Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2013-01-01

A class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the L2(H 1) for pressure and in the L∞(L2) and L2(H1) for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions. © 2013 Societ y for Industrial and Applied Mathematics.

2.5-D poroelastic wave modelling in double porosity media

Science.gov (United States)

Liu, Xu; Greenhalgh, Stewart; Wang, Yanghua

2011-09-01

To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as a way to represent the sum of the convolution integrals for both the solid particle velocity and the macroscopic fluid flux in the governing equations. By application of the memory equations, the field quantities at every time step need not be stored. However, this approximation allows just two Zener relaxation times to represent the very complex double porosity and dual permeability attenuation mechanism, and thus reduce the difficulty. The 2.5-D governing equations are numerically solved by a time-splitting method for the non-stiff parts and an explicit fourth-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. The 2.5-D solution has the advantage of producing a 3-D wavefield (point source) for a 2-D model but is much more computationally efficient than the full 3-D solution. As an illustrative example, we firstly show the computed 2.5-D wavefields in a homogeneous single porosity model for which we reformulated an analytic solution. Results for a two-layer, water-saturated double porosity model and a laterally heterogeneous double porosity structure are also presented.

Coupling multipoint flux mixed finite element methodswith continuous Galerkin methods for poroelasticity

KAUST Repository

Wheeler, Mary

2013-11-16

We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. © Springer Science+Business Media Dordrecht 2013.

Dispersion in poroelastic systems

International Nuclear Information System (INIS)

Berryman, James G.; Wang, Herbert F.

2001-01-01

We address one key source of the known discrepancies between theory and experiment in poroelasticity, i.e., the fact that Gassmann's equations for the bulk and shear moduli predict that the shear modulus is independent of the saturating fluid properties, whereas it is observed on the contrary that at high enough frequencies the shear modulus can in fact depend on the fluid's elastic properties in many porous materials. One clue to understanding this behavior comes from effective medium theory, which shows that the shear modulus does depend on the fluid properties in many circumstances. In comparison to values predicted by effective medium theory, Gassmann's equations predict different, smaller values for both the effective bulk and shear moduli of porous media. Sorting through these apparent (but not actual) disagreements among theory and theory, and theory and experiment is the main thrust of the paper

Well-Posedness of a fully coupled thermo-chemo-poroelastic system with applications to petroleum rock mechanics

Directory of Open Access Journals (Sweden)

Tetyana Malysheva

2017-05-01

Full Text Available We consider a system of fully coupled parabolic and elliptic equations constituting the general model of chemical thermo-poroelasticity for a fluid-saturated porous media. The main result of this paper is the developed well-posedness theory for the corresponding initial-boundary problem arising from petroleum rock mechanics applications. Using the proposed pseudo-decoupling method, we establish, subject to some natural assumptions imposed on matrices of diffusion coefficients, the existence, uniqueness, and continuous dependence on initial and boundary data of a weak solution to the problem. Numerical experiments confirm the applicability of the obtained well-posedness results for thermo-chemo-poroelastic models with real-data parameters.

Effect of Poroelasticity on Hydraulic Fracture Interactions

DEFF Research Database (Denmark)

Usui, Tomoya; Salimzadeh, Saeed; Paluszny, Adriana

2017-01-01

This study investigates, by performing finite element-based simulations, the influence of fluid leak-off and poroelasticity on growth of multiple hydraulic fractures that initiate from a single horizontal well. In this research, poroelastic deformation of the matrix is coupled with fluid flow in ...

Ultra Low Noise Poroelastic Road Surfaces

Directory of Open Access Journals (Sweden)

Jerzy A. Ejsmont

2016-04-01

Full Text Available Noise is one of the most important environmental problems related to road traffic. During the last decades, the noise emitted by the engines and powertrains of vehicles was greatly reduced and tires became a clearly dominant noise source. The article describes the concept of low noise poroelastic road surfaces that are composed of mineral and rubber aggregate bound by polyurethane resin. Those surfaces have a porous structure and are much more flexible than standard asphalt or cement concrete pavements due to high content of rubber aggregate and elastic binder. Measurements performed in several European countries indicate that such surfaces decrease tire/road noise between 7 dB and 12 dB with respect to reference surfaces such as dense asphalt concrete or stone matrix asphalt. Furthermore, poroelastic road surfaces ascertain the rolling resistance of car tires, which is comparable to classic pavements. One of the unforeseen properties of the poroelastic road surfaces is their ability to decrease the risks related to car fires with fuel spills. The article presents the road and laboratory results of noise, rolling resistance, and fire tests performed on a few types of poroelastic road surfaces.

A hydrologic view on Biot's theory of poroelasticity

Energy Technology Data Exchange (ETDEWEB)

Silin, D.B.; Korneev, V.A.; Goloshubin, G.M.; Patzek, T.W.

2004-01-13

The main objective of this work is to obtain a simplified asymptotic representation of the reflection of seismic signal from a fluid-saturated porous medium in the low-frequency domain. In the first part, we derive the equations of low-frequency harmonic waves in a fluid-saturated elastic porous medium from the basic concepts of filtration theory. We demonstrate that the obtained equations can be related to the poroelasticity model of Frenkel-Gassmann-Biot, and to pressure diffusion model routinely used in well test analysis as well. We thus try to put the poroelastic and filtration theories on the same ground. We study the reflection of a low-frequency signal from a plane interface between elastic and elastic fluid-saturated porous media. We obtain an asymptotic scaling of the frequency-dependent component of the reflection coefficient with respect to a dimensionless parameter depending on the frequency of the signal and the reservoir fluid mobility. We also investigate the impact of the relaxation time and tortuosity on this scaling.

Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2013-01-01

We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two-phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L2(H1) for saturation and in L∞(H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.

Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

KAUST Repository

Kou, Jisheng

2013-06-20

We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two-phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L2(H1) for saturation and in L∞(H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.

Experimental measurement of compressibility coefficients of synthetic sandstone in hydrostatic conditions

International Nuclear Information System (INIS)

Asaei, H; Moosavi, M

2013-01-01

For the characterization of the mechanical behavior of porous media in elastic conditions, the theory of poroelasticity is used. The number of poroelastic coefficients is greater in elastic conditions because of the complexity of porous media. The laboratory measurement of poroelastic coefficients needs a system that can control and measure the variables of poroelasticity. In this paper, experimental measurements of these coefficients are presented. Laboratory tests are performed using a system designed by the authors. Laboratory hydrostatic tests are performed on cylindrical samples in drained, pore pressure loading, undrained and dry conditions. Compressibilities (bulk and pore compressibility), effective stress and Skempton coefficients are measured by these tests. Samples are made of a composition (sand and cement) and are made by a compaction process synthetically. Calibration tests are performed for the setup to identify possible errors in the system and to correct the results of the main tests. This is done by performing similar compressibility tests at each stress level on a cylindrical steel sample (5.47 mm in diameter) with a longitudinal hole along it (hollow cylinder). A steel sample is used to assume an incompressible sample. The results of the tests are compared with the theory of poroelasticity and the obtained graphs and their errors are analyzed. This study shows that the results of the drained and pore pressure loading tests are compatible with poroelastic formulation, while the undrained results have errors because of extra fluid volume in the pore pressure system and calibration difficulties. (paper)

Efficient Wavefield Extrapolation In Anisotropic Media

KAUST Repository

Alkhalifah, Tariq; Ma, Xuxin; Waheed, Umair bin; Zuberi, Mohammad Akbar Hosain

2014-01-01

Various examples are provided for wavefield extrapolation in anisotropic media. In one example, among others, a method includes determining an effective isotropic velocity model and extrapolating an equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. The effective isotropic velocity model can be based upon a kinematic geometrical representation of an anisotropic, poroelastic or viscoelastic wavefield. Extrapolating the equivalent propagation can use isotopic, acoustic or elastic operators based upon the determined effective isotropic velocity model. In another example, non-transitory computer readable medium stores an application that, when executed by processing circuitry, causes the processing circuitry to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. In another example, a system includes processing circuitry and an application configured to cause the system to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield.

Efficient Wavefield Extrapolation In Anisotropic Media

KAUST Repository

Alkhalifah, Tariq

2014-07-03

Various examples are provided for wavefield extrapolation in anisotropic media. In one example, among others, a method includes determining an effective isotropic velocity model and extrapolating an equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. The effective isotropic velocity model can be based upon a kinematic geometrical representation of an anisotropic, poroelastic or viscoelastic wavefield. Extrapolating the equivalent propagation can use isotopic, acoustic or elastic operators based upon the determined effective isotropic velocity model. In another example, non-transitory computer readable medium stores an application that, when executed by processing circuitry, causes the processing circuitry to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield. In another example, a system includes processing circuitry and an application configured to cause the system to determine the effective isotropic velocity model and extrapolate the equivalent propagation of an anisotropic, poroelastic or viscoelastic wavefield.

Analysis of radial vibrations of poroelastic circular cylindrical shells ...

African Journals Online (AJOL)

DR OKE

vanished, the considered problem reduces to the problem of radial vibrations of fluid-filled poroelastic circular cylindrical shell. (2). When the .... the volume change of the solid to that of liquid. ..... When the outer fluid density is zero, that is, ρof = 0 then the poroelastic cylindrical shell immersed in an acoustic medium will.

Dynamics of poroelastic foams

Science.gov (United States)

Forterre, Yoel; Sobac, Benjamin

2010-11-01

Soft poroelastic structures are widespread in biological tissues such as cartilaginous joints in bones, blood-filled placentae or plant organs. Here we investigate the dynamics of open elastic foams immersed in viscous fluids, as model soft poroelastic materials. The experiment consists in slowly compacting blocs of polyurethane solid foam embedded in silicon oil-tanks and studying their relaxation to equilibrium when the confining stress is suddenly released. Measurements of the local fluid pressure and foam velocity field are compared with a simple two-phase flow approach. For small initial compactions, the results show quantitative agreement with the classical diffusion theory of soil consolidation (Terzaghi, Biot). On the other hand, for large initial compactions, the dynamics exhibits long relaxation times and decompaction fronts, which are mainly controlled by the highly non-linear mechanical response of the foam. The analogy between this process and the evaporation of a polymer melt close to the glass transition will be briefly discussed.

Complex three dimensional modelling of porous media using high performance computing and multi-scale incompressible approach

Science.gov (United States)

Martin, R.; Orgogozo, L.; Noiriel, C. N.; Guibert, R.; Golfier, F.; Debenest, G.; Quintard, M.

2013-05-01

computed by sending batteries of codes in a mass production procedure. Some constraints can now be provided for poro-elastic imaging at the scale of reservoirs, for CO2 storage monitoring or geophysical exploration. 1. Golfier F. et al., Biofilms in porous media: Development of macroscopic transport equations va volume averaging with closure for local mass equilibrium conditions, Advances in Water Resources, 32, 463-485 (2009). 2. Orgogozo L. et al., Upscaling of transport processes in porous media with biofilms in non-equilibrium conditions, Advances in Water Resources, 33(5), 585-600 (2010). 3. Davit Y. et al., Modeling non-equilibrium mass transport in biologically reactive porous media, Advances in Water Resources, 33, 1075-1093, (2010). 4. Davit Y. et al., Imaging biofilm in porous media using X-ray computed micro-tomography, Journal of Microscopy, 242(1), 15-25 (2010). 5. Noiriel C. et al., Upscaling calcium carbonate precipitation rates from pore to continuum scale, Chemical Geology, 318-319, 60-74 (2012).

Normal Mode Analysis to a Poroelastic Half-Space Problem under Generalized Thermoelasticity

Directory of Open Access Journals (Sweden)

Chunbao Xiong

Full Text Available Abstract The thermo-hydro-mechanical problems associated with a poroelastic half-space soil medium with variable properties under generalized thermoelasticity theory were investigated in this study. By remaining faithful to Biot’s theory of dynamic poroelasticity, we idealized the foundation material as a uniform, fully saturated, poroelastic half-space medium. We first subjected this medium to time harmonic loads consisting of normal or thermal loads, then investigated the differences between the coupled thermohydro-mechanical dynamic models and the thermo-elastic dynamic models. We used normal mode analysis to solve the resulting non-dimensional coupled equations, then investigated the effects that non-dimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution exerted on the poroelastic half-space medium and represented them graphically.

Equivalence between short-time biphasic and incompressible elastic material responses.

Science.gov (United States)

Ateshian, Gerard A; Ellis, Benjamin J; Weiss, Jeffrey A

2007-06-01

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltatelasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.

Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

KAUST Repository

Kou, Jisheng

2014-03-22

Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc.

Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2014-01-01

Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc.

Guided Circumferential Waves in Layered Poroelastic Cylinders

Directory of Open Access Journals (Sweden)

Shah S.A.

2016-12-01

Full Text Available The present paper investigates the propagation of time harmonic circumferential waves in a two-dimensional hollow poroelastic cylinder with an inner shaft (shaft-bearing assembly. The hollow poroelastic cylinder and inner shaft are assumed to be infinite in axial direction. The outer surface of the cylinder is stress free and at the interface, between the inner shaft and the outer cylinder, it is assumed to be free sliding and the interfacial shear stresses are zero, also the normal stress and radial displacements are continuous. The frequency equation of guided circumferential waves for a permeable and an impermeable surface is obtained. When the angular wave number vanish the frequency equation of guided circumferential waves for a permeable and an impermeable surface degenerates and the dilatational and shear waves are uncoupled. Shear waves are independent of the nature of surface. The frequency equation of a permeable and an impermeable surface for bore-piston assembly is obtained as a particular case of the model under consideration when the outer radius of the hollow poroelastic cylinder tends to infinity. Results of previous studies are obtained as a particular case of the present study. Nondimensional frequency as a function of wave number is presented graphically for two types of models and discussed. Numerical results show that, in general, the first modes are linear for permeable and impermeable surfaces and the frequency of a permeable surface is more than that of an impermeable surface.

Variational continuum multiphase poroelasticity theory and applications

CERN Document Server

Serpieri, Roberto

2017-01-01

This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics. The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations. It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the...

Simultaneous measurements of transport and poroelastic properties of rocks.

Science.gov (United States)

Hasanov, Azar K; Prasad, Manika; Batzle, Michael L

2017-12-01

A novel laboratory apparatus has been developed for simultaneous measurements of transport and poroelastic rock properties. These transport and poroelastic properties at reservoir pressure and temperature conditions are required inputs for various geoscience applications, such as reservoir simulation, basin modeling, or modeling of pore pressure generation. Traditionally, the transport and poroelastic properties are measured separately using, for example, the oscillating pore pressure method to measure hydraulic transport properties, static strain measurements for elastic properties, and pore volumometry for storage capacity. In addition to time, the separate set of measurements require either aliquot cores or subjecting the same core to multiple pressure tests. We modified the oscillating pore pressure method to build an experimental setup, capable of measuring permeability, storage capacity, and pseudo-bulk modulus of rocks simultaneously. We present here the test method, calibration measurements (capillary tube), and sample measurements (sandstone) of permeability and storage capacity at reservoir conditions. We establish that hydraulically measured storage capacities were overestimated by an order of magnitude when compared to elastically derived ones. Our concurrent measurement of elastic properties during the hydraulic experiment provides an independent constraint on storage capacity.

Sound transmission through triple-panel structures lined with poroelastic materials

Science.gov (United States)

Liu, Yu

2015-03-01

In this paper, previous theories on the prediction of sound transmission loss for a double-panel structure lined with poroelastic materials are extended to address the problem of a triple-panel structure. Six typical configurations are considered for a triple-panel structure based on the method of coupling the porous layers to the facing panels which determines critically the sound insulation performance of the system. The transfer matrix method is employed to solve the system by applying appropriate types of boundary conditions for these configurations. The transmission loss of the triple-panel structures in a diffuse sound field is calculated as a function of frequency and compared with that of corresponding double-panel structures. Generally, the triple-panel structure with poroelastic linings has superior acoustic performance to the double-panel counterpart, remarkably in the mid-high frequency range and possibly at low frequencies, by selecting appropriate configurations in which those with two air gaps in the structure exhibit the best overall performance over the entire frequency range. The poroelastic lining significantly lowers the cut-on frequency above which the triple-panel structure exhibits noticeably higher transmission loss. Compared with a double-panel structure, the wider range of system parameters for a triple-panel structure due to the additional partition provides more design space for tuning the sound insulation performance. Despite the increased structural complexity, the triple-panel structure lined with poroelastic materials has the obvious advantages in sound transmission loss while without the penalties in weight and volume, and is hence a promising replacement for the widely used double-panel sandwich structure.

Large poroelastic deformation of a soft material

Science.gov (United States)

MacMinn, Christopher W.; Dufresne, Eric R.; Wettlaufer, John S.

2014-11-01

Flow through a porous material will drive mechanical deformation when the fluid pressure becomes comparable to the stiffness of the solid skeleton. This has applications ranging from hydraulic fracture for recovery of shale gas, where fluid is injected at high pressure, to the mechanics of biological cells and tissues, where the solid skeleton is very soft. The traditional linear theory of poroelasticity captures this fluid-solid coupling by combining Darcy's law with linear elasticity. However, linear elasticity is only volume-conservative to first order in the strain, which can become problematic when damage, plasticity, or extreme softness lead to large deformations. Here, we compare the predictions of linear poroelasticity with those of a large-deformation framework in the context of two model problems. We show that errors in volume conservation are compounded and amplified by coupling with the fluid flow, and can become important even when the deformation is small. We also illustrate these results with a laboratory experiment.

Examination of the PCICE method in the nearly incompressible, as well as strictly incompressible, limits

International Nuclear Information System (INIS)

Berry, Ray A.; Martineau, Richard C.

2007-01-01

The conservative-form, pressure-based PCICE numerical method (Martineau and Berry, 2004) (Berry, 2006), recently developed for computing transient fluid flows of all speeds from very low to very high (with strong shocks), is simplified and generalized. Though the method automatically treats a continuous transition of compressibility, three distinct, limiting compressibility regimes are formally defined for purposes of discussion and comparison with traditional methods - the strictly incompressible limit, the nearly incompressible limit, and the fully compressible limit. The PCICE method's behavior is examined in each limiting regime. In the strictly incompressible limit the PCICE algorithm reduces to the traditional MAC-type method with velocity divergence driving the pressure Poisson equation. In the nearly incompressible limit the PCICE algorithm is found to reduce to a generalization of traditional incompressible methods, i.e. to one in which not only the velocity divergence effect, but also the density gradient effect is included as a driving function in the pressure Poisson equation. This nearly incompressible regime has received little attention, and it appears that in the past, strictly incompressible methods may have been conveniently applied to flows in this regime at the expense of ignoring a potentially important coupling mechanism. This could be significant in many important flows; for example, in natural convection flows resulting from high heat flux. In the fully compressible limit or regime, the algorithm is found to reduce to an expression equivalent to density-based methods for high-speed flow. (author)

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

Science.gov (United States)

Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J

2009-11-28

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.

Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system

Directory of Open Access Journals (Sweden)

Tetyana Malysheva

2016-01-01

Full Text Available This article addresses the well-posedness of a coupled parabolic-elliptic system modeling fully coupled thermal, chemical, hydraulic, and mechanical processes in porous formations that impact drilling and borehole stability. The underlying thermo-chemo-poroelastic model is a system of time-dependent parabolic equations describing thermal, solute, and fluid diffusions coupled with Navier-type elliptic equations that attempt to capture the elastic behavior of rock around a borehole. An existence and uniqueness theory for a corresponding initial-boundary value problem is an open problem in the field. We give sufficient conditions for the well-posedness in the sense of Hadamard of a weak solution to a fully coupled parabolic-elliptic initial-boundary value problem describing homogeneous and isotropic media.

Increase in transmission loss of a double panel system by addition of mass inclusions to a poro-elastic layer: A comparison between theory and experiment

Science.gov (United States)

Idrisi, Kamal; Johnson, Marty E.; Toso, Alessandro; Carneal, James P.

2009-06-01

This paper is concerned with the modeling and optimization of heterogeneous (HG) blankets, which are used in this investigation to reduce the sound transmission through double panel systems. HG blankets consist of poro-elastic media with small embedded masses, which act similarly to a distributed mass-spring-damper-system. HG blankets have shown significant potential to reduce low frequency radiated sound from structures, where traditional poro-elastic materials have little effect. A mathematical model of a double panel system with an acoustic cavity and HG blanket was developed using impedance and mobility methods. The predicted responses of the source and the receiving panel due to a point force are validated with experimental measurements. The presented results indicate that proper tuning of the HG blankets can result in broadband noise reduction below 500 Hz with less than 10% added mass.

Multiphase poroelastic finite element models for soft tissue structures

International Nuclear Information System (INIS)

Simon, B.R.

1992-01-01

During the last two decades, biological structures with soft tissue components have been modeled using poroelastic or mixture-based constitutive laws, i.e., the material is viewed as a deformable (porous) solid matrix that is saturated by mobile tissue fluid. These structures exhibit a highly nonlinear, history-dependent material behavior; undergo finite strains; and may swell or shrink when tissue ionic concentrations are altered. Give the geometric and material complexity of soft tissue structures and that they are subjected to complicated initial and boundary conditions, finite element models (FEMs) have been very useful for quantitative structural analyses. This paper surveys recent applications of poroelastic and mixture-based theories and the associated FEMs for the study of the biomechanics of soft tissues, and indicates future directions for research in this area. Equivalent finite-strain poroelastic and mixture continuum biomechanical models are presented. Special attention is given to the identification of material properties using a porohyperelastic constitutive law ans a total Lagrangian view for the formulation. The associated FEMs are then formulated to include this porohyperelastic material response and finite strains. Extensions of the theory are suggested in order to include inherent viscoelasticity, transport phenomena, and swelling in soft tissue structures. A number of biomechanical research areas are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested. 62 refs., 11 figs., 3 tabs

Multiscale modeling and topology optimization of poroelastic actuators

DEFF Research Database (Denmark)

Andreasen, Casper Schousboe; Sigmund, Ole

2012-01-01

This paper presents a method for design of optimized poroelastic materials which under internal pressurization turn into actuators for application in, for example, linear motors. The actuators are modeled in a two-scale fluid–structure interaction approach. The fluid saturated material microstruc...

Models for seismic wave propagation in periodically layered porous media

NARCIS (Netherlands)

Kudarova, A.; Van Dalen, K.N.; Drijkoningen, G.G.

2014-01-01

Several models are discussed for seismic wave propagation in periodically layered poroelastic media where layers represent mesoscopic-scale heterogeneities that are larger than the pore and grain sizes but smaller than the wavelength. The layers behave according to Biot’s theory. Wave propagation

Application of a Three-Dimensional Poroelastic BEM to Modeling the Biphasic Mechanics of Cell-Matrix Interactions in Articular Cartilage (REVISION).

Science.gov (United States)

Haider, Mansoor A; Guilak, Farshid

2007-06-15

Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.

Analysis of flexural wave propagation in poroelastic composite ...

African Journals Online (AJOL)

DR OKE

dimensional solution for free vibration problem of homogeneous isotropic cylindrical ... Abousleiman and Cui (1998) presented poroelastic solutions in an inclined ...... The Biot-willis elastic coefficients for a sandstone, Journal of Applied Mechanics, Vol. ... Study of wave motions in fluid-saturated porous rocks, Journal of the ...

Poroelastic Modeling as a Proof of Concept for Modular Representation of Coupled Geophysical Processes

Science.gov (United States)

Walker, R. L., II; Knepley, M.; Aminzadeh, F.

2017-12-01

We seek to use the tools provided by the Portable, Extensible Toolkit for Scientific Computation (PETSc) to represent a multiphysics problem in a form that decouples the element definition from the fully coupled equation through the use of pointwise functions that imitate the strong form of the governing equation. This allows allows individual physical processes to be expressed as independent kernels that may be then coupled with the existing finite element framework, PyLith, and capitalizes upon the flexibility offered by the solver, data management, and time stepping algorithms offered by PETSc. To demonstrate a characteristic example of coupled geophysical simulation devised in this manner, we present a model of a synthetic poroelastic environment, with and without the consideration of inertial effects, with fluid initially represented as a single phase. Matrix displacement and fluid pressure serve as the desired unknowns, with the option for various model parameters represented as dependent variables of the central unknowns. While independent of PyLith, this model also serves to showcase the adaptability of physics kernels for synthetic forward modeling. In addition, we seek to expand the base case to demonstrate the impact of modeling fluid as single phase compressible versus a single incompressible phase. As a goal, we also seek to include multiphase fluid modeling, as well as capillary effects.

In?situ permeability from integrated poroelastic reflection coefficients

NARCIS (Netherlands)

Van Dalen, K.N.; Ghose, R.; Drijkoningen, C.G.; Smeulders, D.M.J.

2010-01-01

A reliable estimate of the in?situ permeability of a porous layer in the subsurface is extremely difficult to obtain. We have observed that at the field seismic frequency band the poroelastic behavior for different seismic wavetypes can differ in such a way that their combination gives unique

Torsional vibrations of infinite composite poroelastic cylinders | Shah ...

African Journals Online (AJOL)

... radius of composite poroelastic solid cylinder to the radius of the inner solid cylinder. Results of previous works are shown as special case of the present analysis. By ignoring liquid effects, the results of purely elastic solid are obtained. International Journal of Engineering, Science and Technology, Vol. 2, No. 6, 2010, pp.

Computational fluid dynamics incompressible turbulent flows

CERN Document Server

Kajishima, Takeo

2017-01-01

This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications. • Introduces CFD techniques for incompressible flow and turbulence with a comprehensive approach; • Enr...

Nearly incompressible fluids: Hydrodynamics and large scale inhomogeneity

International Nuclear Information System (INIS)

Hunana, P.; Zank, G. P.; Shaikh, D.

2006-01-01

A system of hydrodynamic equations in the presence of large-scale inhomogeneities for a high plasma beta solar wind is derived. The theory is derived under the assumption of low turbulent Mach number and is developed for the flows where the usual incompressible description is not satisfactory and a full compressible treatment is too complex for any analytical studies. When the effects of compressibility are incorporated only weakly, a new description, referred to as 'nearly incompressible hydrodynamics', is obtained. The nearly incompressible theory, was originally applied to homogeneous flows. However, large-scale gradients in density, pressure, temperature, etc., are typical in the solar wind and it was unclear how inhomogeneities would affect the usual incompressible and nearly incompressible descriptions. In the homogeneous case, the lowest order expansion of the fully compressible equations leads to the usual incompressible equations, followed at higher orders by the nearly incompressible equations, as introduced by Zank and Matthaeus. With this work we show that the inclusion of large-scale inhomogeneities (in this case time-independent and radially symmetric background solar wind) modifies the leading-order incompressible description of solar wind flow. We find, for example, that the divergence of velocity fluctuations is nonsolenoidal and that density fluctuations can be described to leading order as a passive scalar. Locally (for small lengthscales), this system of equations converges to the usual incompressible equations and we therefore use the term 'locally incompressible' to describe the equations. This term should be distinguished from the term 'nearly incompressible', which is reserved for higher-order corrections. Furthermore, we find that density fluctuations scale with Mach number linearly, in contrast to the original homogeneous nearly incompressible theory, in which density fluctuations scale with the square of Mach number. Inhomogeneous nearly

Radial vibrations of an infinitely long poroelastic composite hollow ...

African Journals Online (AJOL)

user

(1997) and Abousleiman and Cui (1998) presented poroelastic solutions in an inclined borehole and transversely ... Basic equations, Formulation and solution of the Problem. The equations of ...... Mechanics and Engineering, Vol.14, pp. 865-877. ... Study of wave motions in fluid-saturated porous rocks, J. Acoust. Soc. Am.

An analytical model for nanoparticles concentration resulting from infusion into poroelastic brain tissue.

Science.gov (United States)

Pizzichelli, G; Di Michele, F; Sinibaldi, E

2016-02-01

We consider the infusion of a diluted suspension of nanoparticles (NPs) into poroelastic brain tissue, in view of relevant biomedical applications such as intratumoral thermotherapy. Indeed, the high impact of the related pathologies motivates the development of advanced therapeutic approaches, whose design also benefits from theoretical models. This study provides an analytical expression for the time-dependent NPs concentration during the infusion into poroelastic brain tissue, which also accounts for particle binding onto cells (by recalling relevant results from the colloid filtration theory). Our model is computationally inexpensive and, compared to fully numerical approaches, permits to explicitly elucidate the role of the involved physical aspects (tissue poroelasticity, infusion parameters, NPs physico-chemical properties, NP-tissue interactions underlying binding). We also present illustrative results based on parameters taken from the literature, by considering clinically relevant ranges for the infusion parameters. Moreover, we thoroughly assess the model working assumptions besides discussing its limitations. While not laying any claims of generality, our model can be used to support the development of more ambitious numerical approaches, towards the preliminary design of novel therapies based on NPs infusion into brain tissue. Copyright © 2015 Elsevier Inc. All rights reserved.

Wave energy focusing to subsurface poroelastic formations to promote oil mobilization

KAUST Repository

Karve, P. M.; Kallivokas, L. F.

2015-01-01

We discuss an inverse source formulation aimed at focusing wave energy produced by ground surface sources to target subsurface poroelastic formations. The intent of the focusing is to facilitate or enhance the mobility of oil entrapped within

Dynamic model of open shell structures buried in poroelastic soils

Science.gov (United States)

Bordón, J. D. R.; Aznárez, J. J.; Maeso, O.

2017-08-01

This paper is concerned with a three-dimensional time harmonic model of open shell structures buried in poroelastic soils. It combines the dual boundary element method (DBEM) for treating the soil and shell finite elements for modelling the structure, leading to a simple and efficient representation of buried open shell structures. A new fully regularised hypersingular boundary integral equation (HBIE) has been developed to this aim, which is then used to build the pair of dual BIEs necessary to formulate the DBEM for Biot poroelasticity. The new regularised HBIE is validated against a problem with analytical solution. The model is used in a wave diffraction problem in order to show its effectiveness. It offers excellent agreement for length to thickness ratios greater than 10, and relatively coarse meshes. The model is also applied to the calculation of impedances of bucket foundations. It is found that all impedances except the torsional one depend considerably on hydraulic conductivity within the typical frequency range of interest of offshore wind turbines.

Simulation of ultrasonic wave propagation in anisotropic poroelastic bone plate using hybrid spectral/finite element method.

Science.gov (United States)

Nguyen, Vu-Hieu; Naili, Salah

2012-08-01

This paper deals with the modeling of guided waves propagation in in vivo cortical long bone, which is known to be anisotropic medium with functionally graded porosity. The bone is modeled as an anisotropic poroelastic material by using Biot's theory formulated in high frequency domain. A hybrid spectral/finite element formulation has been developed to find the time-domain solution of ultrasonic waves propagating in a poroelastic plate immersed in two fluid halfspaces. The numerical technique is based on a combined Laplace-Fourier transform, which allows to obtain a reduced dimension problem in the frequency-wavenumber domain. In the spectral domain, as radiation conditions representing infinite fluid halfspaces may be exactly introduced, only the heterogeneous solid layer needs to be analyzed by using finite element method. Several numerical tests are presented showing very good performance of the proposed procedure. A preliminary study on the first arrived signal velocities computed by using equivalent elastic and poroelastic models will be presented. Copyright © 2012 John Wiley & Sons, Ltd.

A locally conservative stabilized continuous Galerkin finite element method for two-phase flow in poroelastic subsurfaces

Science.gov (United States)

Deng, Q.; Ginting, V.; McCaskill, B.; Torsu, P.

