the above cases behaves similarly in higher and lower magnetic diffusivity regimes. However, our dynamo with a meridional circulation containing four cells in...
Backward Calculation Based on the Advection and Diffusion of Oil Spills on the Sea Surface
Institute of Scientific and Technical Information of China (English)
LIU Hao; YIN Baoshu; LIN Jianguo
2005-01-01
In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & diffusion equation, on the one hand,the advection term itself has the strong unilateral property, which means information in the upper reaches is transmitted downstream via the advection term; on the other hand,because of the opposite direction of calculation, it is essential for information to be conveyed upstream by means of the advection term. In addition, unlike that in the forward calculation, the diffusion term in the backward calculation is prone to accumulate errors, and thus renders the whole scheme unstable. Therefore, we adopt the central difference to deal with both the convectional term and the diffusion term. By examining two practical examples (1) under the unlimited boundary condition, and (2) under the limited boundary condition, it is proven that this method could achieve fundamentally satisfactory results not only in the open ocean but also in the closed or semi-closed bay.
Some numerical studies of interface advection properties of level set method
Indian Academy of Sciences (India)
A Salih; S Ghosh Moulic
2009-04-01
In this paper, we discuss the results of a series of tests carried out to assess the level set methodology for capturing interfaces between two immiscible ﬂuids. The tests are designed to investigate the accuracy of convection process, the preservation of interface shape, and the mass conservation properties of individual ﬂuids. These test cases involve the advection of interfaces of different shapes exposed to translation, rotation, deformation, and shear ﬂow. Prescribed solenoidal velocity ﬁelds are used and no attempt is made to couple the advection of the level set function with the momentum equations. For the solution of level set equation we have employed ﬁrst-order upwind scheme, MacCormack method, second-order ENO scheme, and ﬁfth-order WENO scheme. Our studies show that the level set method perform well when higher-order schemes are used for the solution of advection equation. However, for certain type of shearing and vortical velocity ﬁelds mass conservation is an issue on coarser meshes even with higher order schemes. Finer mesh must be used in such situations to reduce numerical diffusion.
Gu, Wei-Min
2012-01-01
By taking into account the local energy balance per unit volume between the viscous heating and the advective cooling plus the radiative cooling, we investigate the vertical structure of radiation pressure-supported accretion disks in spherical coordinates. Our solutions show that the photosphere of the disk is close to the polar axis and therefore the disk seems to be extremely thick. However, the profile of density implies that most of the accreted matter exists in a moderate range around the equatorial plane. We show that the well-known polytropic relation between the pressure and the density is unsuitable for describing the vertical structure of radiation pressure-supported disks. More importantly, we find that the energy advection is significant even for slightly sub-Eddington accretion disks. We argue that the non-negligible advection may help to understand why the standard thin disk model is likely to be inaccurate above \\sim 0.3 Eddington luminosity, which was found by some works on the black hole spi...
Stochastic analysis of field-scale heat advection in heterogeneous aquifers
Directory of Open Access Journals (Sweden)
C.-M. Chang
2012-03-01
Full Text Available Owing to the analogy between the solute and heat transport processes, it can be expected that the rate of growth of the spatial second moments of the heat flux in a heterogeneous aquifer over relatively large space scales is greater than that predicted by applying the classical heat transport model. The motivation of stochastic analysis of heat transport at the field scale is therefore to quantify the enhanced growth of the field-scale second moments caused by the spatially varying specific discharge field. Within the framework of stochastic theory, an effective advection-dispersion equation containing effective parameters (namely, the macrodispersion coefficients is developed to model the mean temperature field. The rate of growth of the field-scale spatial second moments of the mean temperature field in the principal coordinate directions is described by the macrodispersion coefficient. The variance of the temperature field is also developed to characterize the reliability to be anticipated in applying the mean heat transport model. It is found that the heterogeneity of the medium and the correlation length of the log hydraulic conductivity are important in enhancing the field-scale heat advection, while the effective thermal conductivity plays the role in reducing the field-scale heat advection.