2017-10-01

We study the application of a stabilized continuous Galerkin finite element method (CGFEM) in the simulation of multiphase flow in poroelastic subsurfaces. The system involves a nonlinear coupling between the fluid pressure, subsurface's deformation, and the fluid phase saturation, and as such, we represent this coupling through an iterative procedure. Spatial discretization of the poroelastic system employs the standard linear finite element in combination with a numerical diffusion term to maintain stability of the algebraic system. Furthermore, direct calculation of the normal velocities from pressure and deformation does not entail a locally conservative field. To alleviate this drawback, we propose an element based post-processing technique through which local conservation can be established. The performance of the method is validated through several examples illustrating the convergence of the method, the effectivity of the stabilization term, and the ability to achieve locally conservative normal velocities. Finally, the efficacy of the method is demonstrated through simulations of realistic multiphase flow in poroelastic subsurfaces.

Upscaling in porous media : Consequences of reducing the phase on the dynamic behavior of a homogenized medium

NARCIS (Netherlands)

Kudarova, A.; van Dalen, K.N.; Drijkoningen, G.G.

2014-01-01

Effective-medium approaches are widely used to model initially heterogeneous systems: it saves computational time. In poroelasticity (two-phase media), it is advantageous to use one-phase effective medium if possible: it simplifies computations even more. In this paper we discuss situations where

Generalization of Eshelby close-quote s Formula for a Single Ellipsoidal Elastic Inclusion to Poroelasticity and Thermoelasticity

International Nuclear Information System (INIS)

Berryman, J.G.

1997-01-01

Eshelby close-quote s formula gives the response of a single ellipsoidal elastic inclusion in an elastic whole space to a uniform strain imposed at infinity. Using a linear combination of results from two simple thought experiments, we show how this formula may be generalized to both poroelasticity and thermoelasticity. The resulting new formulas are important for applications to analysis of poroelastic and thermoelastic composites, including but not restricted to rocks. copyright 1997 The American Physical Society

Effect of normal stress under an excitation in poroelastic flat slabs

African Journals Online (AJOL)

user

Biot's poroelastic theory is employed to investigate stresses under an ... Keywords: Flat slab, radial normal stress, pervious surface, impervious ... warranted, because of above mentioned applications. ...... M.Tajuddin, and G. Narayan Reddy, Effect of boundaries on the dynamic interaction of a liquid filled porous layer and a.

Optimal variable-grid finite-difference modeling for porous media

International Nuclear Information System (INIS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-01-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs. (paper)

Wavelets for the stimulation of turbulent incompressible flows

International Nuclear Information System (INIS)

Deriaz, E.

2006-02-01

This PhD thesis presents original wavelet methods aimed at simulating incompressible fluids. In order to construct 2D and 3D wavelets designed for incompressible flows, we resume P-G Lemarie-Rieussets and K. Urbans works on divergence free wavelets. We show the existence of associated fast algorithms. In the following, we use divergence-free wavelet construction to define the Helmholtz decomposition of 2D and 3D vector fields. All these algorithms provide a new method for the numerical resolution of the incompressible Navier-Stokes equations. (author)

Cells competition in tumor growth poroelasticity

Science.gov (United States)

Fraldi, Massimiliano; Carotenuto, Angelo R.

2018-03-01

Growth of biological tissues has been recently treated within the framework of Continuum Mechanics, by adopting heterogeneous poroelastic models where the interaction between soft matrix and interstitial fluid flow is coupled with inelastic effects ad hoc introduced to simulate the macroscopic volumetric growth determined by cells division, cells growth and extracellular matrix changes occurring at the micro-scale level. These continuum models seem to overcome some limitations intrinsically associated to other alternative approaches based on mass balances in multiphase systems, because the crucial role played by residual stresses accompanying growth and nutrients walkway is preserved. Nevertheless, when these strategies are applied to analyze solid tumors, mass growth is usually assigned in a prescribed form that essentially copies the in vitro measured intrinsic growth rates of the cell species. As a consequence, some important cell-cell dynamics governing mass evolution and invasion rates of cancer cells, as well as their coupling with feedback mechanisms associated to in situ stresses, are inevitably lost and thus the spatial distribution and the evolution with time of the growth inside the tumor -which would be results rather than inputs- are forced to enter in the model simply as data. In order to solve this paradox, it is here proposed an enhanced multi-scale poroelastic model undergoing large deformations and embodying inelastic growth, where the net growth terms directly result from the "interspecific" predator-prey (Volterra/Lotka-like) competition occurring at the micro-scale level between healthy and abnormal cell species. In this way, a system of fully-coupled non-linear PDEs is derived to describe how the fight among cell species to grab the available common resources, stress field, pressure gradients, interstitial fluid flows driving nutrients and inhomogeneous growth all simultaneously interact to decide the tumor fate.

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo

2008-12-20

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings. © 2008 Springer Science+Business Media, LLC.

An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations

KAUST Repository

Jeong, C.; Kallivokas, L. F.

2016-01-01

This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.

An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations

KAUST Repository

Jeong, C.

2016-07-04

This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.

Plane strain deformation of a multi-layered poroelastic half-space by ...

Indian Academy of Sciences (India)

The Biot linearized quasi-static theory of fluid-infiltrated porous materials is used to formulate the problem of the two-dimensional plane strain deformation of a multi-layered poroelastic half-space by surface loads. The Fourier–Laplace transforms of the stresses, displacements, pore pressure and fluid flux in each ...

Wave energy focusing to subsurface poroelastic formations to promote oil mobilization

KAUST Repository

Karve, P. M.

2015-04-22

We discuss an inverse source formulation aimed at focusing wave energy produced by ground surface sources to target subsurface poroelastic formations. The intent of the focusing is to facilitate or enhance the mobility of oil entrapped within the target formation. The underlying forward wave propagation problem is cast in two spatial dimensions for a heterogeneous poroelastic target embedded within a heterogeneous elastic semi-infinite host. The semi-infiniteness of the elastic host is simulated by augmenting the (finite) computational domain with a buffer of perfectly matched layers. The inverse source algorithm is based on a systematic framework of partial-differential-equation-constrained optimization. It is demonstrated, via numerical experiments, that the algorithm is capable of converging to the spatial and temporal characteristics of surface loads that maximize energy delivery to the target formation. Consequently, the methodology is well-suited for designing field implementations that could meet a desired oil mobility threshold. Even though the methodology, and the results presented herein are in two dimensions, extensions to three dimensions are straightforward.

Modeling the poroelastic response to megathrust earthquakes: A look at the 2012 Mw 7.6 Costa Rican event

Science.gov (United States)

McCormack, Kimberly A.; Hesse, Marc A.

2018-04-01

We model the subsurface hydrologic response to the 7.6 Mw subduction zone earthquake that occurred on the plate interface beneath the Nicoya peninsula in Costa Rica on September 5, 2012. The regional-scale poroelastic model of the overlying plate integrates seismologic, geodetic and hydrologic data sets to predict the post-seismic poroelastic response. A representative two-dimensional model shows that thrust earthquakes with a slip width less than a third of their depth produce complex multi-lobed pressure perturbations in the shallow subsurface. This leads to multiple poroelastic relaxation timescales that may overlap with the longer viscoelastic timescales. In the three-dimensional model, the complex slip distribution of 2012 Nicoya event and its small width to depth ratio lead to a pore pressure distribution comprising multiple trench parallel ridges of high and low pressure. This leads to complex groundwater flow patterns, non-monotonic variations in predicted well water levels, and poroelastic relaxation on multiple time scales. The model also predicts significant tectonically driven submarine groundwater discharge off-shore. In the weeks following the earthquake, the predicted net submarine groundwater discharge in the study area increases, creating a 100 fold increase in net discharge relative to topography-driven flow over the first 30 days. Our model suggests the hydrological response on land is more complex than typically acknowledged in tectonic studies. This may complicate the interpretation of transient post-seismic surface deformations. Combined tectonic-hydrological observation networks have the potential to reduce such ambiguities.

Effective equations for fluid-structure interaction with applications to poroelasticity

KAUST Repository

Brown, Donald; Popov, Peter V.; Efendiev, Yalchin R.

2012-01-01

Modeling of fluid-solid interactions in porous media is a challenging and computationally demanding task. Due to the multiscale nature of the problem, simulating the flow and mechanics by direct numerical simulation is often not feasible and an effective model is preferred. In this work, we formally derive an effective model for Fluid-Structure Interaction (FSI). In earlier work, assuming infinitesimal pore-scale deformations, an effective poroelastic model of Biot was derived. We extend this model to a nonlinear Biot model that includes pore-scale deformation into the effective description. The main challenge is the difference in coordinate systems of the fluid and solid equations. This is circumvented by utilizing the Arbitrary Lagrange-Eulerian (ALE) formulation of the FSI equations, giving a unified frame in which to apply two-scale asymptotic techniques. In the derived nonlinear Biot model, the local cell problem are coupled to the macroscopic equations via the effective coefficients. These coefficients may be viewed as tabular functions of the macroscopic parameters. After simplifying this dependence, we assume the coefficients depend on macroscopic pressure only. Using a three dimensional pore geometry we calculate, as a proof-of-concept example, the effective permeability and Biot coefficients for various values or pressure. We observe that, for this geometry, a stronger pressure dependence on flow quantities than on mechanically based effective quantities. © 2014 Taylor & Francis Group, LLC.

Effective equations for fluid-structure interaction with applications to poroelasticity

KAUST Repository

Brown, Donald

2012-11-05

Modeling of fluid-solid interactions in porous media is a challenging and computationally demanding task. Due to the multiscale nature of the problem, simulating the flow and mechanics by direct numerical simulation is often not feasible and an effective model is preferred. In this work, we formally derive an effective model for Fluid-Structure Interaction (FSI). In earlier work, assuming infinitesimal pore-scale deformations, an effective poroelastic model of Biot was derived. We extend this model to a nonlinear Biot model that includes pore-scale deformation into the effective description. The main challenge is the difference in coordinate systems of the fluid and solid equations. This is circumvented by utilizing the Arbitrary Lagrange-Eulerian (ALE) formulation of the FSI equations, giving a unified frame in which to apply two-scale asymptotic techniques. In the derived nonlinear Biot model, the local cell problem are coupled to the macroscopic equations via the effective coefficients. These coefficients may be viewed as tabular functions of the macroscopic parameters. After simplifying this dependence, we assume the coefficients depend on macroscopic pressure only. Using a three dimensional pore geometry we calculate, as a proof-of-concept example, the effective permeability and Biot coefficients for various values or pressure. We observe that, for this geometry, a stronger pressure dependence on flow quantities than on mechanically based effective quantities. © 2014 Taylor & Francis Group, LLC.

Mobility Effect on Poroelastic Seismic Signatures in Partially Saturated Rocks With Applications in Time-Lapse Monitoring of a Heavy Oil Reservoir

Science.gov (United States)

Zhao, Luanxiao; Yuan, Hemin; Yang, Jingkang; Han, De-hua; Geng, Jianhua; Zhou, Rui; Li, Hui; Yao, Qiuliang

2017-11-01

Conventional seismic analysis in partially saturated rocks normally lays emphasis on estimating pore fluid content and saturation, typically ignoring the effect of mobility, which decides the ability of fluids moving in the porous rocks. Deformation resulting from a seismic wave in heterogeneous partially saturated media can cause pore fluid pressure relaxation at mesoscopic scale, thereby making the fluid mobility inherently associated with poroelastic reflectivity. For two typical gas-brine reservoir models, with the given rock and fluid properties, the numerical analysis suggests that variations of patchy fluid saturation, fluid compressibility contrast, and acoustic stiffness of rock frame collectively affect the seismic reflection dependence on mobility. In particular, the realistic compressibility contrast of fluid patches in shallow and deep reservoir environments plays an important role in determining the reflection sensitivity to mobility. We also use a time-lapse seismic data set from a Steam-Assisted Gravity Drainage producing heavy oil reservoir to demonstrate that mobility change coupled with patchy saturation possibly leads to seismic spectral energy shifting from the baseline to monitor line. Our workflow starts from performing seismic spectral analysis on the targeted reflectivity interface. Then, on the basis of mesoscopic fluid pressure diffusion between patches of steam and heavy oil, poroelastic reflectivity modeling is conducted to understand the shift of the central frequency toward low frequencies after the steam injection. The presented results open the possibility of monitoring mobility change of a partially saturated geological formation from dissipation-related seismic attributes.

Refinement of elastic, poroelastic, and osmotic tissue properties of intervertebral disks to analyze behavior in compression.

Science.gov (United States)

Stokes, Ian A F; Laible, Jeffrey P; Gardner-Morse, Mack G; Costi, John J; Iatridis, James C

2011-01-01

Intervertebral disks support compressive forces because of their elastic stiffness as well as the fluid pressures resulting from poroelasticity and the osmotic (swelling) effects. Analytical methods can quantify the relative contributions, but only if correct material properties are used. To identify appropriate tissue properties, an experimental study and finite element analytical simulation of poroelastic and osmotic behavior of intervertebral disks were combined to refine published values of disk and endplate properties to optimize model fit to experimental data. Experimentally, nine human intervertebral disks with adjacent hemi-vertebrae were immersed sequentially in saline baths having concentrations of 0.015, 0.15, and 1.5 M and the loss of compressive force at constant height (force relaxation) was recorded over several hours after equilibration to a 300-N compressive force. Amplitude and time constant terms in exponential force-time curve-fits for experimental and finite element analytical simulations were compared. These experiments and finite element analyses provided data dependent on poroelastic and osmotic properties of the disk tissues. The sensitivities of the model to alterations in tissue material properties were used to obtain refined values of five key material parameters. The relaxation of the force in the three bath concentrations was exponential in form, expressed as mean compressive force loss of 48.7, 55.0, and 140 N, respectively, with time constants of 1.73, 2.78, and 3.40 h. This behavior was analytically well represented by a model having poroelastic and osmotic tissue properties with published tissue properties adjusted by multiplying factors between 0.55 and 2.6. Force relaxation and time constants from the analytical simulations were most sensitive to values of fixed charge density and endplate porosity.

Real-Time Incompressible Fluid Simulation on the GPU

Directory of Open Access Journals (Sweden)

Xiao Nie

2015-01-01

Full Text Available We present a parallel framework for simulating incompressible fluids with predictive-corrective incompressible smoothed particle hydrodynamics (PCISPH on the GPU in real time. To this end, we propose an efficient GPU streaming pipeline to map the entire computational task onto the GPU, fully exploiting the massive computational power of state-of-the-art GPUs. In PCISPH-based simulations, neighbor search is the major performance obstacle because this process is performed several times at each time step. To eliminate this bottleneck, an efficient parallel sorting method for this time-consuming step is introduced. Moreover, we discuss several optimization techniques including using fast on-chip shared memory to avoid global memory bandwidth limitations and thus further improve performance on modern GPU hardware. With our framework, the realism of real-time fluid simulation is significantly improved since our method enforces incompressibility constraint which is typically ignored due to efficiency reason in previous GPU-based SPH methods. The performance results illustrate that our approach can efficiently simulate realistic incompressible fluid in real time and results in a speed-up factor of up to 23 on a high-end NVIDIA GPU in comparison to single-threaded CPU-based implementation.

A parametric model order reduction technique for poroelastic finite element models.

Science.gov (United States)

Lappano, Ettore; Polanz, Markus; Desmet, Wim; Mundo, Domenico

2017-10-01

This research presents a parametric model order reduction approach for vibro-acoustic problems in the frequency domain of systems containing poroelastic materials (PEM). The method is applied to the Finite Element (FE) discretization of the weak u-p integral formulation based on the Biot-Allard theory and makes use of reduced basis (RB) methods typically employed for parametric problems. The parametric reduction is obtained rewriting the Biot-Allard FE equations for poroelastic materials using an affine representation of the frequency (therefore allowing for RB methods) and projecting the frequency-dependent PEM system on a global reduced order basis generated with the proper orthogonal decomposition instead of standard modal approaches. This has proven to be better suited to describe the nonlinear frequency dependence and the strong coupling introduced by damping. The methodology presented is tested on two three-dimensional systems: in the first experiment, the surface impedance of a PEM layer sample is calculated and compared with results of the literature; in the second, the reduced order model of a multilayer system coupled to an air cavity is assessed and the results are compared to those of the reference FE model.

Poroelastic behaviour of the degenerating human intervertebral disc: a ten-day study in a loaded disc culture system

Directory of Open Access Journals (Sweden)

KS Emanuel

2015-06-01

Full Text Available The intervertebral disc (IVD allows flexibility to the vertebral column, and transfers the predominant axial loads during daily activities. Its axial biomechanical behaviour is poroelastic, due to the water-binding and releasing capacity of the nucleus pulposus. Degeneration of the intervertebral disc presumably affects both the instantaneous elastic response to the load on the IVD and the subsequent interstitial flow of fluid. This study aims to quantify the poroelastic behaviour of the IVD and its change with degeneration, as defined by the magnetic resonance imaging-based Pfirrmann Score (PS. For a period of ten days, 36 human lumbar IVDs were loaded with a simulated physiological axial loading regime, while deformation was monitored. The IVDs responded to the loads with instantaneous elastic and slow poroelastic axial deformation. Several mechanical parameters changed throughout the first five days of the experiment, until the IVDs settled into a dynamic equilibrium. In this equilibrium, degeneration was significantly related to a decrease in disc height loss during the daytime high load phase (ρ = -0.49, and to a decrease in the rate of this deformation during the final half hour of each day (ρ = -0.53. These properties were related to the nucleus glycosaminoglycan/hydroxyproline (GAG/HYP ratio, rather than GAG content alone, indicating that remodelling of the extracellular matrix reduces poroelastic properties of the IVD. This implies that the degenerated discs have a reduced capacity to bind water and/or a reduced resistance against fluid flow. The resulting loss in hydrostatic pressure may further change cell behaviour in the nucleus pulposus.

Aseismic and seismic slip induced by fluid injection from poroelastic and rate-state friction modeling

Science.gov (United States)

Liu, Y.; Deng, K.; Harrington, R. M.; Clerc, F.

2016-12-01

Solid matrix stress change and pore pressure diffusion caused by fluid injection has been postulated as key factors for inducing earthquakes and aseismic slip on pre-existing faults. In this study, we have developed a numerical model that simulates aseismic and seismic slip in a rate-and-state friction framework with poroelastic stress perturbations from multi-stage hydraulic fracturing scenarios. We apply the physics-based model to the 2013-2015 earthquake sequences near Fox Creek, Alberta, Canada, where three magnitude 4.5 earthquakes were potentially induced by nearby hydraulic fracturing activity. In particular, we use the relocated December 2013 seismicity sequence to approximate the fault orientation, and find the seismicity migration spatiotemporally correlate with the positive Coulomb stress changes calculated from the poroelastic model. When the poroelastic stress changes are introduced to the rate-state friction model, we find that slip on the fault evolves from aseismic to seismic in a manner similar to the onset of seismicity. For a 15-stage hydraulic fracturing that lasted for 10 days, modeled fault slip rate starts to accelerate after 3 days of fracking, and rapidly develops into a seismic event, which also temporally coincides with the onset of induced seismicity. The poroelastic stress perturbation and consequently fault slip rate continue to evolve and remain high for several weeks after hydraulic fracturing has stopped, which may explain the continued seismicity after shut-in. In a comparison numerical experiment, fault slip rate quickly decreases to the interseismic level when stress perturbations are instantaneously returned to zero at shut-in. Furthermore, when stress perturbations are removed just a few hours after the fault slip rate starts to accelerate (that is, hydraulic fracturing is shut down prematurely), only aseismic slip is observed in the model. Our preliminary results thus suggest the design of fracturing duration and flow

Modeling Poroelastic Wave Propagation in a Real 2-D Complex Geological Structure Obtained via Self-Organizing Maps

Science.gov (United States)

Itzá Balam, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

2018-03-01

Two main stages of seismic modeling are geological model building and numerical computation of seismic response for the model. The quality of the computed seismic response is partly related to the type of model that is built. Therefore, the model building approaches become as important as seismic forward numerical methods. For this purpose, three petrophysical facies (sands, shales and limestones) are extracted from reflection seismic data and some seismic attributes via the clustering method called Self-Organizing Maps (SOM), which, in this context, serves as a geological model building tool. This model with all its properties is the input to the Optimal Implicit Staggered Finite Difference (OISFD) algorithm to create synthetic seismograms for poroelastic, poroacoustic and elastic media. The results show a good agreement between observed and 2-D synthetic seismograms. This demonstrates that the SOM classification method enables us to extract facies from seismic data and allows us to integrate the lithology at the borehole scale with the 2-D seismic data.

Sound transmission through a double-panel construction lined with poroelastic material in the presence of mean flow

Science.gov (United States)

Zhou, Jie; Bhaskar, Atul; Zhang, Xin

2013-08-01

This paper investigates the sound transmission characteristics through a system of double-panel lined with poroelastic material in the core. The panels are surrounded by external and internal fluid media where a uniform external mean flow exists on one side. Biot's theory is used to model the porous material. Three types of constructions—bonded-bonded, bonded-unbonded and unbonded-unbonded—are considered. The effect of Mach number of the external flow on the sound transmission over a wide frequency range in a diffuse sound field is examined. External mean flow is shown to give a modest increase in transmission loss at low frequency, but a significant increase at high frequency. It is brought out that calculations based on static air on the incidence side provide a conservative estimate of sound transmission through the sandwich structure. The acoustic performance of the sandwich panel for different configurations is presented. The effect of curvature of the panel is also brought out by using shallow shell theory.

Sound transmission through triple-panel structures lined with poroelastic materials

OpenAIRE

Liu, Y

2015-01-01

In this paper, previous theories on the prediction of sound transmission loss for a double-panel structure lined with poroelastic materials are extended to address the problem of a triple-panel structure. Six typical configurations are considered for a triple-panel structure based on the method of coupling the porous layers to the facing panels which determines critically the sound insulation performance of the system. The transfer matrix method is employed to solve the system by applying app...

Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows

International Nuclear Information System (INIS)

Tasso, H.; Throumoulopoulos, G.N.

1997-12-01

It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)

Inverse problem in anisotropic poroelasticity: drained constants from undrained ultrasound measurements.

Science.gov (United States)

Berryman, James G; Nakagawa, Seiji

2010-02-01

Poroelastic analysis has traditionally focused on the relationship between dry and drained constants, which are assumed known, and the saturated or undrained constants, which are assumed unknown. However, there are many applications in this field of study for which the main measurements can only be made on the saturated/undrained system, and then it is uncertain what the effects of the fluids were on the system, since the drained constants remain a mystery. The work presented here shows how to deduce drained constants from undrained constants for anisotropic systems having symmetries ranging from isotropic to orthotropic. Laboratory ultrasound data are then inverted for the drained constants in three granular packings: one of glass beads, and two others for distinct types of more or less angular sand grain packings. Experiments were performed under uniaxial stress, which resulted in hexagonal (transversely isotropic) symmetry of the poroelastic response. One important conclusion from the general analysis is that the drained constants are uniquely related to the undrained constants, assuming that porosity, grain bulk modulus, and pore fluid bulk modulus are already known. Since the resulting system of equations for all the drained constants is linear, measurement error in undrained constants also propagates linearly into the computed drained constants.

Inverse problem in anisotropic poroelasticity: Drained constants from undrained ultrasound measurements

Energy Technology Data Exchange (ETDEWEB)

Berryman, J.G.; Nakagawa, S.

2009-11-20

Poroelastic analysis has traditionally focused on the relationship between dry or drained constants which are assumed known and the saturated or undrained constants which are assumed unknown. However, there are many applications in this field of study for which the main measurements can only be made on the saturated/undrained system, and then it is uncertain what the eects of the uids were on the system, since the drained constants remain a mystery. The work presented here shows how to deduce drained constants from undrained constants for anisotropic systems having symmetries ranging from isotropic to orthotropic. Laboratory ultrasound data are then inverted for the drained constants in three granular packings: one of glass beads, and two others for distinct types of more or less angular sand grain packings. Experiments were performed under uniaxial stress, which resulted in hexagonal (transversely isotropic) symmetry of the poroelastic response. One important conclusion from the general analysis is that the drained constants are uniquely related to the undrained constants, assuming that porosity, grain bulk modulus, and pore uid bulk modulus are already known. Since the resulting system of equations for all the drained constants is linear, measurement error in undrained constants also propagates linearly into the computed drained constants.

Nearly incompressible MHD turbulence in the solar wind

International Nuclear Information System (INIS)

Matthaeus, W.H.; Zhou, Y.

1989-01-01

Observational studies indicate that solar wind plasma and magnetic field fluctuations may be meaningfully viewed as an example of magnetohydrodynamic turbulence. This paper presents a brief summary of some relevant results of turbulence theory and reviews a turbulence style description of 'typical' solar wind conditions. Recent results, particularly those regarding the radial evolution of inertial range cross helicity, support the viewpoint that interplanetary turbulence is active and evolving with heliocentric distance. A number of observed properties can be understood by appeal to incompressible turbulence mechanisms. This connection may be understood by appeal to incompressible turbulence mechanisms. This connection may be understood in terms of theories of pseudosound density fluctuations and nearly incompressible magnetohydrodynamics, which are also reviewed here. Finally, we summarize a recent two-scale dynamical theory of the radial and temporal evolution of the turbulence, which may provide an additional framework for understanding the observations. (author). 49 refs

The incompressibility assumption in computational simulations of nasal airflow.

Science.gov (United States)

Cal, Ismael R; Cercos-Pita, Jose Luis; Duque, Daniel

2017-06-01

Most of the computational works on nasal airflow up to date have assumed incompressibility, given the low Mach number of these flows. However, for high temperature gradients, the incompressibility assumption could lead to a loss of accuracy, due to the temperature dependence of air density and viscosity. In this article we aim to shed some light on the influence of this assumption in a model of calm breathing in an Asian nasal cavity, by solving the fluid flow equations in compressible and incompressible formulation for different ambient air temperatures using the OpenFOAM package. At low flow rates and warm climatological conditions, similar results were obtained from both approaches, showing that density variations need not be taken into account to obtain a good prediction of all flow features, at least for usual breathing conditions. This agrees with most of the simulations previously reported, at least as far as the incompressibility assumption is concerned. However, parameters like nasal resistance and wall shear stress distribution differ for air temperatures below [Formula: see text]C approximately. Therefore, density variations should be considered for simulations at such low temperatures.

Sound transmission through lined, composite panel structures: Transversely isotropic poro-elastic model

Science.gov (United States)

Kim, Jeong-Woo

A joint experimental and analytical investigation of the sound transmission loss (STL) and two-dimensional free wave propagation in composite sandwich panels is presented here. An existing panel, a Nomex honeycomb sandwich panel, was studied in detail. For the purpose of understanding the typical behavior of sandwich panels, a composite structure comprising two aluminum sheets with a relatively soft, poro-elastic foam core was also constructed and studied. The cores of both panels were modeled using an anisotropic (transversely isotropic) poro-elastic material theory. Several estimation methods were used to obtain the material properties of the honeycomb core and the skin plates to be used in the numerical calculations. Appropriate values selected from among the estimates were used in the STL and free wave propagation models. The prediction model was then verified in two ways: first, the calculated wave speeds and STL of a single poro-elastic layer were numerically verified by comparison with the predictions of a previously developed isotropic model. Secondly, to physically validate the transversely isotropic model, the measured STL and the phase speeds of the sandwich panels were compared with their predicted values. To analyze the actual treatment of a fuselage structure, multi-layered configurations, including a honeycomb panel and several layers such as air gaps, acoustic blankets and membrane partitions, were formulated. Then, to find the optimal solution for improving the sound barrier performance of an actual fuselage system, air layer depth and glass fiber lining effects were investigated by using these multi-layer models. By using the free wave propagation model, the first anti-symmetric and symmetric modes of the sandwich panels were characterized to allow the identification of the coincidence frequencies of the sandwich panel. The behavior of the STL could then be clearly explained by comparison with the free wave propagation solutions. By performing a

Analysis of Dynamic Fracture Compliance Based on Poroelastic Theory - Part II: Results of Numerical and Experimental Tests

Science.gov (United States)

Wang, Ding; Ding, Pin-bo; Ba, Jing

2018-03-01

In Part I, a dynamic fracture compliance model (DFCM) was derived based on the poroelastic theory. The normal compliance of fractures is frequency-dependent and closely associated with the connectivity of porous media. In this paper, we first compare the DFCM with previous fractured media theories in the literature in a full frequency range. Furthermore, experimental tests are performed on synthetic rock specimens, and the DFCM is compared with the experimental data in the ultrasonic frequency band. Synthetic rock specimens saturated with water have more realistic mineral compositions and pore structures relative to previous works in comparison with natural reservoir rocks. The fracture/pore geometrical and physical parameters can be controlled to replicate approximately those of natural rocks. P- and S-wave anisotropy characteristics with different fracture and pore properties are calculated and numerical results are compared with experimental data. Although the measurement frequency is relatively high, the results of DFCM are appropriate for explaining the experimental data. The characteristic frequency of fluid pressure equilibration calculated based on the specimen parameters is not substantially less than the measurement frequency. In the dynamic fracture model, the wave-induced fluid flow behavior is an important factor for the fracture-wave interaction process, which differs from the models at the high-frequency limits, for instance, Hudson's un-relaxed model.

Computation of Viscous Incompressible Flows

CERN Document Server

Kwak, Dochan

2011-01-01

This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engine...

Geophysical models of heat and fluid flow in damageable poro-elastic continua

Czech Academy of Sciences Publication Activity Database

Roubíček, Tomáš

2017-01-01

Roč. 29, č. 2 (2017), s. 625-646 ISSN 0935-1175 R&D Projects: GA ČR(CZ) GA16-03823S; GA ČR GA14-15264S Institutional support: RVO:61388998 Keywords : poro-elastic rocks * damage * biot model Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 2.529, year: 2016 https://link.springer.com/article/10.1007/s00161-016-0547-5

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

Science.gov (United States)

Tóth, Gyula I.

2016-09-01

In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional) and (ii) can influence nonequilibrium pattern formation significantly.

Parallel simulation of two-phase incompressible and immiscible flows in porous media using a finite volume formulation and a modified IMPES approach

International Nuclear Information System (INIS)

Da Silva, R S; De Carvalho, D K E; Antunes, A R E; Lyra, P R M; Willmersdorf, R B

2010-01-01

In this paper a finite volume method with a 'Modified Implicit Pressure, Explicit Saturation' (MIMPES) approach is used to model the 3-D incompressible and immiscible two-phase flow of water and oil in heterogeneous and anisotropic porous media. A vertex centered finite volume method with an edge-based data structure is adopted to discretize both the elliptic pressure and the hyperbolic saturation equations using parallel computers with distributed memory. Due to the explicit solution of the saturation equation in the IMPES method, severe time step restrictions are imposed on the simulation. In order to circumvent this problem, an edge-based implementation of the MIMPES method was used. In this method, the pressure equation is solved and the velocity field is computed much less frequently than the saturation field. Following the work of Hurtado, a mean relative variation of the velocity field throughout the simulation is used to automatically control the updating process, allowing for much larger time-steps in a very simple way. In order to run large scale problems, we have developed a parallel implementation using clusters of PC's. The simulator uses open source parallel libraries like FMDB, ParMetis and PETSc. Results of speed-up and efficiency are presented to validate the performance of the parallel simulator.

Stable discretization of poroelasticity problems and efficient preconditioners for arising saddle point type matrices

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe; Blaheta, Radim; Byczanski, Petr

2012-01-01

Roč. 15, č. 4 (2012), s. 191-207 ISSN 1432-9360 R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:68145535 Keywords : poroelasticity * saddle point matrices * preconditioning * stability of discretization Subject RIV: BA - General Mathematics http://link.springer.com/article/10.1007/s00791-013-0209-0

Fully-developed conjugate heat transfer in porous media with uniform heating

NARCIS (Netherlands)

Lopez Penha, D.J.; Stolz, S.; Kuerten, Johannes G.M.; Nordlund, M.; Kuczaj, Arkadiusz K.; Geurts, Bernardus J.

2012-01-01

We propose a computational method for approximating the heat transfer coefficient of fully-developed flow in porous media. For a representative elementary volume of the porous medium we develop a transport model subject to periodic boundary conditions that describes incompressible fluid flow through

Shock and rarefaction waves in a hyperbolic model of incompressible materials

Directory of Open Access Journals (Sweden)

Tommaso Ruggeri

2013-01-01

Full Text Available The aim of the present paper is to investigate shock and rarefaction waves in a hyperbolic model of incompressible materials. To this aim, we use the so-called extended quasi-thermal-incompressible (EQTI model, recently proposed by Gouin & Ruggeri (H. Gouin, T. Ruggeri, Internat. J. Non-Linear Mech. 47 688–693 (2012. In particular, we use as constitutive equation a variant of the well-known Bousinnesq approximation in which the specific volume depends not only on the temperature but also on the pressure. The limit case of ideal incompressibility, namely when the thermal expansion coefficient and the compressibility factor vanish, is also considered.

On compressible and piezo-viscous flow in thin porous media.

Science.gov (United States)

Pérez-Ràfols, F; Wall, P; Almqvist, A

2018-01-01

In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

Incompressibility of asymmetric nuclear matter

International Nuclear Information System (INIS)

Chen, Liewen; Cai, Baojun; Shen, Chun; Ko, Cheming; Xu, Jun; Li, Baoan

2010-01-01

Using an isospin- and momentum-dependent modified Gogny (MDI) interaction, the Skyrme-Hartree-Fock (SHF) approach, and a phenomenological modified Skyrme-like (MSL) model, we have studied the incompressibility K sat (δ) of isospin asymmetric nuclear matter at its saturation density. Our results show that in the expansion of K sat (δ) in powers of isospin asymmetry δ, i.e., K sat (δ) = K 0 + K sat,2 δ 2 + K sat,4 δ 4 + O(δ 6 ), the magnitude of the 4th-order K sat,4 parameter is generally small. The 2nd-order K sat,2 parameter thus essentially characterizes the isospin dependence of the incompressibility of asymmetric nuclear matter at saturation density. Furthermore, the K sat,2 can be expressed as K sat,2 = K sym – 6L – J 0 /K 0 L in terms of the slope parameter L and the curvature parameter K sym of the symmetry energy and the third-order derivative parameter J 0 of the energy of symmetric nuclear matter at saturation density, and we find the higher order J 0 contribution to K sat,2 generally cannot be neglected. Also, we have found a linear correlation between K sym and L as well as between J 0 /K 0 and K 0 . Using these correlations together with the empirical constraints on K 0 and L, the nuclear symmetry energy E sym (ρ0) at normal nuclear density, and the nucleon effective mass, we have obtained an estimated value of K sat,2 = -370 ± 120 MeV for the 2nd-order parameter in the isospin asymmetry expansion of the incompressibility of asymmetric nuclear matter at its saturation density. (author)

I-Love relations for incompressible stars and realistic stars

Science.gov (United States)

Chan, T. K.; Chan, AtMa P. O.; Leung, P. T.

2015-02-01

In spite of the diversity in the equations of state of nuclear matter, the recently discovered I-Love-Q relations [Yagi and Yunes, Science 341, 365 (2013), 10.1126/science.1236462], which relate the moment of inertia, tidal Love number (deformability), and the spin-induced quadrupole moment of compact stars, hold for various kinds of realistic neutron stars and quark stars. While the physical origin of such universality is still a current issue, the observation that the I-Love-Q relations of incompressible stars can well approximate those of realistic compact stars hints at a new direction to approach the problem. In this paper, by establishing recursive post-Minkowskian expansion for the moment of inertia and the tidal deformability of incompressible stars, we analytically derive the I-Love relation for incompressible stars and show that the so-obtained formula can be used to accurately predict the behavior of realistic compact stars from the Newtonian limit to the maximum mass limit.

A blended pressure/density based method for the computation of incompressible and compressible flows

International Nuclear Information System (INIS)

Rossow, C.-C.

2003-01-01

An alternative method to low speed preconditioning for the computation of nearly incompressible flows with compressible methods is developed. For this approach the leading terms of the flux difference splitting (FDS) approximate Riemann solver are analyzed in the incompressible limit. In combination with the requirement of the velocity field to be divergence-free, an elliptic equation to solve for a pressure correction to enforce the divergence-free velocity field on the discrete level is derived. The pressure correction equation established is shown to be equivalent to classical methods for incompressible flows. In order to allow the computation of flows at all speeds, a blending technique for the transition from the incompressible, pressure based formulation to the compressible, density based formulation is established. It is found necessary to use preconditioning with this blending technique to account for a remaining 'compressible' contribution in the incompressible limit, and a suitable matrix directly applicable to conservative residuals is derived. Thus, a coherent framework is established to cover the discretization of both incompressible and compressible flows. Compared with standard preconditioning techniques, the blended pressure/density based approach showed improved robustness for high lift flows close to separation

Review of the modified finite particle method and application to incompressible solids

Directory of Open Access Journals (Sweden)

D Asprone

2016-10-01

Full Text Available This paper focuses on the application of the Modified Finite Particle Method (MFPM on incompressibile elasticity problems. MFPM belongs to the class of meshless methods, nowadays widely investigated due to their characteristics of being totally free of any kind of grid or mesh. This characteristic makes meshless methods potentially useful for the study of large deformations problems and fluid dynamics. In particular, the aim of the work is to compare the results obtained with a simple displacement-based formulation, in the limit of incompressibility, and some formulations proposed in the literature for full incompressibility, where the typical divergence-free constraint is replaced by a different equation, the so-called Pressure Poisson Equation. The obtained results show that the MFPM achieves the expected second-order accuracy on formulation where the equations imposed as constraint satisfies also the original incompressibility equation. Other formulations, differently, do not satisfy the incompressibility constraint, and thus, they are not successfully applicable with the Modified Finite Particle Method.

Accurate solution algorithms for incompressible multiphase flows

International Nuclear Information System (INIS)

Rider, W.J.; Kothe, D.B.; Mosso, S.J.; Cerutti, J.H.; Hochstein, J.I.

1994-01-01

A number of advances in modeling multiphase incompressible flow are described. These advances include high-order Godunov projection methods, piecewise linear interface reconstruction and tracking and the continuum surface force model. Examples are given

Existence Results for Incompressible Magnetoelasticity

Czech Academy of Sciences Publication Activity Database

Kružík, Martin; Stefanelli, U.; Zeman, J.

2015-01-01

Roč. 35, č. 6 (2015), s. 2615-2623 ISSN 1078-0947 R&D Projects: GA ČR GA13-18652S Institutional support: RVO:67985556 Keywords : magnetoelasticity * magnetostrictive solids * incompressibility * existence of minimizers * quasistatic evolution * energetic solution Subject RIV: BA - General Mathematics Impact factor: 1.127, year: 2015 http://library.utia.cas.cz/separaty/2015/MTR/kruzik-0443017.pdf

Effective stress principle for partially saturated media

International Nuclear Information System (INIS)

McTigue, D.F.; Wilson, R.K.; Nunziato, J.W.

1984-04-01

In support of the Nevada Nuclear Waste Storage Investigation (NNWSI) Project, we have undertaken a fundamental study of water migration in partially saturated media. One aspect of that study, on which we report here, has been to use the continuum theory of mixtures to extend the classical notion of effective stress to partially saturated media. Our analysis recovers previously proposed phenomenological representations for the effective stress in terms of the capillary pressure. The theory is illustrated by specializing to the case of linear poroelasticity, for which we calculate the deformation due to the fluid pressure in a static capillary fringe. We then examine the transient consolidation associated with liquid flow induced by an applied surface load. Settlement accompanies this flow as the liquid is redistributed by a nonlinear diffusion process. For material properties characteristic of tuff from the Nevada Test Site, these effects are found to be vanishingly small. 14 references, 7 figures, 1 table

Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows

International Nuclear Information System (INIS)

Moawad, S. M.; Ibrahim, D. A.

2016-01-01

The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.

Transient poroelastic stress coupling between the 2015 M7.8 Gorkha, Nepal earthquake and its M7.3 aftershock

Science.gov (United States)

Tung, S.; Masterlark, T.; Dovovan, T.

2018-05-01

The large M7.3 aftershock occurred 17 days after the 2015 M7.8 Gorkha earthquake. We investigate if this sequence is mechanically favored by the mainshock via time-dependent fluid migration and pore pressure recovery. This study uses finite element models of fully-coupled poroelastic coseismic and postseismic behavior to simulate the evolving stress and pore-pressure fields. Using simulations of a reasonable permeability, the hypocenter was destabilized by an additional 0.15 MPa of Coulomb failure stress change (ΔCFS) and 0.17 MPa of pore pressure (Δp), the latter of which induced lateral and upward diffusive fluid flow (up to 2.76 mm/day) in the aftershock region. The M7.3 location is predicted next to a local maximum of Δp and a zone of positive ΔCFS northeast of Kathmandu. About 60% of the aftershocks occurred within zones having either Δp > 0 or ΔCFS > 0. Particularly in the eastern flank of the epicentral area, 83% of the aftershocks experienced postseismic fluid pressurization and 88% of them broke out with positive pore pressure, which are discernibly more than those with positive ΔCFS (71%). The transient scalar field of fluid pressurization provides a good proxy to predict aftershock-prone areas in space and time, because it does not require extraction of an assumed vector field from transient stress tensor fields as is the case for ΔCFS calculations. A bulk permeability of 8.32 × 10-18 m2 is resolved to match the transient response and the timing of the M7.3 rupture which occurred at the peak of the ΔCFS time-series. This estimate is consistent with the existing power-law permeability-versus-depth models, suggesting an intermediately-fractured upper crust coherent with the local geology of the central Himalayas. The contribution of poroelastic triggering is verified against different poroelastic moduli and surface flow-pressure boundaries, suggesting that a poroelastic component is essential to account for the time interval separating the

Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions

International Nuclear Information System (INIS)

Lin, Hongxia; Du, Lili

2013-01-01

In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations. (paper)

Error estimation and adaptivity for incompressible hyperelasticity

KAUST Repository

Whiteley, J.P.; Tavener, S.J.

2014-01-01

SUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined

Poroelastic behaviour of the degenerating human intervertebral disc: a ten-day study in a loaded disc culture system

NARCIS (Netherlands)

Emanuel, K. S.; Vergroesen, P.-P. A.; Peeters, M.; Holewijn, R. M.; Kingma, I.; Smit, T. H.

2015-01-01

The intervertebral disc (IVD) allows flexibility to the vertebral column, and transfers the predominant axial loads during daily activities. Its axial biomechanical behaviour is poroelastic, due to the water-binding and releasing capacity of the nucleus pulposus. Degeneration of the intervertebral

The Theory of Nearly Incompressible Magnetohydrodynamic Turbulence: Homogeneous Description

Science.gov (United States)

Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.; Avinash, K.

2017-09-01

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed to understand the apparent incompressibility of the solar wind and other plasma environments, particularly the relationship of density fluctuations to incompressible manifestations of turbulence in the solar wind and interstellar medium. Of interest was the identification of distinct leading-order incompressible descriptions for plasma beta β ≫ 1 and β ∼ 1 or ≪ 1 environments. In the first case, the “dimensionality” of the MHD description is 3D whereas for the latter two, there is a collapse of dimensionality in that the leading-order incompressible MHD description is 2D in a plane orthogonal to the large-scale or mean magnetic field. Despite the success of NI MHD in describing fluctuations in a low-frequency plasma environment such as the solar wind, a basic turbulence description has not been developed. Here, we rewrite the NI MHD system in terms of Elsässer variables. We discuss the distinction that emerges between the three cases. However, we focus on the β ∼ 1 or ≪ 1 regimes since these are appropriate to the solar wind and solar corona. In both cases, the leading-order turbulence model describes 2D turbulence and the higher-order description corresponds to slab turbulence, which forms a minority component. The Elsäasser β ∼ 1 or ≪ 1 formulation exhibits the nonlinear couplings between 2D and slab components very clearly, and shows that slab fluctuations respond in a passive scalar sense to the turbulently evolving majority 2D component fluctuations. The coupling of 2D and slab fluctuations through the β ∼ 1 or ≪ 1 NI MHD description leads to a very natural emergence of the “Goldreich-Sridhar” critical balance scaling parameter, although now with a different interpretation. Specifically, the critical balance parameter shows that the energy flux in wave number space is a consequence of the intensity of Alfvén wave sweeping versus passive scalar

Skinfold creep under load of caliper. Linear visco- and poroelastic model simulations.

Science.gov (United States)

Nowak, Joanna; Nowak, Bartosz; Kaczmarek, Mariusz

2015-01-01

This paper addresses the diagnostic idea proposed in [11] to measure the parameter called rate of creep of axillary fold of tissue using modified Harpenden skinfold caliper in order to distinguish normal and edematous tissue. Our simulations are intended to help understanding the creep phenomenon and creep rate parameter as a sensitive indicator of edema existence. The parametric analysis shows the tissue behavior under the external load as well as its sensitivity to changes of crucial hydro-mechanical tissue parameters, e.g., permeability or stiffness. The linear viscoelastic and poroelastic models of normal (single phase) and oedematous tissue (twophase: swelled tissue with excess of interstitial fluid) implemented in COMSOL Multiphysics environment are used. Simulations are performed within the range of small strains for a simplified fold geometry, material characterization and boundary conditions. The predicted creep is the result of viscosity (viscoelastic model) or pore fluid displacement (poroelastic model) in tissue. The tissue deformations, interstitial fluid pressure as well as interstitial fluid velocity are discussed in parametric analysis with respect to elasticity modulus, relaxation time or permeability of tissue. The creep rate determined within the models of tissue is compared and referred to the diagnostic idea in [11]. The results obtained from the two linear models of subcutaneous tissue indicate that the form of creep curve and the creep rate are sensitive to material parameters which characterize the tissue. However, the adopted modelling assumptions point to a limited applicability of the creep rate as the discriminant of oedema.

Combination of poroelasticity theory and constant strain rate test in modelling land subsidence due to groundwater extraction

Science.gov (United States)

Pham, Tien Hung; Rühaak, Wolfram; Sass, Ingo

2017-04-01

Extensive groundwater extraction leads to a drawdown of the ground water table. Consequently, soil effective stress increases and can cause land subsidence. Analysis of land subsidence generally requires a numerical model based on poroelasticity theory, which was first proposed by Biot (1941). In the review of regional land subsidence accompanying groundwater extraction, Galloway and Burbey (2011) stated that more research and application is needed in coupling of stress-dependent land subsidence process. In geotechnical field, the constant rate of strain tests (CRS) was first introduced in 1969 (Smith and Wahls 1969) and was standardized in 1982 through the designation D4186-82 by American Society for Testing and Materials. From the reading values of CRS tests, the stress-dependent parameters of poroelasticity model can be calculated. So far, there is no research to link poroelasticity theory with CRS tests in modelling land subsidence due to groundwater extraction. One dimensional CRS tests using conventional compression cell and three dimension CRS tests using Rowe cell were performed. The tests were also modelled by using finite element method with mixed elements. Back analysis technique is used to find the suitable values of hydraulic conductivity and bulk modulus that depend on the stress or void ratio. Finally, the obtained results are used in land subsidence models. Biot, M. A. (1941). "General theory of three-dimensional consolidation." Journal of applied physics 12(2): 155-164. Galloway, D. L. and T. J. Burbey (2011). "Review: Regional land subsidence accompanying groundwater extraction." Hydrogeology Journal 19(8): 1459-1486. Smith, R. E. and H. E. Wahls (1969). "Consolidation under constant rates of strain." Journal of Soil Mechanics & Foundations Div.

Stresses, strains, and displacements in a poroelastic layered pavement model subject to a moving load

International Nuclear Information System (INIS)

Morshedi, C.

1982-01-01

The response of a layered poroelastic halfspace to a progressing normally distributed load applied at the surface is evaluated for the case in which the constant velocity of the moving load is less than that of the elastic waves in each layer. It is assumed that a steady state exists with respect to the coordinate axes attached to a moving load. A three-dimensional problem for Biot's consolidated equations is then solved by taking Fourier transforms in the horizontal directions to evaluate stresses and displacements at any point in the medium. The analysis is illustrated by numerical examples using an algorithm based on one previously developed to calculate the response to a static load for axisymmetric poroelastic layers. To reduce the amount of computation, attention is restricted to a two-dimensional problem in which the load extends infinitely in the transverse direction. Results are presented for two and three-layered pavement models composed of concrete and gravel over a clay subbase responding to moving traffic, but the method is applicable to any number of layers. The effect of varying the velocity of the load and layer properties is observed

On preconditioning incompressible non-Newtonian flow problems

NARCIS (Netherlands)

He, X.; Neytcheva, M.; Vuik, C.

2013-01-01

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space

Inviscid incompressible limits on expanding domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Nečasová, Šárka; Sun, Y.

2014-01-01

Roč. 27, č. 10 (2014), s. 2465-2477 ISSN 0951-7715 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokes system * large domain * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 1.208, year: 2014 http://iopscience.iop.org/0951-7715/27/10/2465/

Nuclear incompressibility: from finite nuclei to nuclear matter

International Nuclear Information System (INIS)

Treiner, J.; Krivine, H.; Bohigas, O.

1981-01-01

The recent increase of experimental data concerning the Giant Monopole Resonance Energy Esub(M) gives information on the incompressibility modulus of nuclear matter, provided one can extrapolate the incompressibility of a nucleus Ksub(A) defined by Esub(M)=[h 2 /m KA/ 2 >]sup(1/2), to the infinite medium. We discuss the theoretical interpretation of the coefficients of an Asup(-1/3) - expansion of Ksub(A) by studying the asymptotic behaviour of two RPA sum rules (corresponding to the scaling and the constrained model), evaluated using self-consistent Thomas-Fermi calculations. We show that the scaling model is the most suitable one as it leads to a rapidly converging Asup(-1/3)-expansion of the corresponding incompressibility Ksub(A)sup(S), whereas this is not the case with the constrained model. Some semi-empirical relations between the coefficients of the expansion of Ksub(A)sup(S) are established, which reduce to one the number of free-parameters in a best fit analysis of the experimental data. This reduction is essential due to the still limited number and accuracy of experimental data. We then show the compatibility of the data given by the various experimental groups with this parametrization and obtain a value of Ksub(nm)=220+-20 MeV, in good agreement with more microscopic analysis

Direct differentiation of the quasi-incompressible fluid formulation of fluid-structure interaction using the PFEM

Science.gov (United States)

Zhu, Minjie; Scott, Michael H.

2017-07-01

Accurate and efficient response sensitivities for fluid-structure interaction (FSI) simulations are important for assessing the uncertain response of coastal and off-shore structures to hydrodynamic loading. To compute gradients efficiently via the direct differentiation method (DDM) for the fully incompressible fluid formulation, approximations of the sensitivity equations are necessary, leading to inaccuracies of the computed gradients when the geometry of the fluid mesh changes rapidly between successive time steps or the fluid viscosity is nonzero. To maintain accuracy of the sensitivity computations, a quasi-incompressible fluid is assumed for the response analysis of FSI using the particle finite element method and DDM is applied to this formulation, resulting in linearized equations for the response sensitivity that are consistent with those used to compute the response. Both the response and the response sensitivity can be solved using the same unified fractional step method. FSI simulations show that although the response using the quasi-incompressible and incompressible fluid formulations is similar, only the quasi-incompressible approach gives accurate response sensitivity for viscous, turbulent flows regardless of time step size.

Compression modes and the nuclear matter incompressibility ...

Indian Academy of Sciences (India)

We review the current status of the nuclear matter ( = and no Coulomb interaction) incompressibility coefficient, , and describe the theoretical and the experimental methods used to determine from properties of compression modes in nuclei. In particular we consider the long standing problem of the conflicting ...

NASA-VOF2D, 2-D Transient Free Surface Incompressible Fluid Dynamic

International Nuclear Information System (INIS)

Torrey, M.D.

1988-01-01

1 - Description of program or function: NASA-VOF2D is a two- dimensional, transient, free surface incompressible fluid dynamics program. It allows multiple free surfaces with surface tension and wall adhesion forces and has a partial cell treatment which allows curved boundaries and interior obstacles. 2 - Method of solution: NASA-VOF2D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The complete Navier-Stokes equations in primitive variables for an incompressible fluid are solved by finite differences with surface tension and wall adhesion included. Optionally the pressure equation can be solved by a conjugate residual method rather than the successive over-relaxation (SOR) method

Biochemomechanical poroelastic theory of avascular tumor growth

Science.gov (United States)

Xue, Shi-Lei; Li, Bo; Feng, Xi-Qiao; Gao, Huajian

2016-09-01

Tumor growth is a complex process involving genetic mutations, biochemical regulations, and mechanical deformations. In this paper, a thermodynamics-based nonlinear poroelastic theory is established to model the coupling among the mechanical, chemical, and biological mechanisms governing avascular tumor growth. A volumetric growth law accounting for mechano-chemo-biological coupled effects is proposed to describe the development of solid tumors. The regulating roles of stresses and nutrient transport in the tumor growth are revealed under different environmental constraints. We show that the mechano-chemo-biological coupling triggers anisotropic and heterogeneous growth, leading to the formation of layered structures in a growing tumor. There exists a steady state in which tumor growth is balanced by resorption. The influence of external confinements on tumor growth is also examined. A phase diagram is constructed to illustrate how the elastic modulus and thickness of the confinements jointly dictate the steady state of tumor volume. Qualitative and quantitative agreements with experimental observations indicate the developed model is capable of capturing the essential features of avascular tumor growth in various environments.

Preconditioned augmented Lagrangian formulation for nearly incompressible cardiac mechanics.

Science.gov (United States)

Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins

2018-04-01

Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the numerical solution of the model. The near-incompressibility is known to cause numerical issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented Lagrangian method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. Numerical results of the augmented Lagrangian method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.

Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence

Energy Technology Data Exchange (ETDEWEB)

Zank, G. P.; Adhikari, L.; Hunana, P. [Center for Space Plasma and Aeronomic Research (CSPAR), University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Shiota, D. [Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8601 (Japan); Bruno, R. [INAF-IAPS Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma (Italy); Telloni, D. [INAF—Astrophysical Observatory of Torino, Via Osservatorio 20, I-10025 Pino Torinese (Italy)

2017-02-01

The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.

Leptodermous expansion of finite-nucleus incompressibility

International Nuclear Information System (INIS)

Nayak, R.C.

1990-01-01

We consider the influence of higher-order terms in the leptodermous expansion used to extract the incompressibility K v of infinite nuclear matter from data on the breathing mode of finite nuclei. The terms we calculate are the curvature term K cv A -2/3 , the surface-symmetry term K ss I 2 A -1/3 , the quartic volume-symmetry term K 4 I 4 , and a Coulomb-exchange term. Working within the framework of the scaling model we derive expressions for their coefficients in terms of quantities that are defined for infinite and semi-infinite nuclear matter. We calculate these coefficients for four different Skyrme-type forces, using the extended Thomas-Fermi (ETF) approximation. With the same forces we also calculate the incompressibility K (A, I) for a number of finite nuclei, fit the results to the leptodermous expansion, and thereby extract new results for the same coefficients. The comparison of the two calculations shows that the leptodermous expansion is converging rapidly. Of the new terms, the term K 4 I 4 is quite negligible, the curvature term should be included, and we discuss to what extent the other higher-order terms are significant. (orig.)

Numerical Multilevel Upscaling for Incompressible Flow in Reservoir Simulation: An Element-based Algebraic Multigrid (AMGe) Approach

DEFF Research Database (Denmark)

Christensen, Max la Cour; Villa, Umberto; Engsig-Karup, Allan Peter

2017-01-01

associated with non-planar interfaces between agglomerates, the coarse velocity space has guaranteed approximation properties. The employed AMGe technique provides coarse spaces with desirable local mass conservation and stability properties analogous to the original pair of Raviart-Thomas and piecewise......We study the application of a finite element numerical upscaling technique to the incompressible two-phase porous media total velocity formulation. Specifically, an element agglomeration based Algebraic Multigrid (AMGe) technique with improved approximation proper ties [37] is used, for the first...... discontinuous polynomial spaces, resulting in strong mass conservation for the upscaled systems. Due to the guaranteed approximation properties and the generic nature of the AMGe method, recursive multilevel upscaling is automatically obtained. Furthermore, this technique works for both structured...

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

Inviscid incompressible limits for rotating fluids

Czech Academy of Sciences Publication Activity Database

Caggio, Matteo; Nečasová, Šárka

2017-01-01

Roč. 163, November (2017), s. 1-18 ISSN 0362-546X R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : compressible Navier -Stokces system * rotating fluids * incompressible limit Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X17301815?via%3Dihub

Inviscid incompressible limits for rotating fluids

Czech Academy of Sciences Publication Activity Database

Caggio, Matteo; Nečasová, Šárka

2017-01-01

Roč. 163, November (2017), s. 1-18 ISSN 0362-546X R&D Projects: GA ČR GA16-03230S Institutional support: RVO:67985840 Keywords : compressible Navier-Stokces system * rotating fluids * incompressible limit Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X17301815?via%3Dihub

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

Efficient Parallel Algorithms for Unsteady Incompressible Flows

KAUST Repository

Guermond, Jean-Luc; Minev, Peter D.

2013-01-01

The objective of this paper is to give an overview of recent developments on splitting schemes for solving the time-dependent incompressible Navier–Stokes equations and to discuss possible extensions to the variable density/viscosity case. A particular attention is given to algorithms that can be implemented efficiently on large parallel clusters.

DOMAIN DECOMPOSITION FOR POROELASTICITY AND ELASTICITY WITH DG JUMPS AND MORTARS

KAUST Repository

GIRAULT, V.

2011-01-01

We couple a time-dependent poroelastic model in a region with an elastic model in adjacent regions. We discretize each model independently on non-matching grids and we realize a domain decomposition on the interface between the regions by introducing DG jumps and mortars. The unknowns are condensed on the interface, so that at each time step, the computation in each subdomain can be performed in parallel. In addition, by extrapolating the displacement, we present an algorithm where the computations of the pressure and displacement are decoupled. We show that the matrix of the interface problem is positive definite and establish error estimates for this scheme. © 2011 World Scientific Publishing Company.

Self-similarity in incompressible Navier-Stokes equations.

Science.gov (United States)

Ercan, Ali; Kavvas, M Levent

2015-12-01

The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

Calculation of incompressible fluid flow through cambered blades

Science.gov (United States)

Hsu, C. C.

1970-01-01

Conformal mapping technique yields linear, approximate solutions for calculating flow of an incompressible fluid through staggered array of cambered blades for the cases of flow with partial cavitation and supercavitation. Lift and drag coefficients, cavitation number, cavity shape, and exit flow conditions can be determined.

On an incompressible model in radiation hydrodynamics

Czech Academy of Sciences Publication Activity Database

Ducomet, B.; Nečasová, Šárka

2015-01-01

Roč. 38, č. 4 (2015), s. 765-774 ISSN 0170-4214 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : radiation hydrodynamics * incompressible Navier-Stokes-Fourier system * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.002, year: 2015 http://onlinelibrary.wiley.com/doi/10.1002/mma.3107/abstract

Physical modelling and the poroelastic model with application to fluid detection in a VTI medium

International Nuclear Information System (INIS)

Li, Shengjie

2013-01-01

In this paper, both poroelasticity theory and pre-stack inversions have been combined to generate a flexible way to derive an effective fluid factor, which is then used to identify the presence of the hydrocarbon in weakly anisotropic VTI reservoirs. The effective fluid factor has been derived by using an approximate fluid substitution equation for anisotropic VTI media. The approximate equation provides a means of performing fluid substitution for elastic moduli along the vertical symmetry axis of a VTI medium with fewer elastic moduli. The effective fluid factor can be used to analyse the sensitivity of seismic attributes to fluid content. In order to examine the effectiveness of the effective fluid factor, an anisotropic physical model has been constructed. The rock properties of artificial sandstone used as a reservoir building material are properly selected by using an empirical model and Gassmann's equation. An effort is made to ensure the physical modelling data represent the 'true’ response of different fluid-filled sands. The fluid detection method is then applied to interpret the inverted seismic impedance obtained from physical modelling seismic data with some known gas-sands and wet-sands. The results shows that the interpretive resolution of seismic fluid detection has been dramatically improved by using the effective fluid factor. In addition, more information on lateral changes in fluid content can be distinguished. This study has demonstrated the potential of this method in detecting different fluid content in weakly anisotropic VTI reservoirs. (paper)

Modeling broadband poroelastic propagation using an asymptotic approach

Energy Technology Data Exchange (ETDEWEB)

Vasco, Donald W.

2009-05-01

An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.

Wellbore stability in shales considering chemo-poroelastic effects

Energy Technology Data Exchange (ETDEWEB)

Araujo, Ewerton M.P.; Pastor, Jorge A.S.C.; Fontoura, Sergio A.B.; Rabe, Claudio [Pontificia Univ. Catolica do Rio de Janeiro (PUC-Rio), RJ (Brazil). Dept. de Engenharia Civil. Grupo de Tecnologia e Engenharia de Petroleo

2004-07-01

Under compaction and low geothermal gradients are deep water characteristics. Both under compaction and low geothermal gradients generate considerable thickness of smectite-rich shales. These rocks are the major source of wellbore stability problems, because they are susceptible to adverse physico-chemical reactions when in contact with inadequate drilling fluids. Due shales are low permeability rocks diffusion processes dominate the changes of pore pressure around wellbore. Diffusion of fluids, ions and temperature occurs in shales during drilling and demand a fully coupled modelling taking account these factors. Despite temperature importance, in this paper wellbore stability in shales is analyzed through a model that considers only the coupling between poroelastic and physico-chemical effects. The coupled equations are solved analytically and have been implemented in a computational simulator with user-friendly interface. Time-dependent simulations of wellbore stability in shales are presented for a typical deep water scenario. The results show that physico-chemical effects change pore pressure around wellbore and have high impact on the wellbore stability. (author)

On PDE analysis of flows of quasi-incompressible fluids

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Lu, Y.; Málek, J.

2016-01-01

Roč. 96, č. 4 (2016), s. 491-508 ISSN 0044-2267 Keywords : quasi-incompressible fluids * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.332, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/zamm.201400229

Qualitative behaviour of incompressible two-phase flows with phase ...

Indian Academy of Sciences (India)

Jan Prüss

2017-11-07

Nov 7, 2017 ... Qualitative behaviour of incompressible two-phase flows with phase ... Germany. 2Graduate School of Human and Environmental Studies, Kyoto University, ... Note that j is a dummy variable as it can be eliminated from the ...

Local mesh refinement for incompressible fluid flow with free surfaces

Energy Technology Data Exchange (ETDEWEB)

Terasaka, H.; Kajiwara, H.; Ogura, K. [Tokyo Electric Power Company (Japan)] [and others

1995-09-01

A new local mesh refinement (LMR) technique has been developed and applied to incompressible fluid flows with free surface boundaries. The LMR method embeds patches of fine grid in arbitrary regions of interest. Hence, more accurate solutions can be obtained with a lower number of computational cells. This method is very suitable for the simulation of free surface movements because free surface flow problems generally require a finer computational grid to obtain adequate results. By using this technique, one can place finer grids only near the surfaces, and therefore greatly reduce the total number of cells and computational costs. This paper introduces LMR3D, a three-dimensional incompressible flow analysis code. Numerical examples calculated with the code demonstrate well the advantages of the LMR method.

Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

Science.gov (United States)

Shaik, Vaseem A.; Ardekani, Arezoo M.

2017-11-01

In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

Time-asymptotic interaction of flocking particles and an incompressible viscous fluid

International Nuclear Information System (INIS)

Bae, Hyeong-Ohk; Choi, Young-Pil; Ha, Seung-Yeal; Kang, Moon-Jin

2012-01-01

We present a new coupled kinetic-fluid model for the interactions between Cucker–Smale (C–S) flocking particles and incompressible fluid on the periodic spatial domain T d . Our coupled system consists of the kinetic C–S equation and the incompressible Navier–Stokes equations, and these two systems are coupled through the drag force. For the proposed model, we provide a global existence of weak solutions and a priori time-asymptotic exponential flocking estimates for any smooth flow, when the kinematic viscosity of the fluid is sufficiently large. The velocity of individual C–S particles and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast

Diffusion-limited mixing by incompressible flows

Science.gov (United States)

Miles, Christopher J.; Doering, Charles R.

2018-05-01

Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenize a passive tracer. However we provide numerical evidence that, in cases where advection and diffusion are both actively present, diffusion may produce negative effects by limiting the mixing effectiveness of incompressible optimal flows. This limitation appears to be due to the presence of a limiting length scale given by a generalised Batchelor length (Batchelor 1959 J. Fluid Mech. 5 113–33). This length scale limitation may in turn affect long-term mixing rates. More specifically, we consider local-in-time flow optimisation under energy and enstrophy flow constraints with the objective of maximising the mixing rate. We observe that, for enstrophy-bounded optimal flows, the strength of diffusion may not impact the long-term mixing rate. For energy-constrained optimal flows, however, an increase in the strength of diffusion can decrease the mixing rate. We provide analytical lower bounds on mixing rates and length scales achievable under related constraints (point-wise bounded speed and rate-of-strain) by extending the work of Lin et al (2011 J. Fluid Mech. 675 465–76) and Poon (1996 Commun. PDE 21 521–39).

Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations

International Nuclear Information System (INIS)

Fouxon, Itzhak; Oz, Yaron

2008-01-01

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them

Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

Science.gov (United States)

Fouxon, Itzhak; Oz, Yaron

2008-12-31

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

The incompressible non-relativistic Navier-Stokes equation from gravity

International Nuclear Information System (INIS)

Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.

2009-01-01

We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

Finite element methods for incompressible flow problems

CERN Document Server

John, Volker

2016-01-01

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

On singularity formation of a 3D model for incompressible Navier–Stokes equations

OpenAIRE

Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu

2012-01-01

We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei (2009) in [15] for axisymmetric 3D incompressible Navier–Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier–Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier–Stokes equations. One of the main results of this paper is that we prove rigorously th...

Incompressible Navier-Stokes equations. Theory and practice

Energy Technology Data Exchange (ETDEWEB)

Gjesdal, T.

1996-12-31

This paper contains notes from a seminar presented at the Dept. of Mathematics in the University of Bergen, Norway, Oct. 1996. It first introduces the theory of existence and uniqueness of solutions to the incompressible Navier-Stokes equation and defines a well-posed initial-boundary value problem. It then discusses different methods for solving numerically the Navier-Stokes equations in velocity-pressure formulation. The emphasis is on pressure correction methods. 19 refs.

Seismicity rate surge on faults after shut-in: poroelastic response to fluid injection

Science.gov (United States)

Chang, K. W.; Yoon, H.; Martinez, M. J.

2017-12-01

Subsurface energy activities such as geological CO2 storage and wastewater injection require injecting large amounts of fluid into the subsurface, which will alter the states of pore pressure and stress in the storage formation. One of the main issues for injection-induced seismicity is the post shut-in increases in the seismicity rate, often observed in the fluid-injection operation sites. The rate surge can be driven by the following mechanisms: (1) pore-pressure propagation into distant faults after shut-in and (2) poroelastic stressing caused by well operations, depending on fault geometry, hydraulic and mechanical properties of the formation, and injection history. We simulate the aerial view of the target reservoir intersected by strike-slip faults, in which injection-induced pressure buildup encounters the faults directly. We examine the poroelastic response of the faults to fluid injection and perform a series of sensitivity tests considering: (1) permeability of the fault zone, (2) locations and the number of faults with respect to the injection point, and (3) well operations with varying the injection rate. Our analysis of the Coulomb stress change suggests that the sealing fault confines pressure diffusion which stabilizes or weakens the nearby conductive fault depending on the injection location. We perform the sensitivity test by changing injection scenarios (time-dependent rates), while keeping the total amount of injected fluids. Sensitivity analysis shows that gradual reduction of the injection rate minimizes the Coulomb stress change and the least seismicity rates are predicted. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

Fluid and solid mechanics in a poroelastic network induced by ultrasound.

Science.gov (United States)

Wang, Peng; Olbricht, William L

2011-01-04

We made a theoretical analysis on the fluid and solid mechanics in a poroelastic medium induced by low-power ultrasound. Using a perturbative approach, we were able to linearize the governing equations and obtain analytical solutions. We found that ultrasound could propagate in the medium as a mechanical wave, but would dissipate due to frictional forces between the fluid and the solid phase. The amplitude of the wave depends on the ultrasonic power input. We applied this model to the problem of drug delivery to soft biological tissues by low-power ultrasound and proposed a mechanism for enhanced drug penetration. We have also found the coexistence of two acoustic waves under certain circumstances and pointed out the importance of very accurate experimental determination of the high-frequency properties of brain tissue. Copyright © 2010 Elsevier Ltd. All rights reserved.

Wind turbine aerodynamics using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the unsteady flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations...

On the solvability of asymmetric quasilinear finite element approximate problems in nonlinear incompressible elasticity

International Nuclear Information System (INIS)

Ruas, V.

1982-09-01

A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt

Poroelastic Mechanical Effects of Hemicelluloses on Cellulosic Hydrogels under Compression

Science.gov (United States)

Lopez-Sanchez, Patricia; Cersosimo, Julie; Wang, Dongjie; Flanagan, Bernadine; Stokes, Jason R.; Gidley, Michael J.

2015-01-01

Hemicelluloses exhibit a range of interactions with cellulose, the mechanical consequences of which in plant cell walls are incompletely understood. We report the mechanical properties of cell wall analogues based on cellulose hydrogels to elucidate the contribution of xyloglucan or arabinoxylan as examples of two hemicelluloses displaying different interactions with cellulose. We subjected the hydrogels to mechanical pressures to emulate the compressive stresses experienced by cell walls in planta. Our results revealed that the presence of either hemicellulose increased the resistance to compression at fast strain rates. However, at slow strain rates, only xyloglucan increased composite strength. This behaviour could be explained considering the microstructure and the flow of water through the composites confirming their poroelastic nature. In contrast, small deformation oscillatory rheology showed that only xyloglucan decreased the elastic moduli. These results provide evidence for contrasting roles of different hemicelluloses in plant cell wall mechanics and man-made cellulose-based composite materials. PMID:25794048

Incompressible limit of the degenerate quantum compressible Navier-Stokes equations with general initial data

Science.gov (United States)

Kwon, Young-Sam; Li, Fucai

2018-03-01

In this paper we study the incompressible limit of the degenerate quantum compressible Navier-Stokes equations in a periodic domain T3 and the whole space R3 with general initial data. In the periodic case, by applying the refined relative entropy method and carrying out the detailed analysis on the oscillations of velocity, we prove rigorously that the gradient part of the weak solutions (velocity) of the degenerate quantum compressible Navier-Stokes equations converge to the strong solution of the incompressible Navier-Stokes equations. Our results improve considerably the ones obtained by Yang, Ju and Yang [25] where only the well-prepared initial data case is considered. While for the whole space case, thanks to the Strichartz's estimates of linear wave equations, we can obtain the convergence of the weak solutions of the degenerate quantum compressible Navier-Stokes equations to the strong solution of the incompressible Navier-Stokes/Euler equations with a linear damping term. Moreover, the convergence rates are also given.

Numerical methods for incompressible viscous flows with engineering applications

Science.gov (United States)

Rose, M. E.; Ash, R. L.

1988-01-01

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

A mathematical model for turbulent incompressible flows through mixing grids

International Nuclear Information System (INIS)

Allaire, G.

1989-01-01

A mathematical model is proposed for the computation of turbulent incompressible flows through mixing grids. This model is obtained as follows: in a three-dimentional-domain we represent a mixing grid by small identical wings of size ε 2 periodically distributed at the nodes of a plane regular mesh of size ε, and we consider incompressible Navier-Stokes equations with a no-slip condition on the wings. Using an appropriate homogenization process we pass to the limit when ε tends to zero and we obtain a Brinkman equation, i.e. a Navier-Stokes equation plus a zero-order term for the velocity, in a homogeneous domain without anymore wings. The interest of this model is that the spatial discretization is simpler in a homogeneous domain, and, moreover, the new term, which expresses the grid's mixing effect, can be evaluated with a local computation around a single wing

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

Science.gov (United States)

Moraleda, Joaquín; Segurado, Javier; LLorca, Javier

2009-09-01

The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10-40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time "quasi-exact" results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.

Rubber and gel origami: visco- and poro-elastic behavior of folded structures

Science.gov (United States)

Evans, Arthur; Bende, Nakul; Na, Junhee; Hayward, Ryan; Santangelo, Christian

2014-11-01

The Japanese art of origami is rapidly becoming a platform for material design, as researchers develop systematic methods to exploit the purely geometric rules that allow paper to folded without stretching. Since any thin sheet couples mechanics strongly to geometry, origami provides a natural template for generating length-scale independent structures from a variety of different materials. In this talk I discuss some of the implications of using polymeric sheets and shells over many length scales to create folded materials with tunable shapes and properties. These implications include visco-elastic snap-through transitions and poro-elastically driven micro origami. In each case, mechanical response, dynamics, and reversible folding is tuned through a combination of geometry and constitutive properties, demonstrating the efficacy of using origami principles for designing functional materials.

Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

Science.gov (United States)

Hejranfar, Kazem; Parseh, Kaveh

2017-09-01

The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.

Unique encoding for streamline topologies of incompressible and inviscid flows in multiply connected domains

Energy Technology Data Exchange (ETDEWEB)

Sakajo, T [Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Sawamura, Y; Yokoyama, T, E-mail: sakajo@math.kyoto-u.ac.jp [JST CREST, Kawaguchi, Saitama 332-0012 (Japan)

2014-06-01

This study considers the flow of incompressible and inviscid fluid in two-dimensional multiply connected domains. For such flows, encoding algorithms to assign a unique sequence of words to any structurally stable streamline topology based on the theory presented by Yokoyama and Sakajo (2013 Proc. R. Soc. A 469 20120558) are proposed. As an application, we utilize the algorithms to characterize the evolution of an incompressible and viscid flow around a flat plate inclined to the uniform flow in terms of the change of the word representations for their instantaneous streamline topologies. (papers)

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

KAUST Repository

Cockburn, Bernardo; Kanschat, Guido; Schö tzau, Dominik

2008-01-01

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability

Five-dimensional truncation of the plane incompressible navier-stokes equations

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C [Camerino Univ. (Italy). Istituto di Matematica; Franceschini, V [Modena Univ. (Italy). Istituto Matematico

1979-01-01

A five-modes truncation of the Navier-Stokes equations for a two dimensional incompressible fluid on a torus is considered. A computer analysis shows that for a certain range of the Reynolds number the system exhibits a stochastic behaviour, approached through an involved sequence of bifurcations.

Oberbeck-Bousinesq approximation for the motion of two incompressible fluids

Czech Academy of Sciences Publication Activity Database

Denisova, I.V.; Nečasová, Šárka

2009-01-01

Roč. 159, č. 4 (2009), s. 436-451 ISSN 1072-3374 R&D Projects: GA AV ČR IAA100190804; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : surface tension * Oberbeck -Bousinesq approximation * incompressible fluids Subject RIV: BA - General Mathematics

A discontinuous finite element approach to cracking in coupled poro-elastic fluid flow models

Science.gov (United States)

Wilson, C. R.; Spiegelman, M. W.; Evans, O.; Ulven, O. I.; Sun, W.

2016-12-01

Reaction-driven cracking is a coupled process whereby fluid-induced reactions drive large volume changes in the host rock which produce stresses leading to crack propagation and failure. This in turn generates new surface area and fluid-flow pathways for subsequent reaction in a potentially self-sustaining system. This mechanism has has been proposed for the pervasive serpentinization and carbonation of peridotite, as well as applications to mineral carbon sequestration and hydrocarbon extraction. The key computational issue in this problem is implementing algorithms that adequately model the formation of discrete fractures. Here we present models using a discontinuous finite element method for modeling fracture formation (Radovitsky et al., 2011). Cracks are introduced along facets of the mesh by the relaxation of penalty parameters once a failure criterion is met. It is fully described in the weak form of the equations, requiring no modification of the underlying mesh structure and allowing fluid properties to be easily adjusted along cracked facets. To develop and test the method, we start by implementing the algorithm for the simplified Biot equations for poro-elasticity using the finite element model assembler TerraFERMA. We consider hydro-fracking around a borehole (Grassl et al., 2015), where elevated fluid pressure in the poro-elastic solid causes it to fail radially in tension. We investigate the effects of varying the Biot coefficient and adjusting the fluid transport properties in the vicinity of the crack and compare our results to related dual-graph models (Ulven & Sun, submitted). We discuss issues arising from this method, including the formation of null spaces and appropriate preconditioning and solution strategies. Initial results suggest that this method provides a promising way to incorporate cracking into our reactive fluid flow models and future work aims to integrate the mechanical and chemical aspects of this process.

On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

Directory of Open Access Journals (Sweden)

Meng Zhi-Jun

2016-01-01

Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

Science.gov (United States)

Hyhlík, Tomáš

2018-06-01

The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

Directory of Open Access Journals (Sweden)

Hyhlík Tomáš

2018-01-01

Full Text Available The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

Laminar motion of the incompressible fluids in self-acting thrust bearings with spiral grooves.

Science.gov (United States)

Velescu, Cornel; Popa, Nicolae Calin

2014-01-01

We analyze the laminar motion of incompressible fluids in self-acting thrust bearings with spiral grooves with inner or external pumping. The purpose of the study is to find some mathematical relations useful to approach the theoretical functionality of these bearings having magnetic controllable fluids as incompressible fluids, in the presence of a controllable magnetic field. This theoretical study approaches the permanent motion regime. To validate the theoretical results, we compare them to some experimental results presented in previous papers. The laminar motion of incompressible fluids in bearings is described by the fundamental equations of fluid dynamics. We developed and particularized these equations by taking into consideration the geometrical and functional characteristics of these hydrodynamic bearings. Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the "pumping" direction. These pressure and speed distributions offer important information, both quantitative (concerning the bearing performances) and qualitative (evidence of the viscous-inertial effects, the fluid compressibility, etc.), for the laminar and permanent motion regime.

Laminar Motion of the Incompressible Fluids in Self-Acting Thrust Bearings with Spiral Grooves

Directory of Open Access Journals (Sweden)

Cornel Velescu

2014-01-01

Full Text Available We analyze the laminar motion of incompressible fluids in self-acting thrust bearings with spiral grooves with inner or external pumping. The purpose of the study is to find some mathematical relations useful to approach the theoretical functionality of these bearings having magnetic controllable fluids as incompressible fluids, in the presence of a controllable magnetic field. This theoretical study approaches the permanent motion regime. To validate the theoretical results, we compare them to some experimental results presented in previous papers. The laminar motion of incompressible fluids in bearings is described by the fundamental equations of fluid dynamics. We developed and particularized these equations by taking into consideration the geometrical and functional characteristics of these hydrodynamic bearings. Through the integration of the differential equation, we determined the pressure and speed distributions in bearings with length in the “pumping” direction. These pressure and speed distributions offer important information, both quantitative (concerning the bearing performances and qualitative (evidence of the viscous-inertial effects, the fluid compressibility, etc., for the laminar and permanent motion regime.

Some axisymmetric equilibria for certain ideal and resistive magnetohydrodynamics with incompressible flows

Directory of Open Access Journals (Sweden)

S.M. Moawad

Full Text Available In this paper, the equilibrium properties of some ideal and resistive magnetohydrodynamics (MHD are investigated. The governing equations are taken in the steady state for parallel and non-parallel flow to magnetic filed. The governing equations are reduced to Bernoulli-Grad-Shafranov system. The problem of finding exact equilibria to the governing equations in the presence of incompressible mass flows is studied. Several nonlinear equilibria of the governing equations are obtained with aid of constructed constraints. The obtained results cover several previously configurations and include new considerations about the nonlinearity of magnetic flux stream variables. The possibility of applying the obtained results to magnetic confinement devices are discussed. Keywords: Magnetohydrodynamics, Axisymmetric plasma, Resistivity, Incompressible flows, Exact equilibria, Magnetic confinement devices

INHOMOGENEOUS NEARLY INCOMPRESSIBLE DESCRIPTION OF MAGNETOHYDRODYNAMIC TURBULENCE

International Nuclear Information System (INIS)

Hunana, P.; Zank, G. P.

2010-01-01

The nearly incompressible theory of magnetohydrodynamics (MHD) is formulated in the presence of a static large-scale inhomogeneous background. The theory is an inhomogeneous generalization of the homogeneous nearly incompressible MHD description of Zank and Matthaeus and a polytropic equation of state is assumed. The theory is primarily developed to describe solar wind turbulence where the assumption of a composition of two-dimensional (2D) and slab turbulence with the dominance of the 2D component has been used for some time. It was however unclear, if in the presence of a large-scale inhomogeneous background, the dominant component will also be mainly 2D and we consider three distinct MHD regimes for the plasma beta β > 1. For regimes appropriate to the solar wind (β 2 s δp is not valid for the leading-order O(M) density fluctuations, and therefore in observational studies, the density fluctuations should not be analyzed through the pressure fluctuations. The pseudosound relation is valid only for higher order O(M 2 ) density fluctuations, and then only for short-length scales and fast timescales. The spectrum of the leading-order density fluctuations should be modeled as k -5/3 in the inertial range, followed by a Bessel function solution K ν (k), where for stationary turbulence ν = 1, in the viscous-convective and diffusion range. Other implications for solar wind turbulence with an emphasis on the evolution of density fluctuations are also discussed.

Incompressible LFR MHD. A fluid model for stability analysis of a fusion plasma

International Nuclear Information System (INIS)

Scheffel, J.; Faghihi, M.

1986-10-01

A fluid model including FLR effects, named Incompressible Finite Larmor Radius MagnetoHydroDynamics, is presented and derived in this paper. It is an extension of ordinary, incompressible MHD to include the Larmor radius effects due to ion gyroviscosity, Hall current and electron diamagnetism. It is intended to use the model for stability analysis, on the Alfven wave time scale, of a fusion plasma and it is consequently based on transport coefficients in the collisionless limit. It will be demonstrated that for a fairly dense and cool plasma, such as for the EXTRAP z-pinch, all three Larmor radius effects may become important, that for a JET-type plasma no FLR effect is pronounced, and that in a reactor plasma the Hall and electron diamagnetism term may play a role. For scaling lengths signigicantly smaller than the plasma radius the effect of the FLR terms becomes enhanced. To study the importance of the choice of equations of state for the model the m=1 and k 2 r 2 towards infinity instability in cylindrical geometry is given special attention for zero Larmor radius. The full stability criterion of the double adiabatic model, including pressure anisotropy, is presented for what we believe to be the first time. It is found that when perpendicular p > parallel p stability can be reached for very high plasma perpendicular β-values. We demonstrate that no less complicated energy conserving fluid model, which takes into account pressure anisotropy, other than the double adiabativ model can be obtained. Since pressure anisotropy generally only weakly affects stability, we can assume isotropy in the Incompressible FLR MHD model. Also, the energy equation is replaced by the incompressibility condition, making FLR terms appearing in the energy equation irrelevant. (authors)

Turbulence in nearly incompressible fluids: density spectrum, flows, correlations and implication to the interstellar medium

Directory of Open Access Journals (Sweden)

S. Dastgeer

2005-01-01

Full Text Available Interstellar scintillation and angular radio wave broadening measurements show that interstellar and solar wind (electron density fluctuations exhibit a Kolmogorov-like k-5/3 power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interstellar medium (ISM density spectrum led to an explanation based on coupling incompressible magnetohydrodynamic (MHD fluctuations to density fluctuations through a 'pseudosound' relation within the context of 'nearly incompressible' (NI hydrodynamics (HD and MHD models. The NI theory provides a fundamentally different explanation for the observed ISM density spectrum in that the density fluctuations can be a consequence of passive scalar convection due to background incompressible fluctuations. The theory further predicts generation of long-scale structures and various correlations between the density, temperature and the (magneto acoustic as well as convective pressure fluctuations in the compressible ISM fluids in different thermal regimes that are determined purely by the thermal fluctuation level. In this paper, we present the results of our two dimensional nonlinear fluid simulations, exploring various nonlinear aspects that lead to inertial range ISM turbulence within the context of a NI hydrodymanics model. In qualitative agreement with the NI predictions and the in-situ observations, we find that i the density fluctuations exhibit a Kolmogorov-like spectrum via a passive convection in the field of the background incompressible fluctuations, ii the compressible ISM fluctuations form long scale flows and structures, and iii the density and the temperature fluctuations are anti-correlated.

Comparative study of incompressible and isothermal compressible flow solvers for cavitating flow dynamics

Energy Technology Data Exchange (ETDEWEB)

Park, Sun Ho [Korea Maritime and Ocean University, Busan (Korea, Republic of); Rhee, Shin Hyung [Seoul National University, Seoul (Korea, Republic of)

2015-08-15

Incompressible flow solvers are generally used for numerical analysis of cavitating flows, but with limitations in handling compressibility effects on vapor phase. To study compressibility effects on vapor phase and cavity interface, pressure-based incompressible and isothermal compressible flow solvers based on a cell-centered finite volume method were developed using the OpenFOAM libraries. To validate the solvers, cavitating flow around a hemispherical head-form body was simulated and validated against the experimental data. The cavity shedding behavior, length of a re-entrant jet, drag history, and the Strouhal number were compared between the two solvers. The results confirmed that computations of the cavitating flow including compressibility effects improved the reproduction of cavitation dynamics.

Mathematical problems of the dynamics of incompressible fluid on a rotating sphere

CERN Document Server

Skiba, Yuri N

2017-01-01

This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.

General quantitative analysis of stress partitioning and boundary conditions in undrained biphasic porous media via a purely macroscopic and purely variational approach

Science.gov (United States)

Serpieri, Roberto; Travascio, Francesco

2016-03-01

In poroelasticity, the effective stress law relates the external stress applied to the medium to the macroscopic strain of the solid phase and the interstitial pressure of the fluid saturating the mixture. Such relationship has been formerly introduced by Terzaghi in form of a principle. To date, no poroelastic theory is capable of recovering a stress partitioning law in agreement with Terzaghi's postulated one in the absence of ad hoc constitutive assumptions on the medium. We recently proposed a variational macroscopic continuum description of two-phase poroelasticity to derive a general biphasic formulation at finite deformations, termed variational macroscopic theory of porous media (VMTPM). Such approach proceeds from the inclusion of the intrinsic volumetric strain among the kinematic descriptors aside to macroscopic displacements, and as a variational theory, uses the Hamilton least-action principle as the unique primitive concept of mechanics invoked to derive momentum balance equations. In a previous related work it was shown that, for the subclass of undrained problems, VMTPM predicts that stress is partitioned in the two phases in strict compliance with Terzaghi's law, irrespective of the microstructural and constitutive features of a given medium. In the present contribution, we further develop the linearized framework of VMTPM to arrive at a general operative formula that allows the quantitative determination of stress partitioning in a jacketed test over a generic isotropic biphasic specimen. This formula is quantitative and general, in that it relates the partial phase stresses to the externally applied stress as function of partitioning coefficients that are all derived by strictly following a purely variational and purely macroscopic approach, and in the absence of any specific hypothesis on the microstructural or constitutive features of a given medium. To achieve this result, the stiffness coefficients of the theory are derived by using

Inviscid incompressible limits of the full Navier-Stokes-Fourier system

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Novotný, A.

2013-01-01

Roč. 321, č. 3 (2013), s. 605-628 ISSN 0010-3616 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 1.901, year: 2013 http://link.springer.com/article/10.1007%2Fs00220-013-1691-4

Equilibrium states for a plane incompressible perfect fluid

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C; Frigio, S [Camerino Univ. (Italy). Istituto di Matematica

1980-01-01

We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.

Increase in transmission loss of single panels by addition of mass inclusions to a poro-elastic layer: Experimental investigation

Science.gov (United States)

Kidner, M. R. F.; Fuller, C. R.; Gardner, B.

2006-06-01

The insertion loss of standard acoustic blankets can be significantly improved at low frequencies by the addition of randomly placed mass inclusions to the poro-elastic layers. The improvement is much greater than that due to the mass effect alone. The mass inclusions act as resonant systems and so increase the structure impedance. This paper reports the results of experimental investigations into this phenomenon. Increases in insertion loss of 15 dB in the 100 Hz third octave band are reported.

Spatial Angular Compounding for Elastography without the Incompressibility Assumption

OpenAIRE

Rao, Min; Varghese, Tomy

2005-01-01

Spatial-angular compounding is a new technique that enables the reduction of noise artifacts in ultrasound elastography. Previous results using spatial angular compounding, however, were based on the use of the tissue incompressibility assumption. Compounded elastograms were obtained from a spatially-weighted average of local strain estimated from radiofrequency echo signals acquired at different insonification angles. In this paper, we present a new method for reducing the noise artifacts in...

Acquisition Challenge: The Importance of Incompressibility in Comparing Learning Curve Models

Science.gov (United States)

2015-10-01

primary platform for analysis based on production history and availability of relevant airframe costs. F-15 airframe costs were acquired from two databases...assembly line at Ford or Toyota . Given this dynamic, assuming the real incompress- ibility factor is somewhere between 0.0 and 0.1 is not implausible

Wind turbine rotor-tower interaction using an incompressible overset grid method

DEFF Research Database (Denmark)

Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

2007-01-01

In this paper 3D Navier-Stokes simulations of the flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations are pres...

Meshless Solution of Incompressible Flow Over Backward-Facing Step

Directory of Open Access Journals (Sweden)

Mužík Juraj

2016-05-01

Full Text Available Article presents the use of the meshless method for numerical simulation of incompressible fluid flow. The article presents the implementation of the meshless local Petrov-Galerkin method (MLPG, with Navier-Stokes equation formulated using the local weighted residual principle. The trial function construction process is the most important part of the meshless method implementation. In this article the radial basis functions (RBF are used for the process of the trial functions construction.

Coupled incompressible Smoothed Particle Hydrodynamics model for continuum-based modelling sediment transport

Science.gov (United States)

Pahar, Gourabananda; Dhar, Anirban

2017-04-01

A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.

Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault

International Nuclear Information System (INIS)

Delorey, Andrew A.; Elst, Nicholas J. van der; Johnson, Paul Allan

2016-01-01

Tidal triggering of earthquakes is hypothesized to provide quantitative information regarding the fault's stress state, poroelastic properties, and may be significant for our understanding of seismic hazard. To date, studies of regional or global earthquake catalogs have had only modest successes in identifying tidal triggering. We posit that the smallest events that may provide additional evidence of triggering go unidentified and thus we developed a technique to improve the identification of very small magnitude events. We identify events applying a method known as inter-station seismic coherence where we prioritize detection and discrimination over characterization. Here we show tidal triggering of earthquakes on the San Andreas Fault. We find the complex interaction of semi-diurnal and fortnightly tidal periods exposes both stress threshold and critical state behavior. Lastly, our findings reveal earthquake nucleation processes and pore pressure conditions – properties of faults that are difficult to measure, yet extremely important for characterizing earthquake physics and seismic hazards.

Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault

Science.gov (United States)

Delorey, Andrew; Van Der Elst, Nicholas; Johnson, Paul

2017-01-01

Tidal triggering of earthquakes is hypothesized to provide quantitative information regarding the fault's stress state, poroelastic properties, and may be significant for our understanding of seismic hazard. To date, studies of regional or global earthquake catalogs have had only modest successes in identifying tidal triggering. We posit that the smallest events that may provide additional evidence of triggering go unidentified and thus we developed a technique to improve the identification of very small magnitude events. We identify events applying a method known as inter-station seismic coherence where we prioritize detection and discrimination over characterization. Here we show tidal triggering of earthquakes on the San Andreas Fault. We find the complex interaction of semi-diurnal and fortnightly tidal periods exposes both stress threshold and critical state behavior. Our findings reveal earthquake nucleation processes and pore pressure conditions – properties of faults that are difficult to measure, yet extremely important for characterizing earthquake physics and seismic hazards.

A poroelastic reservoir model for predicting subsidence and mapping subsurface pressure fronts

International Nuclear Information System (INIS)

Du, J.; Olson, J.E.

2001-01-01

A forward model was constructed to numerically predict surface subsidence and reservoir compaction following the approach of Segall [Pure Appl. Phys. 139 (1992) 536]. A nucleus of poroelastic strain is numerically integrated over a rectangular prism assuming constant pressure change. This fundamental geometry allows a reservoir to be divided into many small cubic blocks in a manner similar to reservoir simulation. The subsidence and compaction effects of the pressure change throughout the reservoir are calculated by the superposition of results from each individual block. Using forward modeling, pressure boundary conditions can be acquired from pressure test data or reservoir simulation predictions. An inversion model also was developed that can track pressure fronts in a subsurface reservoir using surface displacements. The capability of the inversion model was demonstrated using synthetic examples of one-well and four-well cases with different layouts of surface observation locations. The impact of noise on the inversion result is also included

NASA-VOF3D, 3-D Transient, Free Surface, Incompressible Fluid Dynamic

International Nuclear Information System (INIS)

Torrey, M.D.

1992-01-01

1 - Description of program or function: NASA-VOF3D is a three- dimensional, transient, free surface, incompressible fluid dynamics program. It is specifically designed to calculate confined flows in a low gravity environment in which surface physics must be accurately treated. It allows multiple free surfaces with surface tension and wall adhesion and includes a partial cell treatment that allows curved boundaries and internal obstacles. Variable mesh spacing is permitted in all three coordinate directions. Boundary conditions available are rigid free-slip wall, rigid no-slip, wall, continuative, periodic, and specified pressure outflow boundary. 2 - Method of solution: NASA-VOF3D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The free surfaces are treated by introducing a function defined to be unity at any point occupied by the fluid and zero elsewhere. The complete Navier- Stokes equations for an incompressible fluid are solved by finite differences with surface tension effects included. Wall adhesion may be included or neglected as a user option. The pressures (and velocities) are advanced in time throughout the computing mesh by either a conjugate residual method or the successive over-relaxation (SOR) method. The conjugate residual method is vectorized for the Cray and uses a scaled coefficient matrix. 3 - Restrictions on the complexity of the problem: NASA-VOF3D is restricted to cylindrical coordinate representation of the geometry. A three-dimensional wall-adhesion procedure is available only for straight-walled containers

Surface incompressibility from semiclassical relativistic mean field calculations

International Nuclear Information System (INIS)

Patra, S.K.; Centelles, M.; Vinas, X.; Estal, M. del

2002-01-01

By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility K A has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of K A for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

Incompressible limit of compressible Navier-Stokes equations

International Nuclear Information System (INIS)

Bessaih, H.