A KdV-like advection-dispersion equation with some remarkable properties
Sen, Abhijit; Thyagaraja, Anantanarayanan; Krishnaswami, Govind S
2011-01-01
We discuss a new non-linear advection-dispersion equation u_t + (2 u_{xx}/u) u_x = epsilon u_{xxx}, invariant under scaling of dependent variable and referred to here as SIdV. This PDE (with dispersion coefficient unity) was discovered in a genetic programming search for equations sharing the Korteweg-de Vries (KdV) solitary wave solution. Indeed, there is a one-parameter family of first order advection equations with cubic dispersion sharing the KdV solitary wave, that interpolate between SIdV and KdV. SIdV is one of the two simplest such translation and space-time reflection-symmetric equations invariant under rescaling of wave amplitude u. The scale-invariant advection in SIdV is reminiscent of the (E x B)/B^2 velocity of plasma physics. We identify two conservation laws, though initial investigations indicate that SIdV does not follow from a polynomial Lagrangian of the KdV sort. Nevertheless, SIdV possesses solitary and periodic travelling waves and recurrence properties usually associated with integrabl...
Energy Technology Data Exchange (ETDEWEB)
Andersen, C. [Risoe National Lab., Dept. of Nucl. Safety Res. and Nucl. Facilities, Roskilde (Denmark); Koopmanns, M.; Meijer, R.J. de [Kernfysische Versneller Inst., Environmental Radioactivity Res., Groningen (Netherlands)
1996-04-01
To assess the effectiveness of mitigative measures against radon ({sup 222}Rn) entry into houses, experiments were conducted in a crawl-space house where the dirt floor of the crawl space was covered with sheets of 0.23 mm polyethylene foil fixed to the walls. The radon concentration was measured below the foil and in the crawl space together with environmental variables such as indoor-outdoor pressure differences. The experimental data was analyzed using various types of models including a simplistic mass-balance model, a regression model, and a two-dimensional numerical model based on Darcy flow or soil gas and combined diffusive and advective transport of radon. The main outcome of the work was that: (i) The soil-gas entry rate per pascal depressurization was at the order of 1 m{sup 3} h{sup -1}, (ii) the stack-related part of the depressurization of the crawl space (approx. 0.1 Pa deg. C{sup -1}) was controlled by the temperature difference between the living room of the house and the outdoors (not by the difference between the crawl space and the outdoors), (iii) that part of the wind-related depressurization that was measured by the pressure transducers seemed to force radon into the crawl space in the same proportion as the stack-related part of the depressurization, (iv) the ratio of advective and diffusive entry was approx. 0.7, when the crawl space was depressurized 1.5 Pa, (v) the effective diffusivity of the foil was found to be three orders of magnitude larger than that measured in the laboratory (the enhanced diffusivity was most likely caused by leaks in the foil and by mixing fans located in the crawl space), and (vi) there was no measurable mitigative impact of having the sheets of foil on the crawl-space floor even if the crawl space was artificially pressurized or depressurized. (au) 28 tabs., 36 ills., 61 refs.