1994-01-01

In this paper we study the system which describes the motion of compressible viscous fluid in a bounded domain Ω of R 3 . When we introduce a parameter λ, that is the inverse of the Mach number, we prove, under small initial data and external force (for barotropic flows), that the solution of Navier-Stokes equations is the incompressible limit of the solution of compressible Navier-Stokes equations, as the Mach number becomes small. For this, we show the existence of a solution verifying estimates independent of λ. Compactness argument allow us to pass to the limit on λ in the nonlinear terms. (author). 17 refs

Toward in vivo lung's tissue incompressibility characterization for tumor motion modeling in radiation therapy

International Nuclear Information System (INIS)

Shirzadi, Zahra; Sadeghi-Naini, Ali; Samani, Abbas

2013-01-01

Purpose: A novel technique is proposed to characterize lung tissue incompressibility variation during respiration. Estimating lung tissue incompressibility parameter variations resulting from air content variation throughout respiration is critical for computer assisted tumor motion tracking. Continuous tumor motion is a major challenge in lung cancer radiotherapy, especially with external beam radiotherapy. If not accounted for, this motion may lead to areas of radiation overdosage for normal tissue. Given the unavailability of imaging modality that can be used effectively for real-time lung tumor tracking, computer assisted approach based on tissue deformation estimation can be a good alternative. This approach involves lung biomechanical model where its fidelity depends on input tissue properties. This investigation shows that considering variable tissue incompressibility parameter is very important for predicting tumor motion accurately, hence improving the lung radiotherapy outcome. Methods: First, an in silico lung phantom study was conducted to demonstrate the importance of employing variable Poisson's ratio for tumor motion predication. After it was established that modeling this variability is critical for accurate tumor motion prediction, an optimization based technique was developed to estimate lung tissue Poisson's ratio as a function of respiration cycle time. In this technique, the Poisson's ratio and lung pressure value were varied systematically until optimal values were obtained, leading to maximum similarity between acquired and simulated 4D CT lung images. This technique was applied in an ex vivo porcine lung study where simulated images were constructed using the end exhale CT image and deformation fields obtained from the lung's FE modeling of each respiration time increment. To model the tissue, linear elastic and Marlow hyperelastic material models in conjunction with variable Poisson's ratio were used. Results: The phantom study showed that

INCOMPRESSIBLE LAMINAR BOUNDARY LAYER CONTROL BY BLOWING AND SUCTION

OpenAIRE

AZZEDINE NAHOUI; LAKHDAR BAHI

2013-01-01

A two-dimensional incompressible laminar boundary layer and its control using blowing and suction over a flat plate and around the NACA 0012 and 661012 profiles, is studied numerically. The study is based on the Prandtl boundary layer model using the finite differences method and the Crank-Nicolson scheme. The velocity distribution, the boundary layer thickness and the friction coefficient, are determined and presented with and without control. The application of the control technique, has de...

Nonlinear sausage-wave propagation in a magnetic slab in an incompressible fluid

International Nuclear Information System (INIS)

Ruderman, M.S.

1993-01-01

Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically. (Author)

A matrix-free, implicit, incompressible fractional-step algorithm for fluid–structure interaction applications

CSIR Research Space (South Africa)

Oxtoby, Oliver F

2012-05-01

Full Text Available In this paper we detail a fast, fully-coupled, partitioned fluid–structure interaction (FSI) scheme. For the incompressible fluid, new fractional-step algorithms are proposed which make possible the fully implicit, but matrixfree, parallel solution...

Viscoelastic and poroelastic effects in the wetting dynamics of soft gels by liquids

Science.gov (United States)

Limat, Laurent; Dervaux, Julien; Roche, Matthieu; Zhao, Menghua; Narita, Tetsuharu; Lequeux, Francois

2017-11-01

We have developed experiments and modeling of elastowetting dynamics on soft gels. First, wetting is very sensitive to the thickness of the gel, when deposited on a rigid basis. We reconsidered Long et al. approach, and extended it to finite depth. This yields a new scaling law, at low thickness, for dynamic contact angle, in very good agreement with experiment but not consistent with recent approachs assuming Neuman triangle to hold even in the dynamics. In a second step, we examined solvent migration in the bulk of the gel, and showed that poroelasticity is an essential ingredient to understand old unsolved issues (hysteresis on elastomers by Extrand and Kumagai), as well as recent puzzling measurements (long life footprints left by drops). Our calculations lead to ridges at the contact lines evolving logarithmically with time, with a very strong infuence on wetting properties of soft materials, and with possible applications to biophysics.

Testing the mutually enhanced magicity effect in nuclear incompressibility via the giant monopole resonance in the {sup 204,206,208}Pb isotopes

Energy Technology Data Exchange (ETDEWEB)

Patel, D. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Garg, U., E-mail: garg@nd.edu [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Fujiwara, M. [Research Center for Nuclear Physics, Osaka University, Osaka 567-0047 (Japan); Adachi, T. [Kernfysisch Versneller Instituut, University of Groningen, 9747 AA Groningen (Netherlands); Akimune, H. [Department of Physics, Konan University, Kobe 568-8501 (Japan); Berg, G.P.A. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Harakeh, M.N. [Kernfysisch Versneller Instituut, University of Groningen, 9747 AA Groningen (Netherlands); GANIL, CEA/DSM-CNRS/IN2P3, 14076 Cean (France); Itoh, M. [Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578 (Japan); Iwamoto, C. [Department of Physics, Konan University, Kobe 568-8501 (Japan); Long, A.; Matta, J.T. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Murakami, T. [Division of Physics and Astronomy, Kyoto University, Kyoto 606-8502 (Japan); Okamoto, A. [Department of Physics, Konan University, Kobe 568-8501 (Japan); Sault, K. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Talwar, R. [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556 (United States); Uchida, M. [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8850 (Japan); and others

2013-10-07

Using inelastic α-scattering at extremely forward angles, including 0°, the strength distributions of the isoscalar giant monopole resonance (ISGMR) have been measured in the {sup 204,206,208}Pb isotopes in order to examine the proposed mutually enhanced magicity (MEM) effect on the nuclear incompressibility. The MEM effect had been suggested as a likely explanation of the “softness” of nuclear incompressibility observed in the ISGMR measurements in the Sn and Cd isotopes. Our experimental results rule out any manifestation of the MEM effect in nuclear incompressibility and leave the question of the softness of the open-shell nuclei unresolved still.

Three dimensional simulation of compressible and incompressible flows through the finite element method

International Nuclear Information System (INIS)

Costa, Gustavo Koury

2004-11-01

Although incompressible fluid flows can be regarded as a particular case of a general problem, numerical methods and the mathematical formulation aimed to solve compressible and incompressible flows have their own peculiarities, in such a way, that it is generally not possible to attain both regimes with a single approach. In this work, we start from a typically compressible formulation, slightly modified to make use of pressure variables and, through augmenting the stabilising parameters, we end up with a simplified model which is able to deal with a wide range of flow regimes, from supersonic to low speed gas flows. The resulting methodology is flexible enough to allow for the simulation of liquid flows as well. Examples using conservative and pressure variables are shown and the results are compared to those published in the literature, in order to validate the method. (author)

A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

KAUST Repository

Bourantas, Georgios; Loukopoulos, Vassilios C.

2013-01-01

A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a

Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids

Czech Academy of Sciences Publication Activity Database

Sokolowski, J.; Stebel, Jan

2011-01-01

Roč. 40, č. 4 (2011), s. 1077-1097 ISSN 0324-8569 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : shape optimization * shape gradient * incompressible viscous fluid Subject RIV: BA - General Mathematics Impact factor: 0.300, year: 2010

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

Science.gov (United States)

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

Global Well-Posedness of the Incompressible Magnetohydrodynamics

Science.gov (United States)

Cai, Yuan; Lei, Zhen

2018-06-01

This paper studies the Cauchy problem of the incompressible magnetohydro dynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initialmagnetic field froma non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν ≧ 0 and all spaces with dimension n ≧ 2. Such a result holds true uniformly in nonnegative viscosity parameters. The proof is based on the inherent strong null structure of the systems introduced by Lei (Commun Pure Appl Math 69(11):2072-2106, 2016) and the ghost weight technique introduced by Alinhac (Invent Math 145(3):597-618, 2001).

CONVEC: a computer program for transient incompressible fluid flow based on quadratic finite elements. Part 1: theoretical aspects

International Nuclear Information System (INIS)

Laval, H.

1981-01-01

This report describes the theoretical and numerical aspects of the finite element computer code CONVEC designed for the transient analysis of two-dimensional plane or three-dimensional axisymmetric incompressible flows including the effects of heat transfer. The governing equations for the above class of problems are the time-dependent incompressible Navier-Stokes equations and the thermal energy equation. The general class of flow problems analysed by CONVEC is discussed and the equations for the initial-boundary value problem are represented. A brief description of the finite element method and the weighted residual formulation is presented. The numerical solution of the incompressible equations is achieved by using a fractional step method. The mass lumping process associated with an explicit time integration scheme is described. The time integration is analysed and the stability conditions are derived. Numerical applications are presented. Standard problems of natural and forced convection are solved and the solutions obtained are compared with other numerical solutions published in the literature

A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains

Science.gov (United States)

Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M.

2012-08-01

We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.

Suitable weak solutions: from compressible viscous to incompressible inviscid fluid flows

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Novotný, A.; Petzeltová, Hana

2013-01-01

Roč. 356, č. 2 (2013), s. 683-702 ISSN 0025-5831 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : relative entropy * incompressible limit * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.201, year: 2013 http://link.springer.com/article/10.1007%2Fs00208-012-0862-5

Numerical Study on Several Stabilized Finite Element Methods for the Steady Incompressible Flow Problem with Damping

Directory of Open Access Journals (Sweden)

Jilian Wu

2013-01-01

Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.

Poroelastic theory of consolidation in unsaturated soils incorporating gravitational body forces

Science.gov (United States)

Lo, Wei-Cheng; Chao, Nan-Chieh; Chen, Chu-Hui; Lee, Jhe-Wei

2017-08-01

The generalization of the poroelasticity theory of consolidation in unsaturated soils to well represent gravitational body forces is presented in the current study. Three partial differential equations featuring the displacement vector of the solid phase, along with the excess pore water and air pressures as dependent variables are derived, with coupling that occurs in the first-order temporal- and spatial- derivative terms. The former arises from viscous drag between solid and fluid, whereas the latter is attributed to the presence of gravity. Given the physically-consistent initial and boundary conditions, these coupled equations are numerically solved under uniaxial strain as a representative example. Our results reveal that variations in the excess pore water pressure due to the existence of gravitational forces increase with soil depth, but these variations are not significant if the soil layer is not sufficiently long. A dimensionless parameter is defined theoretically to quantify the impact of those forces on the final total settlement. This impact is shown to become greater as the soil layer is less stiff and has more length, and bears an inversely-proportional trend with initial water saturation.

Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material.

Science.gov (United States)

Gautier, G; Kelders, L; Groby, J P; Dazel, O; De Ryck, L; Leclaire, P

2011-09-01

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives. © 2011 Acoustical Society of America

Incompressible Navier-Stokes equation from Einstein-Maxwell and Gauss-Bonnet-Maxwell theories

International Nuclear Information System (INIS)

Niu Chao; Tian Yu; Wu Xiaoning; Ling Yi

2012-01-01

The dual fluid description for a general cutoff surface at radius r=r c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε 2 ). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, whose ratio to entropy density η/s is independent of both the cutoff r c and the black brane charge. Then, we extend our discussion to the Gauss-Bonnet-Maxwell case, where the incompressible Navier-Stokes equation with external force density is also obtained at a general cutoff surface. In this case, it turns out that the ratio η/s is independent of the cutoff r c but dependent on the charge density of the black brane.

Structure-Preserving Variational Multiscale Modeling of Turbulent Incompressible Flow with Subgrid Vortices

Science.gov (United States)

Evans, John; Coley, Christopher; Aronson, Ryan; Nelson, Corey

2017-11-01

In this talk, a large eddy simulation methodology for turbulent incompressible flow will be presented which combines the best features of divergence-conforming discretizations and the residual-based variational multiscale approach to large eddy simulation. In this method, the resolved motion is represented using a divergence-conforming discretization, that is, a discretization that preserves the incompressibility constraint in a pointwise manner, and the unresolved fluid motion is explicitly modeled by subgrid vortices that lie within individual grid cells. The evolution of the subgrid vortices is governed by dynamical model equations driven by the residual of the resolved motion. Consequently, the subgrid vortices appropriately vanish for laminar flow and fully resolved turbulent flow. As the resolved velocity field and subgrid vortices are both divergence-free, the methodology conserves mass in a pointwise sense and admits discrete balance laws for energy, enstrophy, and helicity. Numerical results demonstrate the methodology yields improved results versus state-of-the-art eddy viscosity models in the context of transitional, wall-bounded, and rotational flow when a divergence-conforming B-spline discretization is utilized to represent the resolved motion.

Mathematical aspects of finite element methods for incompressible viscous flows

Science.gov (United States)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Dissipation of Alfven waves in compressible inhomogeneous media

International Nuclear Information System (INIS)

Malara, F.; Primavera, L.; Veltri, P.

1997-01-01

In weakly dissipative media governed by the magnetohydrodynamics (MHD) equations, any efficient mechanism of energy dissipation requires the formation of small scales. Using numerical simulations, we study the properties of Alfven waves propagating in a compressible inhomogeneous medium, with an inhomogeneity transverse to the direction of wave propagation. Two dynamical effects, energy pinching and phase mixing, are responsible for the small-scales formation, similarly to the incompressible case. Moreover, compressive perturbations, slow waves and a static entropy wave are generated; the former are subject to steepening and form shock waves, which efficiently dissipate their energy, regardless of the Reynolds number. Rough estimates show that the dissipation times are consistent with those required to dissipate Alfven waves of photospheric origin inside the solar corona

Taylor Instability of Incompressible Liquids

Science.gov (United States)

Fermi, E.; von Neumann, J.

1955-11-01

A discussion is presented in simplified form of the problem of the growth of an initial ripple on the surface of an incompressible liquid in the presence of an acceleration, g, directed from the outside into the liquid. The model is that of a heavy liquid occupying at t = 0 the half space above the plane z = 0, and a rectangular wave profile is assumed. The theory is found to represent correctly one feature of experimental results, namely the fact that the half wave of the heavy liquid into the vacuum becomes rapidly narrower while the half wave pushing into the heavy liquid becomes more and more blunt. The theory fails to account for the experimental results according to which the front of the wave pushing into the heavy liquid moves with constant velocity. The case of instability at the boundary of 2 fluids of different densities is also explored. Similar results are obtained except that the acceleration of the heavy liquid into the light liquid is reduced.

Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers. M.S. Thesis

Science.gov (United States)

Berry, S. A.

1986-01-01

An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.

High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

Science.gov (United States)

Li, Weidong

2017-09-01

This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

Boundary treatment for fourth-order staggered mesh discretizations of the incompressible Navier-Stokes equations

NARCIS (Netherlands)

Sanderse, B.; Verstappen, R.W.C.P.; Koren, B.

2014-01-01

A discretization method for the incompressible Navier–Stokes equations conserving the secondary quantities kinetic energy and vorticity was introduced, besides the primary quantities mass and momentum. This method was extended to fourth order accuracy. In this paper we propose a new consistent

Solutions to three-dimensional Navier-Stokes equations for incompressible fluids

Directory of Open Access Journals (Sweden)

Jorma Jormakka

2010-07-01

Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.

Poroelastic Parameters of Peru Margin Sediments: Implications for Flow and Transport at Multiple Scales in the Marine Biosphere

Science.gov (United States)

Gettemy, G. L.; Cikoski, C.; Tobin, H. J.

2004-12-01

As part of a broader investigation of the deep marine subsurface environment, the first biosphere-focused drilling expedition, Leg 201, of the Ocean Drilling Program (ODP) occupied five unique sites in the Peru Margin (in a 1200 km2 region centered at 10 S, 80E). These sites represent the entire range of shallow biogeological conditions associated with this convergent margin:deep-water, mixed clay-pelagic sediments ocean-ward of the trench; slope-apron and prism toe sediments at the deformation front; and several distinct lithostratigraphic sequences on the continental shelf. Microbial enumeration and pore-water geochemistry results show that each particular site is both consistent and unique--consistent in terms of general biotic quantity and activity as predicted by energy flux and redox potential given the depositional environment and sedimentary record, but unique at key biogeological boundaries such as lithologic and/or physical property interfaces. This research addresses questions related to our understanding of how and why these boundaries form by looking at poroelastic and hydrologic parameters measured at multiple scales, from sub-millimeter to several centimeters. The issue of measurement scale, especially in regard to permeability and diffusivity characterization, is vital to interpreting observations of biologically-mediated diagenetic fronts (e.g., dolomitic lenses, depth- or time-varying barite fronts). These parameters are derived from (i) hydrologic and wave propagation experiments, (ii) SEM images, and (iii) shipboard split-core measurements, and structured in a modified Biot poroelasticity framework. This approach also allows quantification of the local heterogeneity of these parameters at the scale applicable to (and controlled by) microbial life; these results can then be used to formulate predictive models of the impact of biogeochemical processes. Ultimately, these models could then be used in interpretation of new remote-sensed data (e

Mathematical models of incompressible fluids as singular limits of complete fluid systems

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2010-01-01

Roč. 78, č. 2 (2010), s. 523-560 ISSN 1424-9286 R&D Projects: GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : scale analysis * Navier-Stokes-Fourier system * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 0.933, year: 2010 http://link.springer.com/article/10.1007%2Fs00032-010-0128-1

Introduction to porous media micro-mechanics; Introduction a la micromecanique des milieux poreux

Energy Technology Data Exchange (ETDEWEB)

Dormieux, L.; Bourgeois, E.

2002-07-01

The study of porous materials can be considered at two different scales: the microscopic scale characterized by the size of the pores and by the domains occupied by the solid and the fluids, and the macroscopic scale which is controlled by the size of the structures under study (backfilling, foundations, dams, oil reservoirs or sedimentary basins). An alternative way, explored since about 30 years, consists in searching the formulation of macroscopic laws in the framework of a scale change approach. This is the point of view considered in this book which proposes a micro-mechanical approach of the modeling of porous environments based on various techniques of homogenization of the heterogenous materials with a random or periodical microstructure: 1 - macroscopic description of porous environments (space scales, skeleton deformation and kinematics, kinematics of fluid components, conservation laws, internal stresses); 2 - scale change techniques (representative elementary volume, averaging operation, application to conservation laws); 3 - Darcy transport (phenomenological approach of the Darcy law, Darcy law interpretation at the microscopic scale, fluid and solid phases interaction, flows inside a rigid porous environment, application); 4 - diffusive transport of a fluid component (solute transport equation, modeling of the macroscopic diffusive flux by scale change, application to pollutant diffusion); 5 - linear poro-elastic behaviour (first approach: empty sphere model, generalisation, estimation of poro-elastic characteristics); 6 - evolution problems in poro-elasticity (problem formulation, resolution, study of poro-elastic consolidation, tide response of an underwater massif, modeling of the formation of a syncline, study of the folding back of a sheet, numerical resolution of coupled problems, realization of a Scilab script); 7 - conclusion. (J.S.)

Viscous potential flow analysis of magnetohydrodynamic interfacial stability through porous media

International Nuclear Information System (INIS)

Obied Allah, M.H.

2013-01-01

In the view of viscous potential flow theory, the hydromagnetic stability of the interface between two infinitely conducting, incompressible plasmas, streaming parallel to the interface and subjected to a constant magnetic field parallel to the streaming direction will be considered. The plasmas are flowing through porous media between two rigid planes and surface tension is taken into account. A general dispersion relation is obtained analytically and solved numerically. For Kelvin-Helmholtz instability problem, the stability criterion is given by a critical value of the relative velocity. On the other hand, a comparison between inviscid and viscous potential flow solutions has been made and it has noticed that viscosity plays a dual role, destabilizing for Rayleigh-Taylor problem and stabilizing for Kelvin-Helmholtz. For Rayleigh-Taylor instability, a new dispersion relation has been obtained in terms of a critical wave number. It has been found that magnetic field, surface tension, and rigid planes have stabilizing effects, whereas critical wave number and porous media have destabilizing effects. (author)

Edge instability in incompressible planar active fluids

Science.gov (United States)

Nesbitt, David; Pruessner, Gunnar; Lee, Chiu Fan

2017-12-01

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014), 10.1140/epjst/e2014-02189-7], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.

An effective dead oil model for two-phase flow in inhomogeneous porous media

International Nuclear Information System (INIS)

Bourgeat, A.

1988-01-01

The authors are investigating displacement process of incompressible two phase flow miscible or immiscible in heterogeneous porous media, including capillary and gravity effects. The authors' aim is to derive rigorously a Global or Effective Model which then allow, in Numerical Simulations, to disconnect the numerical mesh size from the heterogeneities size inside the reservoir itself. The reservoir is assumed to be made of uniformly (or non uniformly) periodically repeated cells. Each cell being made with different types of porous media. Then, calling ε the ratio of the cell size to the Reservoir size, we get equations depending on the parameter ε because the Porosity and Permeabilities, say Phi/sup ε/ and Κ/sup ε/ are themselves rapidly oscillating. From these ε-parametrized equations the authors derive simpler ''Effective Equations'' no more dependant on ε, called ''Homongenized Equations by the mathematical technique of Homogenization. In these new equations, which are describing Global Displacement process throughout a Globally Equivallent homogenous media where now //Phi and Κ are no more depending on the space variable or ε

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures

International Nuclear Information System (INIS)

Yamasaki, K; Iwayama, T; Yajima, T

2011-01-01

The Okubo-Weiss field, frequently used for partitioning incompressible two-dimensional (2D) fluids into coherent and incoherent regions, corresponds to the Gaussian curvature of the stream function. Therefore, we consider the differential geometric structures of stream functions and calculate the Gaussian curvatures of some basic flows. We find the following. (I) The vorticity corresponds to the mean curvature of the stream function. Thus, the stream-function surface for an irrotational flow and that for a parallel shear flow correspond to the minimal surface and a developable surface, respectively. (II) The relationship between the coherency and the magnitude of the vorticity is interpreted by the curvatures. (III) Using the Gaussian curvature, stability of single and double point vortex streets is analyzed. The results of this analysis are compared with the well-known linear stability analysis. (IV) Conformal mapping in fluid mechanics is the physical expression of the geometric fact that the sign of the Gaussian curvature does not change in conformal mapping. These findings suggest that the curvatures of stream functions are useful for understanding the geometric structure of an incompressible 2D flow.

Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS Instability

Energy Technology Data Exchange (ETDEWEB)

Belyaev, Mikhail A., E-mail: mbelyaev@berkeley.edu [Astronomy Department, University of California, Berkeley, CA 94720 (United States)

2017-02-01

We present an instability for exciting incompressible modes (e.g., gravity or Rossby modes) at the surface of a star accreting through a boundary layer. The instability excites a stellar mode by sourcing an acoustic wave in the disk at the boundary layer, which carries a flux of energy and angular momentum with the opposite sign as the energy and angular momentum density of the stellar mode. We call this instability the acoustic Chandrasekhar–Friedman–Schutz (CFS) instability, because of the direct analogy to the CFS instability for exciting modes on a rotating star by emission of energy in the form of gravitational waves. However, the acoustic CFS instability differs from its gravitational wave counterpart in that the fluid medium in which the acoustic wave propagates (i.e., the accretion disk) typically rotates faster than the star in which the incompressible mode is sourced. For this reason, the instability can operate even for a non-rotating star in the presence of an accretion disk. We discuss applications of our results to high-frequency quasi-periodic oscillations in accreting black hole and neutron star systems and dwarf nova oscillations in cataclysmic variables.

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Science.gov (United States)

Lavery, N.; Taylor, C.

1999-07-01

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

Birds, magnets, soap, and sandblasting: surprising connections in the theory of incompressible flocks

Science.gov (United States)

Toner, John

In this talk I'll describe the hydrodynamic theory of the motion of incompressible flocks: that is, collections of self-propelled entities (birds\\x9D) that are packed so tightly together that their density cannot change as they move. In two dimensions, this problem can be mapped onto an equilibrium magnet with a peculiar constraint. This problem, in turn, can be shown to be equivalent to a 2d smectic (soap\\x9D), with the flow lines of the flock playing the role of the smectic layers. Finally, this smectic problem can be mapped onto the 1+1 dimensional KPZ equation, which describes the growth or corrosion (sandblasting\\x9D) of a one dimensional interface. The scaling properties of this last system, which have been known exactly for a long time, can thereby be used to determine those of incompressible 2d flocks. One important implication of the resulting scaling laws is that such flocks can exhibit long-ranged order in two dimensions, unlike their equilibrium counterparts.

Discrete-fracture-model of multi–scale time-splitting two–phase flow including nanoparticles transport in fractured porous media

KAUST Repository

El-Amin, Mohamed

2017-11-23

In this article, we consider a two-phase immiscible incompressible flow including nanoparticles transport in fractured heterogeneous porous media. The system of the governing equations consists of water saturation, Darcy’s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat, as well as, porosity and permeability variation due to the nanoparticles deposition/entrapment on/in the pores. The discrete-fracture model (DFM) is used to describe the flow and transport in fractured porous media. Moreover, multiscale time-splitting strategy has been employed to manage different time-step sizes for different physics, such as saturation, concentration, etc. Numerical examples are provided to demonstrate the efficiency of the proposed multi-scale time splitting approach.

Discrete-fracture-model of multi–scale time-splitting two–phase flow including nanoparticles transport in fractured porous media

KAUST Repository

El-Amin, Mohamed; Kou, Jisheng; Sun, Shuyu

2017-01-01

In this article, we consider a two-phase immiscible incompressible flow including nanoparticles transport in fractured heterogeneous porous media. The system of the governing equations consists of water saturation, Darcy’s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat, as well as, porosity and permeability variation due to the nanoparticles deposition/entrapment on/in the pores. The discrete-fracture model (DFM) is used to describe the flow and transport in fractured porous media. Moreover, multiscale time-splitting strategy has been employed to manage different time-step sizes for different physics, such as saturation, concentration, etc. Numerical examples are provided to demonstrate the efficiency of the proposed multi-scale time splitting approach.

The direct and inverse problems of an air-saturated poroelastic cylinder submitted to acoustic radiation

Directory of Open Access Journals (Sweden)

Erick Ogam

2011-09-01

Full Text Available A wave-fluid saturated poroelastic structure interaction model based on the modified Biot theory (MBT and plane-wave decomposition using orthogonal cylindrical functions is developed. The model is employed to recover from real data acquired in an anechoic chamber, the poromechanical properties of a soft cellular melamine cylinder submitted to an audible acoustic radiation. The inverse problem of acoustic diffraction is solved by constructing the objective functional given by the total square of the difference between predictions from the MBT interaction model and diffracted field data from experiment. The faculty of retrieval of the intrinsic poromechanical parameters from the diffracted acoustic fields, indicate that a wave initially propagating in a light fluid (air medium, is able to carry in the absence of mechanical excitation of the specimen, information on the macroscopic mechanical properties which depend on the microstructural and intrinsic properties of the solid phase.

A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

DEFF Research Database (Denmark)

Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri

Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...

A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

DEFF Research Database (Denmark)

Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri

2014-01-01

Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...

Pointwise decay of stationary rotational viscous incompressible flows with nonzero velocity at infinity

Czech Academy of Sciences Publication Activity Database

Deuring, P.; Kračmar, S.; Nečasová, Šárka

2013-01-01

Roč. 255, č. 7 (2013), s. 1576-1606 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : stationary incompressible Navier-Stokes system * rotating body * fundamental solution Subject RIV: BA - General Mathematics Impact factor: 1.570, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022039613002106

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

2009-01-01

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

Science.gov (United States)

Liska, Sebastian; Colonius, Tim

2017-02-01

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

Helically symmetric equilibria with pressure anisotropy and incompressible plasma flow

Science.gov (United States)

Evangelias, A.; Kuiroukidis, A.; Throumoulopoulos, G. N.

2018-02-01

We derive a generalized Grad-Shafranov equation governing helically symmetric equilibria with pressure anisotropy and incompressible flow of arbitrary direction. Through the most general linearizing ansatz for the various free surface functions involved therein, we construct equilibrium solutions and study their properties. It turns out that pressure anisotropy can act either paramegnetically or diamagnetically, the parallel flow has a paramagnetic effect, while the non-parallel component of the flow associated with the electric field has a diamagnetic one. Also, pressure anisotropy and flow affect noticeably the helical current density.

Two compressible and immiscible flow in porous media: mathematical and numerical analysis

International Nuclear Information System (INIS)

Khalil, Z.

2010-01-01

The aim of this thesis is the study of Cauchy problem (existence of weak solutions) for three degenerate highly coupled parabolic systems modeling compressible immiscible flow in porous media. The motivation of this work is a benchmark of the GNR MoMaS, to study the impact of the gas flow due to the corrosion of ferrous materials in a radioactive waste storage site. This thesis is divided into three independent chapters. Firstly, we look at a problem modeling the flow of two immiscible phases and considering one phase is compressible and the other is incompressible (water/gas). Secondly, we consider the problem modeling two-compressible immiscible flow in porous media. An existence results for both problems established by a semi-discretization method. Finally, The fourth chapter is devoted to the construction and convergence of a multi-dimensional finite volume method (upwind scheme) for the gas-water model under the assumption that the gas density is a function of a global pressure. (author)

Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids

Science.gov (United States)

Ha, Seung-Yeal; Xiao, Qinghua; Zhang, Xiongtao

2018-04-01

We study the dynamics of infinitely many Cucker-Smale (C-S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier-Stokes (N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd (d = 2 , 3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2 : =R2 /Z2, we show that the velocities of C-S particles and fluids are asymptotically aligned to two constant velocities which may be different.

Formal solution of the Navier-Stokes initial- and boundary-value problem for incompressible fluids

International Nuclear Information System (INIS)

Alankus, T.

1984-01-01

A general formal solution of the integral equivalent of Navier-Stokes equation for incompressible viscous fluids is presented through a linear operator acting on the functionals of solenoidal vector fields. This solution operator is completely determined by the Green functions of Laplace and diffusion equations corresponding to the flow region

INCOMPRESSIBLE LAMINAR BOUNDARY LAYER CONTROL BY BLOWING AND SUCTION

Directory of Open Access Journals (Sweden)

AZZEDINE NAHOUI

2013-12-01

Full Text Available A two-dimensional incompressible laminar boundary layer and its control using blowing and suction over a flat plate and around the NACA 0012 and 661012 profiles, is studied numerically. The study is based on the Prandtl boundary layer model using the finite differences method and the Crank-Nicolson scheme. The velocity distribution, the boundary layer thickness and the friction coefficient, are determined and presented with and without control. The application of the control technique, has demonstrated its positive effect on the transition point and the friction coefficient. Both control procedures are compared for different lengths, speeds and angles of blowing and suction.

A method of fundamental solutions in poroelasticity to model the stress field in geothermal reservoirs

CERN Document Server

Augustin, Matthias Albert

2015-01-01

This monograph focuses on the numerical methods needed in the context of developing a reliable simulation tool to promote the use of renewable energy. One very promising source of energy is the heat stored in the Earth’s crust, which is harnessed by so-called geothermal facilities. Scientists from fields like geology, geo-engineering, geophysics and especially geomathematics are called upon to help make geothermics a reliable and safe energy production method. One of the challenges they face involves modeling the mechanical stresses at work in a reservoir. The aim of this thesis is to develop a numerical solution scheme by means of which the fluid pressure and rock stresses in a geothermal reservoir can be determined prior to well drilling and during production. For this purpose, the method should (i) include poroelastic effects, (ii) provide a means of including thermoelastic effects, (iii) be inexpensive in terms of memory and computational power, and (iv) be flexible with regard to the locations of data ...

Incompressible Turbulent Flow Simulation Using the κ-ɛ Model and Upwind Schemes

Directory of Open Access Journals (Sweden)

V. G. Ferreira

2007-01-01

Full Text Available In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds κ-ɛ model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005 is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994 methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000. A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

A discontinuous Galerkin finite element discretization of the Euler equations for compressible and incompressible fluids

NARCIS (Netherlands)

Pesch, L.; van der Vegt, Jacobus J.W.

2008-01-01

Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The

Development of Multigrid Methods for diffusion, Advection, and the incompressible Navier-Stokes Equations

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.

Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

Czech Academy of Sciences Publication Activity Database

Šístek, Jakub; Cirak, F.

2015-01-01

Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace methods Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045793015003023

Multimode Coupling Theory for Kelvin–Helmholtz Instability in Incompressible Fluid

International Nuclear Information System (INIS)

Li-Feng, Wang; Ying-Jun, Li; Wen-Hua, Ye; Zheng-Feng, Fan

2009-01-01

A weakly nonlinear model is proposed for multimode Kelvin–Helmholtz instability. The second-order mode coupling formula for Kelvin–Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not

Étalement d'une goutte stratifiée incompressible

Science.gov (United States)

de Gennes, Pierre-Gilles; Cazabat, Anne-Marie

L'étalement de films ultraminces de liquides simples sur une surface lisse horizontale conduit souvent à des gouttes à gradins d'une épaisseur moléculaire ([1]-[3]). Nous construisons ici un modèle pour la dynamique de l'étalement, en supposant que : (a) chaque gradin est un liquide bidimensionnel incompressible; (b) les molécules de la n-ième couche sont soumises à un potentiel (Wn) qui exprime leurs interactions à longue portée avec le solide; (c) on a un écoulement parallèle de cisaillement, et un écoulement normal de perméation. La perméation intervient seulement dans un certain « ruban » de largeur ξ sur le bord de chaque gradin. Dans le cas usuel, où le rayon du n-ième gradin Rn est trs supérieur à ξ, la dissipation est dominée par le cisaillement, et on arrive à des lois simples pour la vitesse de dilatation (ou de contraction) dotR_n. Very thin films of simple liquids often spread with well defined steps of molecular thickness ([1]-[3]). We construct a model for the dynamics of spreading assuming that: (a) each layer is an incompressible, 2 dimensional fluid; (b) the molecules in the (nth) layer experience a long range potential (e.g. Van der Waals) from the solid; (c) two types of flow occur: shear between layers and permeation normal to the layers. We find that permeation is important only in an annulus of small size ξ near each step. Between steps, the viscous effects in simple shear dominate, and this leads to simple laws for the dilation (or contraction) of the various layers.

Finite element modelling of radial lentotomy cuts to improve the accommodation performance of the human lens.

Science.gov (United States)

Burd, H J; Wilde, G S

2016-04-01

The use of a femtosecond laser to form planes of cavitation bubbles within the ocular lens has been proposed as a potential treatment for presbyopia. The intended purpose of these planes of cavitation bubbles (referred to in this paper as 'cutting planes') is to increase the compliance of the lens, with a consequential increase in the amplitude of accommodation. The current paper describes a computational modelling study, based on three-dimensional finite element analysis, to investigate the relationship between the geometric arrangement of the cutting planes and the resulting improvement in lens accommodation performance. The study is limited to radial cutting planes. The effectiveness of a variety of cutting plane geometries was investigated by means of modelling studies conducted on a 45-year human lens. The results obtained from the analyses depend on the particular modelling procedures that are employed. When the lens substance is modelled as an incompressible material, radial cutting planes are found to be ineffective. However, when a poroelastic model is employed for the lens substance, radial cuts are shown to cause an increase in the computed accommodation performance of the lens. In this case, radial cuts made in the peripheral regions of the lens have a relatively small influence on the accommodation performance of the lens; the lentotomy process is seen to be more effective when cuts are made near to the polar axis. When the lens substance is modelled as a poroelastic material, the computational results suggest that useful improvements in lens accommodation performance can be achieved, provided that the radial cuts are extended to the polar axis. Radial cuts are ineffective when the lens substance is modelled as an incompressible material. Significant challenges remain in developing a safe and effective surgical procedure based on this lentotomy technique.

Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities

Science.gov (United States)

Li, Yinghua; Huang, Mingxia

2018-06-01

In this paper, we investigate a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain Ω \\subset R^N(N=2,3). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function ρ _0 has a positive lower bound.

Parallel iterative solution of the incompressible Navier-Stokes equations with application to rotating wings

Czech Academy of Sciences Publication Activity Database

Šístek, Jakub; Cirak, F.

2015-01-01

Roč. 122, 20 November (2015), s. 165-183 ISSN 0045-7930 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : Navier-Stokes * incompressible flow * Krylov subspace method s Subject RIV: BA - General Mathematics Impact factor: 1.891, year: 2015 http://www. science direct.com/ science /article/pii/S0045793015003023

Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

Science.gov (United States)

Pradipto; Purqon, Acep

2017-07-01

Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.

Boundary layers and the vanishing viscosity limit for incompressible 2D flow

OpenAIRE

Filho, Milton C. Lopes

2007-01-01

This manuscript is a survey on results related to boundary layers and the vanishing viscosity limit for incompressible flow. It is the lecture notes for a 10 hour minicourse given at the Morningside Center, Academia Sinica, Beijing, PRC from 11/28 to 12/07, 2007. The main topics covered are: a derivation of Prandtl's boundary layer equation; an outline of the rigorous theory of Prandtl's equation, without proofs; Kato's criterion for the vanishing viscosity limit; the vanishing viscosity limi...

Projection methods for the calculation of incompressible or dilatable flows; Methodes de projection pour le calcul d'ecoulements incompressibles ou dilatables

Energy Technology Data Exchange (ETDEWEB)

Jobelin, M

2006-10-15

This thesis treats of time resolution methods for the Navier-Stokes equations. Based on the well-known projection method of Chorin and Temam, an original pressure correction method, named 'projection-penalty' is developed. Its specificity concerns the addition of a penalty term in the prediction step, which constrains the predicted velocity to fit with the mass balance. The precision improvements added by this method are demonstrated by some analysis results and by some numerical experiments of incompressible or dilatable flows. Finally, the potentialities offered by the use of the joint finite elements method in this type of fractionary step scheme is studied. Two applications are presented, one for local refinement purpose, the other for the resolution of a multi-physics problem. (J.S.)

Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

KAUST Repository

Chen, Huangxin; Sun, Shuyu; Zhang, Tao

2017-01-01

In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i

Error estimation and adaptivity for incompressible hyperelasticity

KAUST Repository

Whiteley, J.P.

2014-04-30

SUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined linearised dual problems with appropriate boundary conditions, a posteriori error estimates are then derived for both linear functionals of the solution and linear functionals of the stress on a boundary, where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution, where the entries of the strain tensor exhibit large, rapid variations, demonstrates the accuracy and sharpness of the error estimators. Finally, using a selection of model problems, the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. © 2014 John Wiley & Sons, Ltd.

Incompressible SPH (ISPH) with fast Poisson solver on a GPU

Science.gov (United States)

Chow, Alex D.; Rogers, Benedict D.; Lind, Steven J.; Stansby, Peter K.

2018-05-01

This paper presents a fast incompressible SPH (ISPH) solver implemented to run entirely on a graphics processing unit (GPU) capable of simulating several millions of particles in three dimensions on a single GPU. The ISPH algorithm is implemented by converting the highly optimised open-source weakly-compressible SPH (WCSPH) code DualSPHysics to run ISPH on the GPU, combining it with the open-source linear algebra library ViennaCL for fast solutions of the pressure Poisson equation (PPE). Several challenges are addressed with this research: constructing a PPE matrix every timestep on the GPU for moving particles, optimising the limited GPU memory, and exploiting fast matrix solvers. The ISPH pressure projection algorithm is implemented as 4 separate stages, each with a particle sweep, including an algorithm for the population of the PPE matrix suitable for the GPU, and mixed precision storage methods. An accurate and robust ISPH boundary condition ideal for parallel processing is also established by adapting an existing WCSPH boundary condition for ISPH. A variety of validation cases are presented: an impulsively started plate, incompressible flow around a moving square in a box, and dambreaks (2-D and 3-D) which demonstrate the accuracy, flexibility, and speed of the methodology. Fragmentation of the free surface is shown to influence the performance of matrix preconditioners and therefore the PPE matrix solution time. The Jacobi preconditioner demonstrates robustness and reliability in the presence of fragmented flows. For a dambreak simulation, GPU speed ups demonstrate up to 10-18 times and 1.1-4.5 times compared to single-threaded and 16-threaded CPU run times respectively.

Numerical solution of compressible and incompressible unsteady flows in channel inspired by vocal tract

Czech Academy of Sciences Publication Activity Database

Pořízková, P.; Kozel, Karel; Horáček, Jaromír

2014-01-01

Roč. 270, November (2014), s. 323-329 ISSN 0377-0427 R&D Projects: GA ČR(CZ) GAP101/11/0207; GA ČR(CZ) GAP101/10/1329 Institutional support: RVO:61388998 Keywords : compressible * incompressible * unsteady * CFD * acoustic * vocal tract Subject RIV: BI - Acoustics Impact factor: 1.266, year: 2014 http://www.sciencedirect.com/science/article/pii/S0377042713007188#

Mechanics of adsorption-deformation coupling in porous media

Science.gov (United States)

Zhang, Yida

2018-05-01

This work extends Coussy's macroscale theory for porous materials interacting with adsorptive fluid mixtures. The solid-fluid interface is treated as an independent phase that obeys its own mass, momentum and energy balance laws. As a result, a surface strain energy term appears in the free energy balance equation of the solid phase, which further introduces the so-called adsorption stress in the constitutive equations of the porous skeleton. This establishes a fundamental link between the adsorption characteristics of the solid-fluid interface and the mechanical response of the porous media. The thermodynamic framework is quite general in that it recovers the coupled conduction laws, Gibbs isotherm and the Shuttleworth's equation for surface stress, and imposes no constraints on the magnitude of deformation and the functional form of the adsorption isotherms. A rich variety of coupling between adsorption and deformation is recovered as a result of combining different poroelastic models (isotropic vs. anisotropic, linear vs. nonlinear) and adsorption models (unary vs. mixture adsorption, uncoupled vs. stretch-dependent adsorption). These predictions are discussed against the backdrop of recent experimental data on coal swelling subjected to CO2 and CO2sbnd CH4 injections, showing the capability and versatility of the theory in capturing adsorption-induced deformation of porous materials.

An energy-stable method for solving the incompressible Navier-Stokes equations with non-slip boundary condition

Science.gov (United States)

Lee, Byungjoon; Min, Chohong

2018-05-01

We introduce a stable method for solving the incompressible Navier-Stokes equations with variable density and viscosity. Our method is stable in the sense that it does not increase the total energy of dynamics that is the sum of kinetic energy and potential energy. Instead of velocity, a new state variable is taken so that the kinetic energy is formulated by the L2 norm of the new variable. Navier-Stokes equations are rephrased with respect to the new variable, and a stable time discretization for the rephrased equations is presented. Taking into consideration the incompressibility in the Marker-And-Cell (MAC) grid, we present a modified Lax-Friedrich method that is L2 stable. Utilizing the discrete integration-by-parts in MAC grid and the modified Lax-Friedrich method, the time discretization is fully discretized. An explicit CFL condition for the stability of the full discretization is given and mathematically proved.

A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements

KAUST Repository

Duddu, Ravindra

2011-10-05

We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.

Dissipative solutions and the incompressible inviscid limits of the compressible magnetohydrodynamic system in unbounded domains

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard; Novotný, A.; Sun, Y.

2014-01-01

Roč. 34, č. 1 (2014), s. 121-143 ISSN 1078-0947 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : compressible MHD system * inviscid limit * incompressible limit Subject RIV: BA - General Mathematics Impact factor: 0.826, year: 2014 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=8717

Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

KAUST Repository

Zhu, Guangpu

2018-04-17

In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

KAUST Repository

Zhu, Guangpu; Kou, Jisheng; Sun, Shuyu; Yao, Jun; Li, Aifen

2018-01-01

In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

Diffusion in Poiseuille and Couette flows of binary mixtures of incompressible newtonian fluids

International Nuclear Information System (INIS)

Caetano Filho, E.; Qassim, R.Y.

1981-07-01

Using the continuum theory of binary mixtures of incompressible Newtonian fluids, Poiseuille and Couette flows are studied with a view to determining whether diffusion occurs in such flows. It is shown that diffusion is absent in the Couette case. However, in Poiseuille flow there are significant differences between the velocities of the species comprising the mixture. This result is in broad agreement with that of Mills for similar mixtures of nonuniform composition. (Author) [pt

Determination of the nuclear incompressibility from the rapidity-dependent elliptic flow in heavy-ion collisions at beam energies 0.4A–1.0A GeV

Directory of Open Access Journals (Sweden)

Yongjia Wang

2018-03-01

Full Text Available Background: The nuclear incompressibility (K0 plays a crucial role in understanding diverse phenomena in nuclear structure and reactions, as well as in astrophysics. Heavy-ion-collision measurements in combination with transport model simulations serve as important tools for extracting the nuclear incompressibility. However, uncertainties in transport models (or model dependence partly affect the reliability of the extracted result. Purpose: In the present work, by using the recently measured data of rapidity-dependent flows, we constrain the incompressibility of nuclear matter and analyze the impact of model uncertainties on the obtained value. Method: The method is based on the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD model in which the Skyrme potential energy-density functional is introduced. Three different Skyrme interactions which give different incompressibilities varying from K0=201 to 271 MeV are adopted. The incompressibility is deduced from the comparison of the UrQMD model simulations and the FOPI data for rapidity-dependent elliptic flow in Au+Au collisions at beam energies 0.4A–1.0A GeV. Results: The elliptic flow v2 as a function of rapidity y0 can be well described by a quadratic fit v2=v20+v22⋅y02. It is found that the quantity v2n defined by v2n=|v20|+|v22| is quite sensitive to the incompressibility K0 and the in-medium nucleon–nucleon cross section, but not sensitive to the slope parameter L of the nuclear symmetry energy. Conclusions: With the FU3FP4 parametrization of the in-medium nucleon–nucleon cross section, an averaged K0=220±40 MeV is extracted from the v2n of free protons and deuterons. However, remaining systematic uncertainties, partly related to the choice of in-medium nucleon–nucleon cross sections, are of the same magnitude (±40 MeV. Overall, the rapidity dependent elliptic flow supports a soft symmetric-matter equation-of-state.

Determination of the nuclear incompressibility from the rapidity-dependent elliptic flow in heavy-ion collisions at beam energies 0.4A-1.0A GeV

Science.gov (United States)

Wang, Yongjia; Guo, Chenchen; Li, Qingfeng; Le Fèvre, Arnaud; Leifels, Yvonne; Trautmann, Wolfgang

2018-03-01

Background: The nuclear incompressibility (K0) plays a crucial role in understanding diverse phenomena in nuclear structure and reactions, as well as in astrophysics. Heavy-ion-collision measurements in combination with transport model simulations serve as important tools for extracting the nuclear incompressibility. However, uncertainties in transport models (or model dependence) partly affect the reliability of the extracted result. Purpose: In the present work, by using the recently measured data of rapidity-dependent flows, we constrain the incompressibility of nuclear matter and analyze the impact of model uncertainties on the obtained value. Method: The method is based on the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model in which the Skyrme potential energy-density functional is introduced. Three different Skyrme interactions which give different incompressibilities varying from K0 = 201 to 271 MeV are adopted. The incompressibility is deduced from the comparison of the UrQMD model simulations and the FOPI data for rapidity-dependent elliptic flow in Au + Au collisions at beam energies 0.4A-1.0A GeV. Results: The elliptic flow v2 as a function of rapidity y0 can be well described by a quadratic fit v2 =v20 +v22 ṡ y02 . It is found that the quantity v2n defined by v2n = |v20 | + |v22 | is quite sensitive to the incompressibility K0 and the in-medium nucleon-nucleon cross section, but not sensitive to the slope parameter L of the nuclear symmetry energy. Conclusions: With the FU3FP4 parametrization of the in-medium nucleon-nucleon cross section, an averaged K0 = 220 ± 40 MeV is extracted from the v2n of free protons and deuterons. However, remaining systematic uncertainties, partly related to the choice of in-medium nucleon-nucleon cross sections, are of the same magnitude (± 40 MeV). Overall, the rapidity dependent elliptic flow supports a soft symmetric-matter equation-of-state.

Attenuation of surface waves in porous media: Shock wave experiments and modelling

NARCIS (Netherlands)

Chao, G.E; Smeulders, D.M.J.; Dongen, van M.E.H.

2005-01-01

In this project we conduct experimental and numerical investigations on the attenuation mechanisms of surface waves in poroelastic materials. Viscous dissipation effects are modelled in the framework of Biot's theory. The experiments are performed using a shock tube technique. Quantitative agreement

Local lubrication model for spherical particles within incompressible Navier-Stokes flows

Science.gov (United States)

Lambert, B.; Weynans, L.; Bergmann, M.

2018-03-01

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

Incompressible Steady Flow with Tensor Conductivity Leaving a Transverse Magnetic Field

International Nuclear Information System (INIS)

Witalis, E.A.

1965-12-01

The straight channel flow of an inviscid, incompressible fluid with tensor conductivity is considered when the flow leaves a region of constant transverse magnetic field. The channel walls are taken to be insulating, and an eddy current system arises. This is investigated by the method of magnetic field analysis as given by Witalis. The spatial distribution of magnetic field and ohmic power loss, both parallel and transverse to the flow, are given as functions of the Hall parameter with consideration also to the magnetic Reynolds number of the fluid. MHD power generator aspects of this problem and the results are discussed

Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

Science.gov (United States)

Lambert, B; Weynans, L; Bergmann, M

2018-03-01

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

Incompressible Steady Flow with Tensor Conductivity Leaving a Transverse Magnetic Field

Energy Technology Data Exchange (ETDEWEB)

Witalis, E A

1965-12-15

The straight channel flow of an inviscid, incompressible fluid with tensor conductivity is considered when the flow leaves a region of constant transverse magnetic field. The channel walls are taken to be insulating, and an eddy current system arises. This is investigated by the method of magnetic field analysis as given by Witalis. The spatial distribution of magnetic field and ohmic power loss, both parallel and transverse to the flow, are given as functions of the Hall parameter with consideration also to the magnetic Reynolds number of the fluid. MHD power generator aspects of this problem and the results are discussed.

An introduction to linear poroelasticity

OpenAIRE

Merxhani, Andi

2016-01-01

This study is an introduction to the theory of three-dimensional consolidation. The point of departure in the description are the basic equations of elasticity (i.e. constitutive law, equations of equilibrium in terms of stresses, and the definition of strain), together with the principle of effective stress, and the law of Darcy for fluid flow in porous media. These equations, together with the principle of mass conservation, are the only premises used to derive a drained description of cons...

On the spurious pressures generated by certain GFEM solutions of the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Sani, R.L.; Gresho, P.M.; Lee, R.L.

1979-01-01

The spurious pressures and acceptable velocities generated when using certain combinations of velocity and pressure approximations in a Galerkin finite element discretization of the primitive variable form of the incompressible Navier-Stokes equations are analyzed both theoretically and numerically for grids composed of quadrilateral finite elements. Schemes for obtaining usable pressure fields from the spurious numerical results are presented for certain cases

On the global attractor of 2D incompressible turbulence with random forcing

Science.gov (United States)

Emami, Pedram; Bowman, John C.

2018-03-01

This study revisits bounds on the projection of the global attractor in the energy-enstrophy plane for 2D incompressible turbulence [Dascaliuc, Foias, and Jolly, 2005, 2010]. In addition to providing more elegant proofs of some of the required nonlinear identities, the treatment is extended from the case of constant forcing to the more realistic case of random forcing. Numerical simulations in particular often use a stochastic white-noise forcing to achieve a prescribed mean energy injection rate. The analytical bounds are demonstrated numerically for the case of white-noise forcing.

Determination of the mechanical and physical properties of cartilage by coupling poroelastic-based finite element models of indentation with artificial neural networks.

Science.gov (United States)

Arbabi, Vahid; Pouran, Behdad; Campoli, Gianni; Weinans, Harrie; Zadpoor, Amir A

2016-03-21

One of the most widely used techniques to determine the mechanical properties of cartilage is based on indentation tests and interpretation of the obtained force-time or displacement-time data. In the current computational approaches, one needs to simulate the indentation test with finite element models and use an optimization algorithm to estimate the mechanical properties of cartilage. The modeling procedure is cumbersome, and the simulations need to be repeated for every new experiment. For the first time, we propose a method for fast and accurate estimation of the mechanical and physical properties of cartilage as a poroelastic material with the aid of artificial neural networks. In our study, we used finite element models to simulate the indentation for poroelastic materials with wide combinations of mechanical and physical properties. The obtained force-time curves are then divided into three parts: the first two parts of the data is used for training and validation of an artificial neural network, while the third part is used for testing the trained network. The trained neural network receives the force-time curves as the input and provides the properties of cartilage as the output. We observed that the trained network could accurately predict the properties of cartilage within the range of properties for which it was trained. The mechanical and physical properties of cartilage could therefore be estimated very fast, since no additional finite element modeling is required once the neural network is trained. The robustness of the trained artificial neural network in determining the properties of cartilage based on noisy force-time data was assessed by introducing noise to the simulated force-time data. We found that the training procedure could be optimized so as to maximize the robustness of the neural network against noisy force-time data. Copyright © 2016 Elsevier Ltd. All rights reserved.

Indentation of a free-falling lance penetrometer into a poroelastic seabed

Science.gov (United States)

Elsworth, Derek; Lee, Dae Sung

2005-02-01

A solution is developed for the build-up, steady and post-arrest dissipative pore fluid pressure fields that develop around a blunt penetrometer that self-embeds from freefall into the seabed. Arrest from freefall considers deceleration under undrained conditions in a purely cohesive soil, with constant shear strength with depth. The resulting decelerating velocity field is controlled by soil strength, geometric bearing capacity factors, and inertial components. At low impact velocities the embedment process is controlled by soil strength, and at high velocities by inertia. With the deceleration defined, a solution is evaluated for a point normal dislocation penetrating in a poroelastic medium with a prescribed decelerating velocity. Dynamic steady pressures, PD, develop relative to the penetrating tip geometry with their distribution conditioned by the non-dimensional penetration rate, UD, incorporating impacting penetration rate, consolidation coefficient and penetrometer radius, and the non-dimensional strength, ND, additionally incorporating undrained shear strength of the sediment. Pore pressures develop to a steady peak magnitude at the penetrometer tip, and drop as PD=1/xD with distance xD behind the tip and along the shaft. Peak induced pressure magnitudes may be correlated with sediment permeabilities, post-arrest dissipation rates may be correlated with consolidation coefficients, and depths of penetration may be correlated with shear strengths. Together, these records enable strength and transport parameters to be recovered from lance penetrometer data. Penetrometer data recorded off La Palma in the Canary Islands (J. Volcanol. Geotherm. Res. 2000; 101:253) are used to recover permeabilities and consolidation coefficients from peak pressure and dissipation response, respectively. Copyright

Large Eddy Simulation for Incompressible Flows An Introduction

CERN Document Server

Sagaut, P

2005-01-01

The first and most exhaustive work of its kind devoted entirely to the subject, Large Eddy Simulation presents a comprehensive account and a unified view of this young but very rich discipline. LES is the only efficient technique for approaching high Reynolds numbers when simulating industrial, natural or experimental configurations. The author concentrates on incompressible fluids and chooses his topics in treating with care both the mathematical ideas and their applications. The book addresses researchers as well as graduate students and engineers. The second edition was a greatly enriched version motivated both by the increasing theoretical interest in LES and the increasing number of applications. Two entirely new chapters were devoted to the coupling of LES with multiresolution multidomain techniques and to the new hybrid approaches that relate the LES procedures to the classical statistical methods based on the Reynolds-Averaged Navier-Stokes equations. This 3rd edition adds various sections to the text...

Fluidic Vectoring of a Planar Incompressible Jet Flow

Science.gov (United States)

Mendez, Miguel Alfonso; Scelzo, Maria Teresa; Enache, Adriana; Buchlin, Jean-Marie

2018-06-01

This paper presents an experimental, a numerical and a theoretical analysis of the performances of a fluidic vectoring device for controlling the direction of a turbulent, bi-dimensional and low Mach number (incompressible) jet flow. The investigated design is the co-flow secondary injection with Coanda surface, which allows for vectoring angles up to 25° with no need of moving mechanical parts. A simple empirical model of the vectoring process is presented and validated via experimental and numerical data. The experiments consist of flow visualization and image processing for the automatic detection of the jet centerline; the numerical simulations are carried out solving the Unsteady Reynolds Average Navier- Stokes (URANS) closed with the k - ω SST turbulence model, using the PisoFoam solver from OpenFOAM. The experimental validation on three different geometrical configurations has shown that the model is capable of providing a fast and reliable evaluation of the device performance as a function of the operating conditions.

Solving the incompressible surface Navier-Stokes equation by surface finite elements

Science.gov (United States)

Reuther, Sebastian; Voigt, Axel

2018-01-01

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g (S ) . The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincaré-Hopf theorem on n-tori.

Incompressible Navier-Stokes inverse design method based on adaptive unstructured meshes

International Nuclear Information System (INIS)

Rahmati, M.T.; Charlesworth, D.; Zangeneh, M.

2005-01-01

An inverse method for blade design based on Navier-Stokes equations on adaptive unstructured meshes has been developed. In the method, unlike the method based on inviscid equations, the effect of viscosity is directly taken into account. In the method, the pressure (or pressure loading) is prescribed. The design method then computes the blade shape that would accomplish the target prescribed pressure distribution. The method is implemented using a cell-centered finite volume method, which solves the incompressible Navier-Stokes equations on unstructured meshes. An adaptive unstructured mesh method based on grid subdivision and local adaptive mesh method is utilized for increasing the accuracy. (author)

A superlinearly convergent finite volume method for the incompressible Navier-Stokes equations on staggered unstructured grids

International Nuclear Information System (INIS)

Vidovic, D.; Segal, A.; Wesseling, P.

2004-01-01

A method for linear reconstruction of staggered vector fields with special treatment of the divergence is presented. An upwind-biased finite volume scheme for solving the unsteady incompressible Navier-Stokes equations on staggered unstructured triangular grids that uses this reconstruction is described. The scheme is applied to three benchmark problems and is found to be superlinearly convergent in space

Diffusing passive tracers in random incompressible flows: Statistical topography aspects

International Nuclear Information System (INIS)

Klyatskin, V.I.; Woyczynski, W.A.; Gurarie, D.

1996-01-01

The paper studies statistical characteristics of the passive tracer concentrations and of its spatial gradient, in random incompressible velocity fields from the viewpoint of statistical topography. The statistics of interest include mean values, probability distributions, as well as various functionals characterizing topographic features of tracers. The functional approach is used. We consider the influence of the mean flow (the linear shear flow) and the molecular diffusion coefficient on the statistics of the tracer. Most of our analysis is carried out in the framework of the delta-correlated (in time) approximation and conditions for its applicability are established. But we also consider the diffusion approximation scheme for finite correlation radius. The latter is applied to a diffusing passive tracer that undergoes sedimentation in a random velocity field

Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth.

Science.gov (United States)

Ambrosi, D; Pezzuto, S; Riccobelli, D; Stylianopoulos, T; Ciarletta, P

2017-12-01

The experimental evidence that a feedback exists between growth and stress in tumors poses challenging questions. First, the rheological properties (the "constitutive equations") of aggregates of malignant cells are still a matter of debate. Secondly, the feedback law (the "growth law") that relates stress and mitotic-apoptotic rate is far to be identified. We address these questions on the basis of a theoretical analysis of in vitro and in vivo experiments that involve the growth of tumor spheroids. We show that solid tumors exhibit several mechanical features of a poroelastic material, where the cellular component behaves like an elastic solid. When the solid component of the spheroid is loaded at the boundary, the cellular aggregate grows up to an asymptotic volume that depends on the exerted compression. Residual stress shows up when solid tumors are radially cut, highlighting a peculiar tensional pattern. By a novel numerical approach we correlate the measured opening angle and the underlying residual stress in a sphere. The features of the mechanobiological system can be explained in terms of a feedback of mechanics on the cell proliferation rate as modulated by the availability of nutrient, that is radially damped by the balance between diffusion and consumption. The volumetric growth profiles and the pattern of residual stress can be theoretically reproduced assuming a dependence of the target stress on the concentration of nutrient which is specific of the malignant tissue.

An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains

Energy Technology Data Exchange (ETDEWEB)

Patel, Saumil S. [Argonne National Lab. (ANL), Argonne, IL (United States); Fischer, Paul F. [Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of Illinois, Urbana-Champaign, IL (United States); Min, Misun [Argonne National Lab. (ANL), Argonne, IL (United States); Tomboulides, Ananias G [Argonne National Lab. (ANL), Argonne, IL (United States); Aristotle Univ., Thessaloniki (Greece)

2017-10-21

In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.

The flow of an incompressible electroconductive fluid past a thin airfoil. The parabolic profile

Directory of Open Access Journals (Sweden)

Adrian CARABINEANU

2014-04-01

Full Text Available We study the two-dimensional steady flow of an ideal incompressible perfectly conducting fluid past an insulating thin parabolic airfoil. We consider the linearized Euler and Maxwell equations and Ohm's law. We use the integral representations for the velocity, magnetic induction and pressure and the boundary conditions to obtain an integral equation for the jump of the pressure across the airfoil. We give some graphic representations for the lift coefficient, velocity and magnetic induction.

Error Analysis of a Fractional Time-Stepping Technique for Incompressible Flows with Variable Density

KAUST Repository

Guermond, J.-L.; Salgado, Abner J.

2011-01-01

In this paper we analyze the convergence properties of a new fractional time-stepping technique for the solution of the variable density incompressible Navier-Stokes equations. The main feature of this method is that, contrary to other existing algorithms, the pressure is determined by just solving one Poisson equation per time step. First-order error estimates are proved, and stability of a formally second-order variant of the method is established. © 2011 Society for Industrial and Applied Mathematics.

Relation between current sheets and vortex sheets in stationary incompressible MHD

Directory of Open Access Journals (Sweden)

D. H. Nickeler

2012-03-01

Full Text Available Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role in the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between current sheets and vortex sheets in incompressible, stationary equilibria. For this approach it is helpful that the similar mathematical structure of magnetohydrostatics and stationary incompressible hydrodynamics allows us to transform static equilibria into stationary ones. The main control function for such a transformation is the profile of the Alfvén-Mach number MA, which is always constant along magnetic field lines, but can change from one field line to another. In the case of a global constant MA, vortices and electric current concentrations are parallel. More interesting is the nonlinear case, where MA varies perpendicular to the field lines. This is a typical situation at boundary layers like the magnetopause, heliopause, the solar wind flowing around helmet streamers and at the boundary of solar coronal holes. The corresponding current and vortex sheets show in some cases also an alignment, but not in every case. For special density distributions in 2-D, it is possible to have current but no vortex sheets. In 2-D, vortex sheets of field aligned-flows can also exist without strong current sheets, taking the limit of small Alfvén Mach numbers into account. The current sheet can vanish if the Alfvén Mach number is (almost constant and the density gradient is large across some boundary layer. It should be emphasized that the used theory is not only valid for small Alfvén Mach numbers MA MA ≲ 1. Connection to other theoretical approaches and observations and physical effects in space plasmas are presented. Differences in the various aspects of theoretical investigations of current sheets and vortex sheets are given.