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Torres Astorga, Romina; Velasco, Hugo; Valladares, Diego L.; Lohaiza, Flavia; Ayub, Jimena Juri; Rizzotto, Marcos [Grupo de Estudios Ambientales. Instituto de Matematica Aplicada San Luis - Universidad Nacional de San Luis - CONICET, San Luis (Argentina)
2014-07-01
{sup 7}Be is a short-lived environmental radionuclide, produced in the upper atmosphere by spallation of nitrogen and oxygen by cosmic rays. After of the production by the nuclear reaction, {sup 7}Be diffuses through the atmosphere until it attaches to atmospheric aerosols. Subsequently, it is deposited on the earth surface mainly as wet fallout. The main physical processes which transport {sup 7}Be in soil are diffusion and advection by water. Migration parameters and measurements confirm that sorption is the main physical process, which confines {sup 7}Be concentration to soil surface. The literature data show that in soils, {sup 7}Be is concentrated near the surface (0-2 cm) as it is adsorbed onto clay minerals after its deposition on the soil surface and does not penetrate deeper into soils due to its short half-life. The maximum mass activity density of {sup 7}Be is found at the point of input of the radionuclide, i.e. at the surface of the soil column, showing a exponential distribution profile typical of a purely diffusive transport. Many studies applying the advection dispersion models have been reported in the literature in order to modelling the transport of {sup 137}Cs in soils. On them, the models are used to achieve information of the mechanisms that govern the transport, i. e. the model is used to explain the soil profile of radionuclide. The effective dispersion coefficient and the apparent advection velocity of radionuclide in soil are also obtained by fitting the analytical solution of the model equation to measured depth distributions of the radionuclide. In this work, the advective dispersive transport model with linear sorption is used to analyze the vertical migration process of {sup 7}Be in soils of undisturbed or reference sites. The deposition history is approximated by pulse-like input functions and time dependent analytical solution of equation model is obtained. The values of dispersion coefficient and apparent advection velocity obtained
Schmuck, Markus; Pradas, Marc; Pavliotis, Grigorios A.; Kalliadasis, Serafim
2014-11-01
Based on thermodynamic and variational principles we formulate novel equations for mixtures of incompressible fluids in strongly heterogeneous domains, such as composites and porous media, using elements from the regular solution theory. Starting with equations that fully resolve the pores of a porous medium, represented as a periodic covering of a single reference pore, we rigorously derive effective macroscopic phase field equations under the assumption of periodic and strongly convective flow. Our derivation is based on the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg-Landau/Cahn-Hilliard-type equations. We discover systematically diffusion-dispersion relations (including Taylor-Aris-dispersion) as in classical convection-diffusion problems. Our results represent a systematic and efficient computational strategy to macroscopically track interfaces in heterogeneous media which together with the well-known versatility of phase field models forms a promising basis for the analysis of a wide spectrum of engineering and scientific applications such as oil recovery, for instance.
Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow (a lumped vortex model
Directory of Open Access Journals (Sweden)
Bai Chenyuan
2014-02-01
Full Text Available For purpose of easy identification of the role of free vortices on the lift and drag and for purpose of fast or engineering evaluation of forces for each individual body, we will extend in this paper the Kutta–Joukowski (KJ theorem to the case of inviscid flow with multiple free vortices and multiple airfoils. The major simplification used in this paper is that each airfoil is represented by a lumped vortex, which may hold true when the distances between vortices and bodies are large enough. It is found that the Kutta–Joukowski theorem still holds provided that the local freestream velocity and the circulation of the bound vortex are modified by the induced velocity due to the outside vortices and airfoils. We will demonstrate how to use the present result to identify the role of vortices on the forces according to their position, strength and rotation direction. Moreover, we will apply the present results to a two-cylinder example of Crowdy and the Wagner example to demonstrate how to perform fast force approximation for multi-body and multi-vortex problems. The lumped vortex assumption has the advantage of giving such kinds of approximate results which are very easy to use. The lack of accuracy for such a fast evaluation will be compensated by a rigorous extension, with the lumped vortex assumption removed and with vortex production included, in a forthcoming paper.