The horizontally homogeneous model equations of incompressible atmospheric flow in general orthogonal coordinates

DEFF Research Database (Denmark)

Jørgensen, Bo Hoffmann

2003-01-01

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 overcomplex 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 employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...

Applying the expansion method in hierarchical functions to the solution of Navier-Stokes equations for incompressible fluids

International Nuclear Information System (INIS)

Sabundjian, Gaiane

1999-01-01

This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

Science.gov (United States)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

Finite element methods for viscous incompressible flows a guide to theory, practice, and algorithms

CERN Document Server

Gunzburger, Max D

2012-01-01

In this book, the author examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms.

NACHOS: a finite element computer program for incompressible flow problems. Part I. Theoretical background

International Nuclear Information System (INIS)

Gartling, D.K.

1978-04-01

The theoretical background for the finite element computer program, NACHOS, is presented in detail. The NACHOS code is designed for the two-dimensional analysis of viscous incompressible fluid flows, including the effects of heat transfer. A general description of the fluid/thermal boundary value problems treated by the program is described. The finite element method and the associated numerical methods used in the NACHOS code are also presented. Instructions for use of the program are documented in SAND77-1334

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.

2010-12-08

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

KAUST Repository

Destrade, M.; Goriely, A.; Saccomandi, G.

2010-01-01

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3

Science.gov (United States)

Correia, Simão; Figueira, Mário

2018-03-01

We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.

High order methods for incompressible fluid flow: Application to moving boundary problems

Energy Technology Data Exchange (ETDEWEB)

Bjoentegaard, Tormod

2008-04-15

Fluid flows with moving boundaries are encountered in a large number of real life situations, with two such types being fluid-structure interaction and free-surface flows. Fluid-structure phenomena are for instance apparent in many hydrodynamic applications; wave effects on offshore structures, sloshing and fluid induced vibrations, and aeroelasticity; flutter and dynamic response. Free-surface flows can be considered as a special case of a fluid-fluid interaction where one of the fluids are practically inviscid, such as air. This type of flows arise in many disciplines such as marine hydrodynamics, chemical engineering, material processing, and geophysics. The driving forces for free-surface flows may be of large scale such as gravity or inertial forces, or forces due to surface tension which operate on a much smaller scale. Free-surface flows with surface tension as a driving mechanism include the flow of bubbles and droplets, and the evolution of capillary waves. In this work we consider incompressible fluid flow, which are governed by the incompressible Navier-Stokes equations. There are several challenges when simulating moving boundary problems numerically, and these include - Spatial discretization - Temporal discretization - Imposition of boundary conditions - Solution strategy for the linear equations. These are some of the issues which will be addressed in this introduction. We will first formulate the problem in the arbitrary Lagrangian-Eulerian framework, and introduce the weak formulation of the problem. Next, we discuss the spatial and temporal discretization before we move to the imposition of surface tension boundary conditions. In the final section we discuss the solution of the resulting linear system of equations. (Author). refs., figs., tabs

Robust mixed finite element methods to deal with incompressibility in finite strain in an industrial framework

International Nuclear Information System (INIS)

Al-Akhrass, Dina

2014-01-01

Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)

Incompressible viscous flow computations for the pump components and the artificial heart

Science.gov (United States)

Kiris, Cetin

1992-01-01

A finite difference, three dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. Here, equations are solved in steadily rotating reference frames by using the steady state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two.

Boundary-layer interactions in the plane-parallel incompressible flows

International Nuclear Information System (INIS)

Nguyen, Toan T; Sueur, Franck

2012-01-01

We study the inviscid limit problem of incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity smoothes out the discontinuity jump by creating a transition layer which has the same amplitude and thickness as the Prandtl layer. In the neighbourhood of the intersection of the impermeable boundary and of the hypersurface, interactions between the boundary and the transition layers must then be considered. In this paper, we initiate a mathematical study of this interaction and carry out a strong convergence in the inviscid limit for the case of the plane-parallel flows introduced by Di Perna and Majda (1987 Commun. Math. Phys. 108 667–89). (paper)

Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

International Nuclear Information System (INIS)

Jarraya, A.; Wali, M.; Dammark, F.

2014-01-01

This paper is focused on the structural shape optimization of incompressible hyperelastic structures. An analytical sensitivity is developed for the rubber like materials. The whole shape optimization process is carried out by coupling a closed geometric shape in R 2 with boundaries, defined by B-splines curves, exact sensitivity analysis and mathematical programming method (S.Q.P: sequential quadratic programming). Design variables are the control points coordinate. The objective function is to minimize Von-Mises stress, constrained to the total material volume of the structure remains constant. In order to validate the exact Jacobian method, the sensitivity calculation is performed: numerically by an efficient finite difference scheme and by the exact Jacobian method. Numerical optimization examples are presented for elastic and hyperelastic materials using the proposed method.

A fast Poisson solver for unsteady incompressible Navier-Stokes equations on the half-staggered grid

Science.gov (United States)

Golub, G. H.; Huang, L. C.; Simon, H.; Tang, W. -P.

1995-01-01

In this paper, a fast Poisson solver for unsteady, incompressible Navier-Stokes equations with finite difference methods on the non-uniform, half-staggered grid is presented. To achieve this, new algorithms for diagonalizing a semi-definite pair are developed. Our fast solver can also be extended to the three dimensional case. The motivation and related issues in using this second kind of staggered grid are also discussed. Numerical testing has indicated the effectiveness of this algorithm.

Asymptotic structure of viscous incompressible flow around a rotating body, with nonvanishing flow field at infinity

Czech Academy of Sciences Publication Activity Database

Deuring, P.; Kračmar, S.; Nečasová, Šárka

2017-01-01

Roč. 68, č. 1 (2017), č. článku 16. ISSN 0044-2275 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : asymptotic profile * Pointwise decay * rotating body * stationary incompressible Navier–Stokes system Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.687, year: 2016 http://link.springer.com/article/10.1007%2Fs00033-016-0760-x

Asymptotic structure of viscous incompressible flow around a rotating body, with nonvanishing flow field at infinity

Czech Academy of Sciences Publication Activity Database

Deuring, P.; Kračmar, S.; Nečasová, Šárka

2017-01-01

Roč. 68, č. 1 (2017), č. článku 16. ISSN 0044-2275 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : asymptotic profile * Pointwise decay * rotating body * stationary incompressible Navier–Stokes system Subject RIV: BA - General Math ematics OBOR OECD: Pure math ematics Impact factor: 1.687, year: 2016 http://link.springer.com/article/10.1007%2Fs00033-016-0760-x

Reflection and transmission characteristics of a layer obeying the two-pressure field poroelastic phenomenological model of Berryman and Wang.

Science.gov (United States)

Kachkouch, F; Franklin, H; Tinel, A

2018-07-01

The characteristics of the reflection and transmission by a fluid-loaded double porosity layer are studied. The medium obeys the two-pressure field poroelastic phenomenological model of Berryman and Wang. The open pore hydraulic conditions applied at the interfaces yield factorized expressions for the coefficients exhibiting on the one hand a separation allowing to distinguish between symmetrical and antisymmetrical motions and on the other hand the way each of the three dilatational waves associate with the shear wave. The numerical study done for a layer of Berea sandstone saturated by water shows clearly the role of each of the dilatational waves. There are peculiarities such as the absence of the fundamental antisymmetrical mode (zero order) and a singular behaviour of the symmetrical fundamental mode. The low frequency approximation for this latter is derived from the proposed formulas and compared with the numerical results. Copyright © 2018 Elsevier B.V. All rights reserved.

Simulation of three-dimensional, time-dependent, incompressible flows by a finite element method

International Nuclear Information System (INIS)

Chan, S.T.; Gresho, P.M.; Lee, R.L.; Upson, C.D.

1981-01-01

A finite element model has been developed for simulating the dynamics of problems encountered in atmospheric pollution and safety assessment studies. The model is based on solving the set of three-dimensional, time-dependent, conservation equations governing incompressible flows. Spatial discretization is performed via a modified Galerkin finite element method, and time integration is carried out via the forward Euler method (pressure is computed implicitly, however). Several cost-effective techniques (including subcycling, mass lumping, and reduced Gauss-Legendre quadrature) which have been implemented are discussed. Numerical results are presented to demonstrate the applicability of the model

A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows

Science.gov (United States)

Borazjani, Iman; Ge, Liang; Le, Trung; Sotiropoulos, Fotis

2013-01-01

We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, Journal of Computational Physics, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data, and its capabilities are demonstrated by simulating the flow past multiple aquatic swimmers and the systolic flow in an anatomic left ventricle with a mechanical heart valve implanted in the aortic position. PMID:23833331

TURBO: a computer program for two-dimensional incompressible fluid flow analysis using a two-equations turbulence model

International Nuclear Information System (INIS)

Botelho, D.A.; Moreira, M.L.

1991-06-01

The Reynolds turbulent transport equations for an incompressible fluid are integrated on a bi-dimensional staggered grid, for velocity and pressure, using the SIMPLER method. With the resulting algebraic relations it was developed the TURBO program, which final objectives are the thermal stratification and natural convection analysis of nuclear reactor pools. This program was tested in problems applications with analytic or experimental solutions previously known. (author)

Numerical simulation of 3-D incompressible, multi-phase flows over cavitating projectiles

Energy Technology Data Exchange (ETDEWEB)

Owis, F.M.; Nayfeh, A.H. [Blacksburg State University, Dept. of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute, VA (United States)

2004-04-01

The hydrodynamic cavitation over axisymmetric projectiles is computed using the unsteady incompressible Navier-Stokes equations for multi-fluid elements. The governing equations are discretized on a structured grid using an upwind difference scheme with flux limits. A preconditioning dual-time stepping method is used for the unsteady computations. The Eigen-system is derived for the Jacobian matrices. This Eigen-system is suitable for high-density ratio multi-fluid flows and it provides high numerical stability and fast convergence. This method can be used to compute single- as well as multi-phase flows. Cavitating flows over projectiles with different geometries are computed and the results are in good agreement with available experimental data and other published computations. (authors)

Improved flux calculations for viscous incompressible flow by the variable penalty method

International Nuclear Information System (INIS)

Kheshgi, H.; Luskin, M.

1985-01-01

The Navier-Stokes system for viscous, incompressible flow is considered, taking into account a replacement of the continuity equation by the perturbed continuity equation. The introduction of the approximation allows the pressure variable to be eliminated to obtain the system of equations for the approximate velocity. The penalty approximation is often applied to numerical discretizations since it provides a reduction in the size and band-width of the system of equations. Attention is given to error estimates, and to two numerical experiments which illustrate the error estimates considered. It is found that the variable penalty method provides an accurate solution for a much wider range of epsilon than the classical penalty method. 8 references

A stable partitioned FSI algorithm for incompressible flow and deforming beams

International Nuclear Information System (INIS)

Li, L.; Henshaw, W.D.; Banks, J.W.; Schwendeman, D.W.; Main, A.

2016-01-01

An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for

A stable partitioned FSI algorithm for incompressible flow and deforming beams

Energy Technology Data Exchange (ETDEWEB)

Li, L., E-mail: lil19@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Henshaw, W.D., E-mail: henshw@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Banks, J.W., E-mail: banksj3@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Schwendeman, D.W., E-mail: schwed@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Main, A., E-mail: amain8511@gmail.com [Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708 (United States)

2016-05-01

An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for

On the motion of rigid bodies in an incompressible or compressible viscous fluid under the action of gravitational forces

Czech Academy of Sciences Publication Activity Database

Ducomet, B.; Nečasová, Šárka

2013-01-01

Roč. 6, č. 5 (2013), s. 1193-1213 ISSN 1937-1632 R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : motion of rigid bodies * incompressible fluid * compressible fluid Subject RIV: BA - General Mathematics https://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=8331

Swimming of a sphere in a viscous incompressible fluid with inertia

International Nuclear Information System (INIS)

Felderhof, B U; Jones, R B

2017-01-01

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier–Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two Hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid. (paper)

Swimming of a sphere in a viscous incompressible fluid with inertia

Energy Technology Data Exchange (ETDEWEB)

Felderhof, B U [Institut für Theorie der Statistischen Physik RWTH Aachen University, Templergraben 55, D-52056 Aachen (Germany); Jones, R B, E-mail: ufelder@physik.rwth-aachen.de, E-mail: r.b.jones@qmul.ac.uk [Queen Mary University of London, The School of Physics and Astronomy, Mile End Road, London E1 4NS (United Kingdom)

2017-08-15

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier–Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two Hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid. (paper)

Swimming of a sphere in a viscous incompressible fluid with inertia

Science.gov (United States)

Felderhof, B. U.; Jones, R. B.

2017-08-01

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two Hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.

Structure of reconnection boundary layers in incompressible MHD

International Nuclear Information System (INIS)

Sonnerup, B.U.Oe.; Wang, D.J.

1987-01-01

The incompressible MHD equations with nonvanishing viscosity and resistivity are simplified by use of the boundary layer approximation to describe the flow and magnetic field in the exit flow regions of magnetic field reconnection configurations when the reconnection rate is small. The conditions are derived under which self-similar solutions exist of the resulting boundary layer equations. For the case of zero viscosity and resistivity, the equations describing such self-similar layers are then solved in terms of quadratures, and the resulting flow and field configurations are described. Symmetric solutions, relevant, for example, to reconnection in the geomagnetic tail, as well as asymmetric solutions, relevant to reconnection at the earth's magnetopause, are found to exist. The nature of the external solutions to which the boundary layer solutions should be matched is discussed briefly, but the actual matching, which is to occur at Alfven-wave characteristic curves in the boundary layer solutions, is not carried out. Finally, it is argued that the solutions obtained may also be used to describe the structure of the intense vortex layers observed to occur at magnetic separatrices in computer simulations and in certain analytical models of the reconnection process

An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

Science.gov (United States)

English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

2013-12-01

We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

'Perfectly disordered' medium as a model for the description of micro-inhomogeneous mixtures

International Nuclear Information System (INIS)

Levin, V M; Markov, M G; Alvarez-Tostado, J M

2004-01-01

The correct description of the macroscopic (overall) physical properties of micro-inhomogeneous (composite) materials by micro-mechanics methods (the self-consistent schemes, for example) requires information about the microstructure and texture of such materials. Often, such information (of shapes inhomogeneities and peculiarities of their spatial distribution) is not available. In this paper, we suggest a method of calculation of the characteristics of micro-inhomogeneous materials that could be applied to a wide class of isotropic materials. This method assumes the absence of a closed order in the material microstructure (a 'perfectly disordered' (PD) medium). We used the PD approximation to predict the effective thermo- and poroelastic, electric and thermal properties of micro-inhomogeneous media. The expressions for the effective characteristics obtained by this method are always inside of the Hashin-Shtrikman universal bounds. For a two-phase material with fluid component, the effective bulk module satisfies Gassmann's relation for fluid-filled porous media and generalizes such a relation to inhomogeneous thermoelastic and poroelastic media. A comparison of the theoretical results with available experimental data shows a satisfactory coincidence even in the case of high contrast of the component properties. The simplicity of the numerical realization of the method makes it attractive for applications in the absence of detailed information about the material's microstructure

Finite element approximation of a new variational principle for compressible and incompressible linear isotropic elasticity

International Nuclear Information System (INIS)

Franca, L.P.; Stenberg, R.

1989-06-01

Stability conditions are described to analyze a variational formulation emanating from a variational principle for linear isotropic elasticity. The variational principle is based on four dependent variables (namely, the strain tensor, augmented stress, pressure and displacement) and is shown to be valid for any compressibility including the incompressible limit. An improved convergence error analysis is established for a Galerkin-least-squares method based upon these four variables. The analysis presented establishes convergence for a wide choice of combinations of finite element interpolations. (author) [pt

Halting Land Subsidence in Tucson, Arizona: Examining the Poroelastic Response to Artificial Recharge

Science.gov (United States)

Miller, M. M.; Shirzaei, M.; Argus, D. F.

2017-12-01

Overexploitation of groundwater results in stressed aquifer systems and surface deformation in the form of land subsidence. Differential land subsidence can lead to earth fissures, which threaten buildings and infrastructure. Therefore, careful water management is necessary to ensure aquifer resources are withdrawn and replenished at a sustainable yield to preserve supplies and minimize surface deformation. Tucson, Arizona is a semi-arid desert city that is reliant on a semi-confined alluvial aquifer system for much of the water supply. To understand the poroelastic response of the aquifer system over time, we analyze data from wells equipped with extensometers, InSAR time series, and GPS. From 1990-2005, compaction of fine-grained, aquitard material is measured up to 8.5 mm/yr at well sites equipped with extensometers. This induces permanent aquifer storage volume losses up to 4.1%. Yet, interferograms from Envisat and RadarSAT-2 C-band satellites, which yield multitemporal deformation maps at high resolution, reveal that subsidence remarkably slows by the late 2000s and nearly halts by 2015. We infer this deceleration corresponds to heightened artificial recharge efforts to bank Colorado River water delivered via canal. After groundwater levels recover, residual compaction continues for just a 6.6-year interval, which suggests a high value for vertical hydraulic conductivity up to 9.8 x10-4 m/day. Successful water management and conservation plans help the city preserve existing and replenish depleted groundwater reserves, decelerate land subsidence, and likely reduce the risks associated with earth fissuring.

Twopool strategy and the combined compressible/incompressible flow problem

International Nuclear Information System (INIS)

Sienicki, J.J.; Abramson, P.B.

1979-01-01

Most recent numerical modeling of two-phase flow involves an implicit determination of a pressure field upon which computational efficiency is strongly dependent. While cell by cell schemes (which treat the pressures in adjacent cells as known source terms) offer fast running times, permit the use of large time steps limited by a Courant condition restriction based on material velocities, and favor enhanced implicit coupling between the thermodynamic and hydrodynamic variables within individual cells, strong implicit coupling (as obtained with elimination schemes) between pressures in adjacent cells in pure single-phase liquid regions is necessary for the calculation of combined two-phase (compressible)/single-phase (incompressible) flows. The TWOPOOL strategy, which consists of a separation in the determination of a pressure field between the single-phase liquid cells where elimination is used and the two-phase cells where a cell by cell scheme is used, constitutes the fastest running strategy which permits the use of large time steps limited only by a Courant condition restriction based on material velocities

Comparison of 3-D finite elements for incompressible fluid flow

International Nuclear Information System (INIS)

Robichaud, M.; Tanguy, P.A.

1985-01-01

In recent years, the finite element method applied to the solution of incompressible fluid flow has been in constant evolution. In the present state-of-the-art, 2-D problems are solved routinely and reliable results are obtained at a reasonable cost. In 3-D the finite element method is still undergoing active research and many methods have been proposed to solve the Navier-Stokes equations at 'low cost'. These methods have in common the choice of the element which has a trilinear velocity and a discontinuous constant pressure (Q1-PO). The prohibitive cost of 3-D finite element method in fluid flow is the reason for this choice: the Q1-PO is the simplest and the cheapest 3-D element. However, as mentioned in (5) and (6), it generates 'spurious' pressure modes phenomenon called checkerboarding. On regular mesh these spurious modes can be filtered but on distorted mesh the pressure solution is meaningless. (author)

Investigation of the use of Prandtl/Navier--Stokes equation procedures for two-dimensional incompressible flows

International Nuclear Information System (INIS)

Anderson, C.R.; Reider, M.B.

1994-01-01

The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown

An efficient implicit direct forcing immersed boundary method for incompressible flows

International Nuclear Information System (INIS)

Cai, S-G; Ouahsine, A; Smaoui, H; Favier, J; Hoarau, Y

2015-01-01

A novel efficient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an effective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressure- correction projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature

Numerical solutions of incompressible Navier-Stokes equations using modified Bernoulli's law

Science.gov (United States)

Shatalov, A.; Hafez, M.

2003-11-01

Simulations of incompressible flows are important for many practical applications in aeronautics and beyond, particularly in the high Reynolds number regime. The present formulation is based on Helmholtz velocity decomposition where the velocity is presented as the gradient of a potential plus a rotational component. Substituting in the continuity equation yields a Poisson equation for the potential which is solved with a zero normal derivative at solid surfaces. The momentum equation is used to update the rotational component with no slip/no penetration surface boundary conditions. The pressure is related to the potential function through a special relation which is a generalization of Bernoulli's law, with a viscous term included. Results of calculations for two- and three-dimensional problems prove that the present formulation is a valid approach, with some possible benefits compared to existing methods.

Immiscible two-phase fluid flows in deformable porous media

Science.gov (United States)

Lo, Wei-Cheng; Sposito, Garrison; Majer, Ernest

Macroscopic differential equations of mass and momentum balance for two immiscible fluids in a deformable porous medium are derived in an Eulerian framework using the continuum theory of mixtures. After inclusion of constitutive relationships, the resulting momentum balance equations feature terms characterizing the coupling among the fluid phases and the solid matrix caused by their relative accelerations. These terms, which imply a number of interesting phenomena, do not appear in current hydrologic models of subsurface multiphase flow. Our equations of momentum balance are shown to reduce to the Berryman-Thigpen-Chen model of bulk elastic wave propagation through unsaturated porous media after simplification (e.g., isothermal conditions, neglect of gravity, etc.) and under the assumption of constant volume fractions and material densities. When specialized to the case of a porous medium containing a single fluid and an elastic solid, our momentum balance equations reduce to the well-known Biot model of poroelasticity. We also show that mass balance alone is sufficient to derive the Biot model stress-strain relations, provided that a closure condition for porosity change suggested by de la Cruz and Spanos is invoked. Finally, a relation between elastic parameters and inertial coupling coefficients is derived that permits the partial differential equations of the Biot model to be decoupled into a telegraph equation and a wave equation whose respective dependent variables are two different linear combinations of the dilatations of the solid and the fluid.

An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities

Science.gov (United States)

Gong, Yuezheng; Zhao, Jia; Wang, Qi

2017-10-01

A quasi-incompressible hydrodynamic phase field model for flows of fluid mixtures of two incompressible viscous fluids of distinct densities and viscosities is derived by using the generalized Onsager principle, which warrants the variational structure, the mass conservation and energy dissipation law. We recast the model in an equivalent form and discretize the equivalent system in space firstly to arrive at a time-dependent ordinary differential and algebraic equation (DAE) system, which preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we develop a temporal discretization scheme for the DAE system, where the mass conservation and the energy dissipation law are once again preserved at the fully discretized level. We prove that the fully discretized algorithm is unconditionally energy stable. Several numerical examples, including drop dynamics of viscous fluid drops immersed in another viscous fluid matrix and mixing dynamics of binary polymeric solutions, are presented to show the convergence property as well as the accuracy and efficiency of the new scheme.

Low-frequency asymptotic analysis of seismic reflection from afluid-saturated medium

Energy Technology Data Exchange (ETDEWEB)

Silin, D.B.; Korneev, V.A.; Goloshubin, G.M.; Patzek, T.W.

2004-04-14

Reflection of a seismic wave from a plane interface betweentwo elastic media does not depend on the frequency. If one of the mediais poroelastic and fluid-saturated, then the reflection becomesfrequency-dependent. This paper presents a low-frequency asymptoticformula for the reflection of seismic plane p-wave from a fluid-saturatedporous medium. The obtained asymptotic scaling of the frequency-dependentcomponent of the reflection coefficient shows that it is asymptoticallyproportional to the square root of the product of the reservoir fluidmobility and the frequency of the signal. The dependence of this scalingon the dynamic Darcy's law relaxation time is investigated as well.Derivation of the main equations of the theory of poroelasticity from thedynamic filtration theory reveals that this relaxation time isproportional to Biot's tortuosity parameter.

A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting

KAUST Repository

Guermond, Jean-Luc

2010-05-01

A new direction-splitting-based fractional time stepping is introduced for solving the incompressible Navier-Stokes equations. The main originality of the method is that the pressure correction is computed by solving a sequence of one-dimensional elliptic problems in each spatial direction. The method is very simple to program in parallel, very fast, and has exactly the same stability and convergence properties as the Poisson-based pressure-correction technique, either in standard or rotational form. © 2010 Académie des sciences.

A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting

KAUST Repository

Guermond, Jean-Luc; Minev, Peter D.

2010-01-01

A new direction-splitting-based fractional time stepping is introduced for solving the incompressible Navier-Stokes equations. The main originality of the method is that the pressure correction is computed by solving a sequence of one-dimensional elliptic problems in each spatial direction. The method is very simple to program in parallel, very fast, and has exactly the same stability and convergence properties as the Poisson-based pressure-correction technique, either in standard or rotational form. © 2010 Académie des sciences.

PELE-IC, 2-D Eulerian Incompressible Hydrodynamic and Bubble Dynamic after LWR LOCA

International Nuclear Information System (INIS)

McMaster, W.H.; Gong, E.Y.

1981-01-01

1 - Description of problem or function: PELE-IC is a two-dimensional semi-implicit Eulerian hydrodynamics program for the solution of incompressible flow coupled to flexible structures. The code was developed to calculate fluid-structure interactions and bubble dynamics of a pressure-suppression system following a loss-of- coolant accident (LOCA). The fluid, structure, and coupling algorithms have been verified by calculation of benchmark problems and air and steam blowdown experiments. The code is written for both plane and cylindrical coordinates. The coupling algorithm is general enough to handle a wide variety of structural shapes. The concepts of void fractions and interface orientation are used to track the movement of free surfaces, allowing great versatility in following fluid-gas interfaces both for bubble definition and water surface motion without the use of marker particles. 2 - Method of solution: The solution strategy is to first solve the Navier-Stokes equations explicitly using values from the previous time-step. Since these values do not necessarily satisfy the continuity equation, the pressure field is iterated upon until the incompressibility condition for each computational cell is satisfied within prescribed limits. The structural motion is computed by a finite element code from the applied pressure at the fluid-structure interface. The shell structure algorithm uses conventional thin-shell theory with transverse shear. The finite-element spatial discretization employs piecewise-linear interpolation functions and one-point quadrature applied to conical frustra. The Newmark implicit time integration method is used as a one-step module. The fluid code then uses the structure's position and velocity as boundary conditions. The fluid pressure field and the structure's response are corrected iteratively until the normal velocities of fluid and structure are equal. The effects of steam condensation and oscillatory chugging on structures are

Frictionless contact of two parallel congruent rigid cylindrical surfaces coated with thin elastic transversely isotropic incompressible layers: an analytic solution

Czech Academy of Sciences Publication Activity Database

Hlaváček, Miroslav

2006-01-01

Roč. 25, č. 3 (2006), s. 497-508 ISSN 0997-7538 R&D Projects: GA ČR(CZ) GA103/04/0150 Institutional research plan: CEZ:AV0Z20710524 Keywords : contact of coated cylinders * elastic transversely isotropic incompressible coating * human ankle joint Subject RIV: JJ - Other Materials Impact factor: 0.897, year: 2006

Efficient simulations of fluid flow coupled with poroelastic deformations in pleated filters

KAUST Repository

Calo, Victor M.; Iliev, Dimitar; Iliev, Oleg; Kirsch, Ralf; Lakdawala, Zahra; Printsypar, Galina

2015-01-01

model describes a free fluid flow coupled with a flow in porous media in a domain that contains the filtering media. To discretize the complex computational domain we use quadrilateral boundary fitted grids which resolve porous-fluid interfaces

The isoscalar giant dipole resonance and nuclear incompressibility

International Nuclear Information System (INIS)

Garg, U.

2000-01-01

Complete text of publication follows. The current status of the experimental work on the ISOSCALAR giant dipole resonance (ISGDR) will be reviewed. ISGDR is an exotic mode of collective nuclear vibration and can be described as a hydrodynamical density oscillation in which the volume of the nucleus remains constant and the state can be visualized in the form of a compression wave-analogous to a sound wave-oscillating back and forth through the nucleus. [1] Convincing evidence for the ISGDR has now been obtained in inelastic α-scattering measurements at 200 MeV (IUCF) [2], 240 MeV (Texas A and M) [3] and 400 MeV (RCNP, Osaka) [4]. In all nuclei studied so far, the ISGDR strength is observed to be spread over a rather wide excitation-energy range (up to ∼ 15 MeV). The excitation energy of the ISGDR is related to the nuclear incompressibility, K ∞ . The ISGDR results so far point to a value for K ∞ that is ∼ 30-40% lower than the obtained from the energies of the other compressional mode, the giant monopole resonance. Results from recent theoretical attempts to reconcile this difference will be presented. This work has been supported in part by the U.S. National Science Foundation. (author)

On sound transmission through double-walled cylindrical shells lined with poroelastic material: Comparison with Zhou's results and further effect of external mean flow

Science.gov (United States)

Liu, Yu; He, Chuanbo

2015-12-01

In this discussion, the corrections to the errors found in the derivations and the numerical code of a recent analytical study (Zhou et al. Journal of Sound and Vibration 333 (7) (2014) 1972-1990) on sound transmission through double-walled cylindrical shells lined with poroelastic material are presented and discussed, as well as the further effect of the external mean flow on the transmission loss. After applying the corrections, the locations of the characteristic frequencies of thin shells remain unchanged, as well as the TL results above the ring frequency where BU and UU remain the best configurations in sound insulation performance. In the low-frequency region below the ring frequency, however, the corrections attenuate the TL amplitude significantly for BU and UU, and hence the BB configuration exhibits the best performance which is consistent with previous observations for flat sandwich panels.

OsB 2 and RuB 2, ultra-incompressible, hard materials: First-principles electronic structure calculations

Science.gov (United States)

Chiodo, S.; Gotsis, H. J.; Russo, N.; Sicilia, E.

2006-07-01

Recently it has been reported that osmium diboride has an unusually large bulk modulus combined with high hardness, and consequently is a most interesting candidate as an ultra-incompressible and hard material. The electronic and structural properties of the transition metal diborides OsB 2 and RuB 2 have been calculated within the local density approximation (LDA). It is shown that the high hardness is the result of covalent bonding between transition metal d states and boron p states in the orthorhombic structure.

A boundary-fitted staggered difference method for incompressible flow using Riemann geometry

International Nuclear Information System (INIS)

Koshizuka, Seiichi; Kondo, Shunsuke; Oka, Yoshiaki.

1990-01-01

A boundary-fitted staggered difference method (BFSDM) is investigated for incompressible flow in nuclear plants. BFSDM employs control cells for scalars, staggered location of velocity components, and integrated formulation of div=0. Governing equations are written as coordinate-free forms using Riemann geometry. Flow velocity is represented with contravariant physical components in the present method. Connection terms emerge as source terms in the coordinate-free governing equations. These terms are studied from the viewpoints of physical meaning, numerical stability, and conservative property. Some flows on a round or slant boundary are solved using boundary-fitted curvilinear (BFC) grids and rectangular grids to compare the present method and the rectangular-type (R-type) staggered difference method (SDM). Supercomputing of the present method, including vector processing, is also discussed compared with the R-type method. (author)

Robust boundary treatment for open-channel flows in divergence-free incompressible SPH

Science.gov (United States)

Pahar, Gourabananda; Dhar, Anirban

2017-03-01

A robust Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed to simulate specified inflow and outflow boundary conditions for open-channel flow. Being purely divergence-free, the framework offers smoothed and structured pressure distribution. An implicit treatment of Pressure Poison Equation and Dirichlet boundary condition is applied on free-surface to minimize error in velocity-divergence. Beyond inflow and outflow threshold, multiple layers of dummy particles are created according to specified boundary condition. Inflow boundary acts as a soluble wave-maker. Fluid particles beyond outflow threshold are removed and replaced with dummy particles with specified boundary velocity. The framework is validated against different cases of open channel flow with different boundary conditions. The model can efficiently capture flow evolution and vortex generation for random geometry and variable boundary conditions.