Generalized Kutta-Joukowski theorem for multi-vortex and multi-airfoil flow (a lumped vortex model)
Institute of Scientific and Technical Information of China (English)
Bai Chenyuan; Wu Ziniu
2014-01-01
For purpose of easy identification of the role of free vortices on the lift and drag and for purpose of fast or engineering evaluation of forces for each individual body, we will extend in this paper the Kutta-Joukowski (KJ) theorem to the case of inviscid flow with multiple free vortices and multiple airfoils. The major simplification used in this paper is that each airfoil is represented by a lumped vortex, which may hold true when the distances between vortices and bodies are large enough. It is found that the Kutta-Joukowski theorem still holds provided that the local freestream velocity and the circulation of the bound vortex are modified by the induced velocity due to the out-side vortices and airfoils. We will demonstrate how to use the present result to identify the role of vortices on the forces according to their position, strength and rotation direction. Moreover, we will apply the present results to a two-cylinder example of Crowdy and the Wagner example to demon-strate how to perform fast force approximation for multi-body and multi-vortex problems. The lumped vortex assumption has the advantage of giving such kinds of approximate results which are very easy to use. The lack of accuracy for such a fast evaluation will be compensated by a rig-orous extension, with the lumped vortex assumption removed and with vortex production included, in a forthcoming paper.
Zhang, Yan; Zhao, Hao-Jie; Bai, Yu
2017-06-01
In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic (MHD) flow and heat transfer of an incompressible generalized Burgers’ fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers’ fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm, whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ 1 and retardation time λ 3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness. Supported by the National Natural Science Foundations of China under Grant Nos. 21576023, 51406008, and the National Key Research Program of China under Grant Nos. 2016YFC0700601, 2016YFC0700603, and 2016YFE0115500
Flow visualization in science and mathematics
Energy Technology Data Exchange (ETDEWEB)
Max, Nelson; Correa, Carlos; Muelder, Chris; Yan Shi; Chen, Cheng-Kai; Ma, Kwan-Liu, E-mail: max@cs.ucdavis.ed [Department of Computer Science, University of California, Davis 1 Shields Ave., Davis California, 95616 (United States)
2009-07-01
We present several methods for visualizing motion, vector fields, and flows, including polygonal surface advection, visibility driven transfer functions, feature extraction and tracking, and motion frequency analysis and enhancement. They are applied to chaotic attractors, turbulent vortices, supernovae, and seismic data.
Measurement of advective soil gas flux: Results of field and laboratory experiments with CO2
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Amonette, James E.; Barr, Jonathan L.; Erikson, Rebecca L.; Dobeck, Laura M.; Barr, Jamie L.; Shaw, Joseph A.
2013-10-01
We modified our multi-channel, steady-state flow-through (SSFT), soil-CO2 flux monitoring system to include an array of inexpensive pyroelectric non-dispersive infrared detectors for full-range (0-100%) coverage of CO2 concentrations without dilution, and a larger-diameter vent tube. We then conducted field testing of this system from late July through mid-September 2010 at the Zero Emissions Research and Technology (ZERT) project site located in Bozeman, MT, and subsequently, laboratory testing at the Pacific Northwest National Laboratory (PNNL) in Richland, WA using a flux bucket filled with dry sand. In the field, an array of twenty-five SSFT and three non-steady-state (NSS) flux chambers was installed in a 10x4 m area, the long boundary of which was directly above a shallow (2-m depth) horizontal injection well located 0.5 m below the water table. Two additional chambers (one SSFT and one NSS) were installed 10 m from the well for background measurements. Volumetric soil moisture sensors were installed at each SSFT chamber to measure mean levels in the top 0.15 m of soil. A total flux of 52 kg CO2 d-1 was injected into the well for 27 d and the efflux from the soil was monitored by the chambers before, during, and for 27 d after the injection. Overall, the results were consistent with those from previous years, showing a radial efflux pattern centered on a known “hot spot”, rapid responses to changes in injection rate and wind power, evidence for movement of the CO2 plume during the injection, and nominal flux levels from the SSFT chambers that were up to 6-fold higher than those measured by adjacent NSS chambers. Soil moisture levels varied during the experiment from moderate to near saturation with the highest levels occurring consistently at the hot spot. The effects of wind on measured flux were complex and decreased as soil moisture content increased. In the laboratory, flux bucket testing with the SSFT chamber showed large measured-flux enhancement
Energy Technology Data Exchange (ETDEWEB)
Fraser, D.W.H. [Univ. of British Columbia (Canada); Abdelmessih, A.H. [Univ. of Toronto, Ontario (Canada)
1995-09-01
A general unified model is developed to predict one-component critical two-phase pipe flow. Modelling of the two-phase flow is accomplished by describing the evolution of the flow between the location of flashing inception and the exit (critical) plane. The model approximates the nonequilibrium phase change process via thermodynamic equilibrium paths. Included are the relative effects of varying the location of flashing inception, pipe geometry, fluid properties and length to diameter ratio. The model predicts that a range of critical mass fluxes exist and is bound by a maximum and minimum value for a given thermodynamic state. This range is more pronounced at lower subcooled stagnation states and can be attributed to the variation in the location of flashing inception. The model is based on the results of an experimental study of the critical two-phase flow of saturated and subcooled water through long tubes. In that study, the location of flashing inception was accurately controlled and adjusted through the use of a new device. The data obtained revealed that for fixed stagnation conditions, the maximum critical mass flux occurred with flashing inception located near the pipe exit; while minimum critical mass fluxes occurred with the flashing front located further upstream. Available data since 1970 for both short and long tubes over a wide range of conditions are compared with the model predictions. This includes test section L/D ratios from 25 to 300 and covers a temperature and pressure range of 110 to 280{degrees}C and 0.16 to 6.9 MPa. respectively. The predicted maximum and minimum critical mass fluxes show an excellent agreement with the range observed in the experimental data.
It is well known that the fate and transport of contaminants in the subsurface are controlled by complex processes including advection, dispersion-diffusion, and chemical reactions. However, the interplay between the physical transport processes and chemical reactions, and their...
Transient eddy current flow metering
Forbriger, Jan
2015-01-01
Measuring local velocities or entire flow rates in liquid metals or semiconductor melts is a notorious problem in many industrial applications, including metal casting and silicon crystal growth. We present a new variant of an old technique which relies on the continuous tracking of a flow-advected transient eddy current that is induced by a pulsed external magnetic field. This calibration-free method is validated by applying it to the velocity of a spinning disk made of aluminum. First tests at a rig with a flow of liquid GaInSn are also presented.
Transient eddy current flow metering
Forbriger, J.; Stefani, F.
2015-10-01
Measuring local velocities or entire flow rates in liquid metals or semiconductor melts is a notorious problem in many industrial applications, including metal casting and silicon crystal growth. We present a new variant of an old technique which relies on the continuous tracking of a flow-advected transient eddy current that is induced by a pulsed external magnetic field. This calibration-free method is validated by applying it to the velocity of a spinning disk made of aluminum. First tests at a rig with a flow of liquid GaInSn are also presented.
Benthuysen, Jessica; Furue, Ryo; McCreary, Julian P.; Bindoff, Nathaniel L.; Phillips, Helen E.
2014-03-01
depth. When the timescale δt is sufficiently short, the poleward current is nearly barotropic. The current's spatial structure over the shelf is controlled by horizontal mixing, having the structure of a Munk layer. Increasing vertical diffusion deepens the upper layer thickness and strengthens the alongshore current speed. Bottom drag leads to an offshore flow along the bottom, reducing the net onshore transport and weakening the current's poleward acceleration. When δt is long, poleward advection of buoyancy forms a density front near the shelf break, intensifying poleward speeds near the surface. With bottom drag, a bottom Ekman flow advects density offshore, shifting the jet core offshore of the shelf break. The resulting cross-shelf density gradient reverses the meridional current's direction at depth, leading to an equatorward undercurrent.
Yoon, Min; Ahn, Junsun; Hwang, Jinyul; Sung, Hyung Jin
2016-08-01
The relationship between the frictional drag and the velocity-vorticity correlations in wall-bounded turbulent flows is derived from the mean vorticity equation. A formula for the skin friction coefficient is proposed and evaluated with regards to three canonical wall-bounded flows: turbulent boundary layer, turbulent channel flow, and turbulent pipe flow. The frictional drag encompasses four terms: advective vorticity transport, vortex stretching, viscous, and inhomogeneous terms. Drag-reduced channel flow with the slip condition is used to test the reliability of the formula. The advective vorticity transport and vortex stretching terms are found to dominate the contributions to the frictional drag.
Wilde, Pat; Quinby-Hunt, Mary S.; Berry, William B. N.
The vast majority of oceanic biomass lives in the surface wind-mixed layer (0-100 m) of the ocean, trophically dependent on light or primary production based on photosynthesis. Waters from the main pycnocline (100-1000 m) or deeper naturally contain decay products from sinking organic matter as a function of the oxidation state of the waters. Such products, in proper concentrations, can inhibit photosynthetic growth or are toxic or debilitating to respirors. Usually, physical oceanographic processes of vertical circulation are slow or volumetrically small enough to permit conditioning or mixing of toxicants of the deep waters with surface waters so that the deleterious effects of deep water are neutralized or localized. However, rapid global to regional scale vertical advection of deep waters into the surface mixed layer could create an ecologic crisis for various marine groups through a combination of: (1) direct toxicity; (2) reduction or modification of nutrient and food supplies through inhibition of photosynthesis; (3) chronic debilitation caused by contact with such toxic waters; or (4) increased predation by more adaptive or less effected taxa. Such events are not necessarily universally deleterious as they could offer new opportunities for taxa ecologically restricted under prior conditions. During cool climates with oxic deep waters, a crisis may be caused by upwelling of metals concentrated with depth and resulting in reduced primary productivity, as well as metal toxic and/or chronic reactions in higher groups. During warm climates with anoxic to dysaerobic waters in the pycnocline, a crisis may result from contact with anoxic waters with a maximum effect on respirors and a minimal to enhanced effect on phytoplankton. Upwelling may come from three redox zones: I- oxic; II- nitric; and III- sulfatic. Each zone would be the source of waters of differing chemistries that could be advected into the photic zone. The effect on specific taxa will be selective
Dissipative advective accretion disc solutions with variable adiabatic index around black holes
Kumar, Rajiv
2014-01-01
We investigated accretion onto black holes in presence of viscosity and cooling, by employing an equation of state with variable adiabatic index and multi-species fluid. We obtained the expression of generalized Bernoulli parameter which is a constant of motion for an accretion flow in presence of viscosity and cooling. We obtained all possible transonic solutions for a variety of boundary conditions, viscosity parameters and accretion rates. We identified the solutions with their positions in the parameter space of generalized Bernoulli parameter and the angular momentum on the horizon. We showed that a shocked solution is more luminous than a shock free one. For particular energies and viscosity parameters, we obtained accretion disc luminosities in the range of 0.001-12 \\% of Eddington luminosity, and the radiative efficiency seemed to increase with the mass accretion rate too. We found steady state shock solutions even for high viscosity parameters, high accretion rates, as well as, for wide range of comp...
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
Ueckermann, M. P.; Lermusiaux, P. F. J.; Sapsis, T. P.
2013-01-01
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier-Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
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Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires
1968-12-01
This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental
DEFF Research Database (Denmark)
Guyonvarch, Estelle; Ramin, Elham; Kulahci, Murat
2015-01-01
The present study aims at using statistically designed computational fluid dynamics (CFD) simulations as numerical experiments for the identification of one-dimensional (1-D) advection-dispersion models – computationally light tools, used e.g., as sub-models in systems analysis. The objective...... using the example of a circular secondary settling tank (SST). First, the significant design and flow factors are screened out by applying the statistical method of two-level fractional factorial design of experiments. Second, based on the number of significant factors identified through the factor...... both in 2-D and 1-D was undertaken. Results suggest that the iCFD model developed for the SST through the proposed methodology is able to predict solid distribution with high accuracy – taking a reasonable computational effort – when compared to multi-dimensional numerical experiments, under a wide...