Lagrange–Galerkin methods for the incompressible Navier-Stokes equations: a review

Directory of Open Access Journals (Sweden)

Bermejo Rodolfo

2016-09-01

Full Text Available We review in this paper the development of Lagrange-Galerkin (LG methods to integrate the incompressible Navier-Stokes equations (NSEs for engineering applications. These methods were introduced in the computational fluid dynamics community in the early eighties of the past century, and at that time they were considered good methods for both their theoretical stability properties and the way of dealing with the nonlinear terms of the equations; however, the numerical experience gained with the application of LG methods to different problems has identified drawbacks of them, such as the calculation of specific integrals that arise in their formulation and the calculation of the ow trajectories, which somehow have hampered the applicability of LG methods. In this paper, we focus on these issues and summarize the convergence results of LG methods; furthermore, we shall briefly introduce a new stabilized LG method suitable for high Reynolds numbers.

Saturated poroelastic actuators generated by topology optimization

DEFF Research Database (Denmark)

Andreasen, Casper Schousboe; Sigmund, Ole

2011-01-01

the coupling of internal fluid pressure and elastic shear stresses a slab of the optimized porous material deflects/deforms when a pressure is imposed and an actuator is created. Several phenomenologically based constraints are imposed in order to get a stable force transmitting actuator.......In this paper the fluid-structure interaction problem of a saturated porous media is considered. The pressure coupling properties of porous saturated materials change with the microstructure and this is utilized in the design of an actuator using a topology optimized porous material. By maximizing...

A deflation based parallel algorithm for spectral element solution of the incompressible Navier-Stokes equations

Energy Technology Data Exchange (ETDEWEB)

Fischer, P.F. [Brown Univ., Providence, RI (United States)

1996-12-31

Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or high-aspect ratio elements.

A Poroelasticity Theory Approach to Study the Mechanisms Leading to Elevated Interstitial Fluid Pressure in Solid Tumours.

Science.gov (United States)

Burazin, Andrijana; Drapaca, Corina S; Tenti, Giuseppe; Sivaloganathan, Siv

2018-05-01

Although the mechanisms responsible for elevated interstitial fluid pressure (IFP) in tumours remain obscure, it seems clear that high IFP represents a barrier to drug delivery (since the resulting adverse pressure gradient implies a reduction in the driving force for transvascular exchange of both fluid and macromolecules). R. Jain and co-workers studied this problem, and although the conclusions drawn from their idealized mathematical models offered useful insights into the causes of elevated IFP, they by no means gave a definitive explanation for this phenomenon. In this paper, we use poroelasticity theory to also develop a macroscopic mathematical model to describe the time evolution of a solid tumour, but focus our attention on the mechanisms responsible for the rise of the IFP, from that for a healthy interstitium to that measured in malignant tumours. In particular, we discuss a number of possible time scales suggested by our mathematical model and propose a tumour-dependent time scale that leads to results in agreement with experimental observations. We apply our mathematical model to simulate the effect of "vascular normalization" (as proposed by Jain in Nat Med 7:987-989, 2001) on the IFP profile and discuss and contrast our conclusions with those of previous work in the literature.

Hydromagnetic perturbations due to localized flows: An eddy theorem

International Nuclear Information System (INIS)

Bird, J.F.

1979-01-01

The hydromagnetic far-field generated by localized regions of incompressible flow of electrically conducting media in uniform magnetic fields is derived explicitly in terms of the spin angular momentum of the flow. Some applications and a corollary result for bounded media are given

A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

Science.gov (United States)

Sohn, J. L.; Heinrich, J. C.

1990-01-01

The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

On a method of construction of exact solutions for equations of two-dimensional hydrodynamics of incompressible liquids

International Nuclear Information System (INIS)

Yurov, A.V.; Yurova, A.A.

2006-01-01

The simple algebraic method for construction of exact solutions of two-dimensional hydrodynamic equations of incompressible flow is proposed. This method can be applied both to nonviscous flow (Euler equations) and to viscous flow (Navier-Stokes equations). In the case of nonviscous flow, the problem is reduced to sequential solving of three linear partial differential equations. In the case of viscous flow, the Navier-Stokes equations are reduced to three linear partial differential equations and one differential equation of the first order [ru

Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

Science.gov (United States)

Chen, Z.; Shu, C.; Tan, D.

2018-05-01

An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

Lyapunov stability of ideal compressible and incompressible fluid equilibria in three dimensions

International Nuclear Information System (INIS)

Holm, D.D.

1985-08-01

Linearized stability of ideal compressible and incompressible fluid equilibria in three dimensions is analyzed using Lyapunov's direct method. An action principle is given for the Eulerian and Lagrangian fluid descriptions and the family of constants of motion due to symmetry under fluid-particle relabelling is derived in the form of Ertel's theorem for each description. In an augmented Euleriah description, the steady equilibrium flows of these two fluids theories are identified as critical points of the conserved Lyapunov functionals defined by the sum, H + C, of the energy H, and the Ertel constants of motion, C. It turns out that unconditional linear Lyapunov stability of these flows in the norm provided by the second variation of H + C is precluded by vortex-particle stretching, even for otherwise shear-stable flows. Conditional Lyapunov stability of these flows is discussed. 24 refs

Vibration analysis of elastic tanks partially filled with incompressible liquids in presence of a gravity field; Analyse vibratoire de reservoirs elastiques partiellement remplis de liquides incompressibles en presence d'un champ de gravite

Energy Technology Data Exchange (ETDEWEB)

Schotte, J.S. [Office National d' Etudes et de Recherches Aerospatiales (ONERA), 92 - Chatillon (France); Ohayon, R. [Conservatoire National des Arts et Metiers (CNAM), Structural Dynamics and Coupled Systems Dept., 75 - Paris (France)

2001-07-01

In order to control the trajectory of liquid propelled launch vehicles, optimum command systems need a realistic model for fluid-structure interactions in tanks partially filled with propellant under apparent gravity. Up to now, the interactions between an elastic tank of arbitrary shape and an internal incompressible homogeneous inviscid liquid with a free surface have been computed with the standard added mass method by omitting the gravity effects. The originality of the present work is to analyze the contributions of all terms depending on this constant acceleration and to show that the gravity effects can be considered as pre-stresses in structure and liquid. (authors)

Level Set Projection Method for Incompressible Navier-Stokes on Arbitrary Boundaries

KAUST Repository

Williams-Rioux, Bertrand

2012-01-12

Second order level set projection method for incompressible Navier-Stokes equations is proposed to solve flow around arbitrary geometries. We used rectilinear grid with collocated cell centered velocity and pressure. An explicit Godunov procedure is used to address the nonlinear advection terms, and an implicit Crank-Nicholson method to update viscous effects. An approximate pressure projection is implemented at the end of the time stepping using multigrid as a conventional fast iterative method. The level set method developed by Osher and Sethian [17] is implemented to address real momentum and pressure boundary conditions by the advection of a distance function, as proposed by Aslam [3]. Numerical results for the Strouhal number and drag coefficients validated the model with good accuracy for flow over a cylinder in the parallel shedding regime (47 < Re < 180). Simulations for an array of cylinders and an oscillating cylinder were performed, with the latter demonstrating our methods ability to handle dynamic boundary conditions.

Numerical simulations of incompressible laminar flows using viscous-inviscid interaction procedures

Science.gov (United States)

Shatalov, Alexander V.

The present method is based on Helmholtz velocity decomposition where velocity is written as a sum of irrotational (gradient of a potential) and rotational (correction due to vorticity) components. Substitution of the velocity decomposition into the continuity equation yields an equation for the potential, while substitution into the momentum equations yields equations for the velocity corrections. A continuation approach is used to relate the pressure to the gradient of the potential through a modified Bernoulli's law, which allows the elimination of the pressure variable from the momentum equations. The present work considers steady and unsteady two-dimensional incompressible flows over an infinite cylinder and NACA 0012 airfoil shape. The numerical results are compared against standard methods (stream function-vorticity and SMAC methods) and data available in literature. The results demonstrate that the proposed formulation leads to a good approximation with some possible benefits compared to the available formulations. The method is not restricted to two-dimensional flows and can be used for viscous-inviscid domain decomposition calculations.

Symmetry-Free, p-Robust Equilibrated Error Indication for the hp-Version of the FEMin Nearly Incompressible Linear Elasticity

OpenAIRE

Dörsek, Philipp; Melenk, Jens M.

2017-01-01

We consider the extension of the p-robust equilibrated error estimator due to Braess, Pillwein and Schöberl to linear elasticity. We derive a formulation where the local mixed auxiliary problems do not require symmetry of the stresses. The resulting error estimator is p-robust, and the reliability estimate is also robust in the incompressible limit if quadratics are included in the approximation space. Extensions to other systems of linear second-order partial differential equations are discu...

Large-scale model of flow in heterogeneous and hierarchical porous media

Science.gov (United States)

Chabanon, Morgan; Valdés-Parada, Francisco J.; Ochoa-Tapia, J. Alberto; Goyeau, Benoît

2017-11-01

Heterogeneous porous structures are very often encountered in natural environments, bioremediation processes among many others. Reliable models for momentum transport are crucial whenever mass transport or convective heat occurs in these systems. In this work, we derive a large-scale average model for incompressible single-phase flow in heterogeneous and hierarchical soil porous media composed of two distinct porous regions embedding a solid impermeable structure. The model, based on the local mechanical equilibrium assumption between the porous regions, results in a unique momentum transport equation where the global effective permeability naturally depends on the permeabilities at the intermediate mesoscopic scales and therefore includes the complex hierarchical structure of the soil. The associated closure problem is numerically solved for various configurations and properties of the heterogeneous medium. The results clearly show that the effective permeability increases with the volume fraction of the most permeable porous region. It is also shown that the effective permeability is sensitive to the dimensionality spatial arrangement of the porous regions and in particular depends on the contact between the impermeable solid and the two porous regions.

Temporal stability of superposed magnetic fluids in porous media

International Nuclear Information System (INIS)

Zakaria, Kadry; Sirwah, Magdy A; Alkharashi, Sameh

2008-01-01

The present work deals with the stability properties of time periodically streaming superposed magnetic fluids through porous media under the influence of an oblique alternating magnetic field. The system is composed of a middle fluid sheet of finite thickness embedded between two other bounded layers. The fluids are assumed to be incompressible and there are no volume charges in the layers of the fluids. Such configurations are of relevance in a variety of astrophysical and space configurations. The solutions of the linearized equations of motion and boundary conditions lead to deriving two more general simultaneous Mathieu equations of damping terms with complex coefficients. The method of multiple time scales is used to obtain approximate solutions and analyze the stability criteria for both the non-resonant and resonant cases and hence transition curves are obtained for such cases. The stability criteria are examined theoretically and numerically from which stability diagrams are obtained. It is found that the fluid sheet thickness plays a destabilizing role in the presence of a constant field and velocity, while the damping role is observed for the resonant cases. Dual roles are observed for the fluid velocity and the porosity in the stability criteria

Integrating a logarithmic-strain based hyper-elastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elasto-plasticity

International Nuclear Information System (INIS)

Dina Al Akhrass; Bruchon, Julien; Drapier, Sylvain; Fayolle, Sebastien

2014-01-01

This paper deals with the treatment of incompressibility in solid mechanics in finite-strain elasto-plasticity. A finite-strain model proposed by Miehe, Apel and Lambrecht, which is based on a logarithmic strain measure and its work-conjugate stress tensor is chosen. Its main interest is that it allows for the adoption of standard constitutive models established in a small-strain framework. This model is extended to take into account the plastic incompressibility constraint intrinsically. In that purpose, an extension of this model to a three-field mixed finite element formulation is proposed, involving displacements, a strain variable and pressure as nodal variables with respect to standard finite element. Numerical examples of finite-strain problems are presented to assess the performance of the formulation. To conclude, an industrial case for which the classical under-integrated elements fail is considered. (authors)

Fuel micro-mechanics: homogenization, cracking, granular media

International Nuclear Information System (INIS)

Monerie, Yann

2010-01-01

This work summarizes about fifteen years of research in the field of micro-mechanics of materials. Emphasis is placed on the most recent work carried out in the context of nuclear safety. Micro-mechanics finds a natural place there, aiming to predict the behavior of heterogeneous materials with an evolving microstructure. The applications concerned mainly involve the nuclear fuel and its tubular cladding. The uranium dioxide fuel is modeled, according to the scales under consideration, as a porous ceramic or a granular medium. The strongly irradiated Zircaloy claddings are identified with a composite medium with a metal matrix and a gradient of properties. The analysis of these classes of material is rich in problems of a more fundamental nature. Three main themes are discussed: 1/ Homogenization, 2/ cracking, rupture and fragmentation, 3/ discrete media and fluid-grain couplings. Homogenization: The analytical scale change methods proposed aim to estimate or limit the linear and equivalent nonlinear behaviors of isotropic porous media and anisotropic composites with a metal matrix. The porous media under consideration are saturated or drained, with a compressible or incompressible matrix, and have one or two scales of spherical or ellipsoid pores, or cracks. The composites studied have a macroscopic anisotropy related to that of the matrix, and to the shape and spatial distribution of the inclusions. Thermoelastic, elastoplastic, and viscoplastic behaviors and ductile damage of these media are examined using different techniques: extensions of classic approaches, linear in particular, variational approaches and approaches using elliptical potentials with thermally activated elementary mechanisms. The models developed are validated on numerical finite element simulations, and their functional relevance is illustrated in comparison to experimental data obtained from the literature. The significant results obtained include a plasticity criterion for Gurson matrix

Dynamic response of a system with internal heat sources cooled by a flowing incompressible fluid

International Nuclear Information System (INIS)

Georgescu, R.; Dobrescu, C.

1975-01-01

The paper investigates the dynamic temperature response of an incompressible fluid which cools a duct with internal heat sources sinusoidally oscillated. The analytical results utilise the Laplace transformation technique. The experimental and calculated results are obtained by transfer function approach. Comparison of the calculated with the experimental data indicates agreement from 6 to 24 percent for the amplitude and up to 30 degree for the phase-shift. All the calculated data are below the experimental ones. The analytical method of transfer function approach presents interest and may be utilized for the initial calculations giving good results for flow rates above 1000 kg per hour

A GPU-accelerated semi-implicit fractional-step method for numerical solutions of incompressible Navier-Stokes equations

Science.gov (United States)

Ha, Sanghyun; Park, Junshin; You, Donghyun

2018-01-01

Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. The Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution methods used in the semi-implicit fractional-step method take advantage of multiple tridiagonal matrices whose inversion is known as the major bottleneck for acceleration on a typical multi-core machine. A novel implementation of the semi-implicit fractional-step method designed for GPU acceleration of the incompressible Navier-Stokes equations is presented. Aspects of the programing model of Compute Unified Device Architecture (CUDA), which are critical to the bandwidth-bound nature of the present method are discussed in detail. A data layout for efficient use of CUDA libraries is proposed for acceleration of tridiagonal matrix inversion and fast Fourier transform. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while the Navier-Stokes equations are computed on a GPU. Performance of the present method using CUDA is assessed by comparing the speed of solving three tridiagonal matrices using ADI with the speed of solving one heptadiagonal matrix using a conjugate gradient method. An overall speedup of 20 times is achieved using a Tesla K40 GPU in comparison with a single-core Xeon E5-2660 v3 CPU in simulations of turbulent boundary-layer flow over a flat plate conducted on over 134 million grids. Enhanced performance of 48 times speedup is reached for the same problem using a Tesla P100 GPU.

A hybridized discontinuous Galerkin framework for high-order particle-mesh operator splitting of the incompressible Navier-Stokes equations

Science.gov (United States)

Maljaars, Jakob M.; Labeur, Robert Jan; Möller, Matthias

2018-04-01

A generic particle-mesh method using a hybridized discontinuous Galerkin (HDG) framework is presented and validated for the solution of the incompressible Navier-Stokes equations. Building upon particle-in-cell concepts, the method is formulated in terms of an operator splitting technique in which Lagrangian particles are used to discretize an advection operator, and an Eulerian mesh-based HDG method is employed for the constitutive modeling to account for the inter-particle interactions. Key to the method is the variational framework provided by the HDG method. This allows to formulate the projections between the Lagrangian particle space and the Eulerian finite element space in terms of local (i.e. cellwise) ℓ2-projections efficiently. Furthermore, exploiting the HDG framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense. By advecting the particles through these velocity fields, the particle distribution remains uniform over time, obviating the need for additional quality control. The presented methodology allows for a straightforward extension to arbitrary-order spatial accuracy on general meshes. A range of numerical examples shows that optimal convergence rates are obtained in space and, given the particular time stepping strategy, second-order accuracy is obtained in time. The model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder.

Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows.

Science.gov (United States)

Yang, L M; Shu, C; Wang, Y

2016-03-01

In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014)]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme.

Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

Directory of Open Access Journals (Sweden)

Svetlana S. Vlasova

2016-09-01

Full Text Available The exact stationary solution of the boundary-value problem that describes the convective motion of an incompressible viscous fluid in the two-dimensional layer with the square heating of a free surface in Stokes's approach is found. The linearization of the Oberbeck–Boussinesq equations allows one to describe the flow of fluid in extreme points of pressure and temperature. The condition under which the counter-current flows (two counter flows in the fluid can be observed, is introduced. If the stagnant point in the fluid exists, six non-closed whirlwinds can be observed.

The effect of external mean flow on sound transmission through double-walled cylindrical shells lined with poroelastic material

Science.gov (United States)

Zhou, Jie; Bhaskar, Atul; Zhang, Xin

2014-03-01

Sound transmission through a system of double shells, lined with poroelastic material in the presence of external mean flow, is studied. The porous material is modeled as an equivalent fluid because shear wave contributions are known to be insignificant. This is achieved by accounting for the energetically most dominant wave types in the calculations. The transmission characteristics of the sandwich construction are presented for different incidence angles and Mach numbers over a wide frequency range. It is noted that the transmission loss exhibits three dips on the frequency axis as opposed to flat panels where there are only two such frequencies—results are discussed in the light of these observations. Flow is shown to decrease the transmission loss below the ring frequency, but increase this above the ring frequency due to the negative stiffness and the damping effect added by the flow. In the absence of external mean flow, porous material provides superior insulation for most part of the frequency band of interest. However, in the presence of external flow, this is true only below the ring frequency—above this frequency, the presence of air gap in sandwich constructions is the dominant factor that determines the acoustic performance. In the absence of external flow, an air gap always improves sound insulation.

Éléments finis pour les fluides incompressibles

CERN Document Server

Azaïez, Mejdi; Mund, Ernest

2011-01-01

Cet ouvrage présente l'ensemble des concepts et méthodes nécessaires à la modélisation numérique par éléments finis du comportement des fluides visqueux newtoniens incompressibles. Après un bref rappel des équations de base et des modèles simplifiés, il expose en détail les techniques d'approximation de ces équations par éléments finis pour les dépendances spatiale et temporelle (problèmes de diffusion, d'advection-diffusion et de transport). Une attention toute particulière est portée à la discrétisation spatiale des équations de Stokes et aux algorithmes temporels pour la simulation numérique directe des équations de Navier-Stokes. Un chapitre ancillaire résume les méthodes de résolution des systèmes algébriques de grande taille à structure creuse, caractéristiques des méthodes d'éléments finis. L'exposé clair, didactique et progressif offre un contenu équilibré entre théorie et pratique. Ce manuel constitue ainsi une référence indispensable pour les étudiants de ma...

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

Science.gov (United States)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows

Science.gov (United States)

Suzuki, Yukihito

2018-03-01

A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn-Hilliard and Allen-Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.

Three dimensional simulation of compressible and incompressible flows through the finite element method; Simulacao tridimensional de escoamentos compressiveis e incompressiveis atraves do metodo dos elementos finitos

Energy Technology Data Exchange (ETDEWEB)

Costa, Gustavo Koury

2004-11-15

Although incompressible fluid flows can be regarded as a particular case of a general problem, numerical methods and the mathematical formulation aimed to solve compressible and incompressible flows have their own peculiarities, in such a way, that it is generally not possible to attain both regimes with a single approach. In this work, we start from a typically compressible formulation, slightly modified to make use of pressure variables and, through augmenting the stabilising parameters, we end up with a simplified model which is able to deal with a wide range of flow regimes, from supersonic to low speed gas flows. The resulting methodology is flexible enough to allow for the simulation of liquid flows as well. Examples using conservative and pressure variables are shown and the results are compared to those published in the literature, in order to validate the method. (author)

Numerical modelling of two phase flow with hysteresis in heterogeneous porous media

Energy Technology Data Exchange (ETDEWEB)

Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)

2008-07-01

Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)

Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flow with large viscosity ratio and high Péclet number

Science.gov (United States)

Meng, Xuhui; Guo, Zhaoli

2015-10-01

A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high Péclet number in this paper. The equilibria in the present model are motivated by the lattice kinetic scheme previously developed by Inamuro et al. [Philos. Trans. R. Soc. London, Ser. A 360, 477 (2002), 10.1098/rsta.2001.0942]. The fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model. As a result, the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model. Numerical validations of the Poiseuille flow and a diffusion-reaction problem demonstrate that the proposed model has second-order accuracy in space. Thereafter, the model is used to simulate flow through a porous medium, and the results show that the proposed model has the advantage to obtain a viscosity-independent permeability, which makes it a robust method for simulating flow in porous media. Finally, a set of simulations are conducted on the viscous miscible displacement between two parallel plates. The results reveal that the present model can be used to simulate, to a high level of accuracy, flows with large viscosity ratios and/or high Péclet numbers. Moreover, the present model is shown to provide superior stability in the limit of high kinematic viscosity. In summary, the numerical results indicate that the present lattice Boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and/or a high Péclet number.

Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM

Directory of Open Access Journals (Sweden)

Petr Sváček

2012-01-01

Full Text Available This paper deals with a numerical solution of the interaction of two-dimensional (2-D incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The profile with two degrees of freedom (2-DOF can rotate around its elastic axis and oscillate in the vertical direction. Its motion is described by a nonlinear system of two ordinary differential equations. Deformations of the computational domain due to the profile motion are treated by the arbitrary Lagrangian-Eulerianmethod. The finite volume method and the finite element method are applied, and the numerical results are compared.

The compactness of front tracking for chromatography electrophoresis and incompressible multiphase flow

International Nuclear Information System (INIS)

Wendroff, B.

1992-01-01

An analysis of the equations of chromatography from the point of view of hyperbolic conservation laws has been reviewed in recent literature. Serre was able to prove that the Lax-Friedrichs difference scheme, Godunov's method, and the viscosity method, have a subsequence converging to a weak solution of the chromatography equations, with no restriction on the size of the initial data. The purpose of this note is to announce that two versions of front tracking can be added to this list. After a brief description of the properties of the chromatography system and a definition of front tracking we give the basic steps of the proof. An example showing the quality of a front tracking solution is given. The equations of idealized electrophoresis and multiphase incompressible flow are very similar to the chromatography equations, but the former have linearly degenerate characteristic field, creating contact discontinuities. In the final section we briefly indicate how our result for chromatography carries over to this case

On Analysis of Stationary Viscous Incompressible Flow Through a Radial Blade Machine

Science.gov (United States)

Neustupa, Tomáš

2010-09-01

The paper is concerned with the analysis of the two dimensional model of incompressible, viscous, stationary flow through a radial blade machine. This type of turbine is sometimes called Kaplan's turbine. In the technical area the use is either to force some regular characteristic to the flow of the medium going through the turbine (flow of melted iron, air conditioning) or to gain some energy from the flowing medium (water). The inflow and outflow part of boundary are in general a concentric circles. The larger one represents an inflow part of boundary the smaller one the outflow part of boundary. Between them are regularly spaced the blades of the machine. We study the existence of the weak solution in the case of nonlinear boundary condition of the "do-nothing" type. The model is interesting for study the behavior of the flow when the boundary is formed by mutually disjoint and separated parts.

Pore-fluid effects on seismic waves in vertically fractured earth with orthotropic symmetry

Energy Technology Data Exchange (ETDEWEB)

Berryman, J.G.

2010-05-15

For elastically noninteracting vertical-fracture sets at arbitrary orientation angles to each other, a detailed model is presented in which the resulting anisotropic fractured medium generally has orthorhombic symmetry overall. Some of the analysis methods and ideas of Schoenberg are emphasized, together with their connections to other similarly motivated and conceptually related methods by Sayers and Kachanov, among others. Examples show how parallel vertical-fracture sets having HTI (horizontal transversely isotropic) symmetry transform into orthotropic fractured media if some subsets of the vertical fractures are misaligned with the others, and then the fractured system can have VTI (vertical transversely isotropic) symmetry if all of the fractures are aligned randomly or half parallel and half perpendicular to a given vertical plane. An orthotropic example having vertical fractures in an otherwise VTI earth system (studied previously by Schoenberg and Helbig) is compared with the other examples treated and it is finally shown how fluids in the fractures affect the orthotropic poroelastic system response to seismic waves. The key result is that fracture-influence parameters are multiplied by a factor of (1-B), where 0 {le} B < 1 is Skempton's second coefficient for poroelastic media. Skempton's B coefficient is itself a measurable characteristic of fluid-saturated porous rocks, depending on porosity, solid moduli, and the pore-fluid bulk modulus. For heterogeneous porous media, connections between the present work and earlier related results of Brown and Korringa are also established.

CCM Continuity Constraint Method: A finite-element computational fluid dynamics algorithm for incompressible Navier-Stokes fluid flows

Energy Technology Data Exchange (ETDEWEB)

Williams, P. T. [Univ. of Tennessee, Knoxville, TN (United States)

1993-09-01

As the field of computational fluid dynamics (CFD) continues to mature, algorithms are required to exploit the most recent advances in approximation theory, numerical mathematics, computing architectures, and hardware. Meeting this requirement is particularly challenging in incompressible fluid mechanics, where primitive-variable CFD formulations that are robust, while also accurate and efficient in three dimensions, remain an elusive goal. This dissertation asserts that one key to accomplishing this goal is recognition of the dual role assumed by the pressure, i.e., a mechanism for instantaneously enforcing conservation of mass and a force in the mechanical balance law for conservation of momentum. Proving this assertion has motivated the development of a new, primitive-variable, incompressible, CFD algorithm called the Continuity Constraint Method (CCM). The theoretical basis for the CCM consists of a finite-element spatial semi-discretization of a Galerkin weak statement, equal-order interpolation for all state-variables, a 0-implicit time-integration scheme, and a quasi-Newton iterative procedure extended by a Taylor Weak Statement (TWS) formulation for dispersion error control. Original contributions to algorithmic theory include: (a) formulation of the unsteady evolution of the divergence error, (b) investigation of the role of non-smoothness in the discretized continuity-constraint function, (c) development of a uniformly H¹ Galerkin weak statement for the Reynolds-averaged Navier-Stokes pressure Poisson equation, (d) derivation of physically and numerically well-posed boundary conditions, and (e) investigation of sparse data structures and iterative methods for solving the matrix algebra statements generated by the algorithm.

Media Education Initiatives by Media Organizations: The Uses of Media Literacy in Hong Kong Media

Science.gov (United States)

Chu, Donna; Lee, Alice Y. L.

2014-01-01

As more media organizations have engaged in media education, this paper investigates the goals and practices of these activities. This article coins media education initiatives by media organizations with the term "media-organization media literac"y (MOML). Four MOML projects in Hong Kong were selected for examination. Built on critical…

Statistical theory of turbulent incompressible multimaterial flow

International Nuclear Information System (INIS)

Kashiwa, B.

1987-10-01

Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of κ-ε modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy κ, and the rate of fluctuational energy dissipation ε, for each material. Hence a set of κ and ε equations must be solved, together with mean mass and momentum conservation equations, for each material. Both κ and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a pipe

Effect of heat treatment upon the mechanical and poro-mechanical behaviour of cement-based materials: hydraulic properties and morphological changes

International Nuclear Information System (INIS)

Chen, Xiao-Ting

2009-01-01

This work investigates the effects of morphological changes of a cement-based material subjected to heat treatment (up to 400 C). For a model W/C=0.5 mortar, we have characterized experimentally hydraulic behaviour (gas permeability), mechanical behaviour (in uniaxial compression, hydrostatic compression with or without deviatoric stress) and poro-mechanical behaviour (incompressibility moduli Kb, Ks and Biot's coefficient b) after a heating/cooling cycle. We have also developed an original experiment aimed at quantifying the accessible pore space volume under hydrostatic compression. The creation of occluded porosity under high confinement is confirmed, which justifies the observed decrease of solid matrix rigidity Ks under high confinement. A gas retention phenomenon was identified under simultaneous thermal and hydrostatic loadings for mortar, and industrial concretes (provided by CERIB and ANDRA). A predictive thermo-elasto-plastic model with isotropic damage and a micro-mechanical approach, which represents micro-cracking, are coupled in order to analyze or predict the evolution of mechanical and poro-elastic properties after heat cycling. (author)

Media Komunitas dan Media Literacy

Directory of Open Access Journals (Sweden)

Pawito .

2013-12-01

Full Text Available Abstract:This essay deals with community media in relation to media literacy. After a short discussion on a number of community media characters is made the essay goes further with somewhat detail theoretical presumptions of the roles of media community with respect primarily to the development as Amartya Sen mentioned about. The author suggests that community media may play some significant roles in the development including (a disseminating information (from varieties of perspective, (b facilitating public discussion, (c helping to reach solutions of problems, (d encouraging participations, and (e encouraging the development of media literacy. Regarding the last point the author remarks that media community may have a dual-roles i.e facilitating community’s member in media participation and facilitating community’s member in media education.

Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

OpenAIRE

Destrade, Michel; Goriely, Alain; Saccomandi, Giuseppe

2011-01-01

We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation c...

A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries

Science.gov (United States)

Dong, S.; Wang, X.

2016-01-01

Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries. PMID:27163909

An asymptotic model of seismic reflection from a permeable layer

Energy Technology Data Exchange (ETDEWEB)

Silin, D.; Goloshubin, G.

2009-10-15

Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot's model of poroelasticity. A review of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and Darcy's law suggests an alternative new physical interpretation of some coefficients of the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number, are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly-permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and at-tribute analysis.

A low-frequency asymptotic model of seismic reflection from a high-permeability layer

Energy Technology Data Exchange (ETDEWEB)

Silin, Dmitriy; Goloshubin, Gennady

2009-03-01

Analysis of compression wave propagation through a high-permeability layer in a homogeneous poroelastic medium predicts a peak of reflection in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of the Biot's model of poroelasticity. A new physical interpretation of some coefficients of the classical poroelasticity is a result of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and the Darcy's law. The velocity of wave propagation, the attenuation factor, and the wave number, are expressed in the form of power series with respect to a small dimensionless parameter. The latter is equal to the product of the kinematic reservoir fluid mobility, an imaginary unit, and the frequency of the signal. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly-permeable layer (a lens). The practical implications of the theory developed here are seismic modeling, inversion, and attribute analysis.

Hall-magnetohydrodynamic waves in flowing ideal incompressible solar-wind plasmas

International Nuclear Information System (INIS)

Zhelyazkov, I

2010-01-01

It is well established now that the solar atmosphere, from the photosphere to the corona and the solar wind, is a highly structured medium. Satellite observations have confirmed the presence of steady flows there. Here, we investigate the propagation of magnetohydrodynamic (MHD) eigenmodes (kink and sausage surface waves) travelling along an ideal incompressible flowing plasma cylinder (flux tube) surrounded by a flowing plasma environment in the framework of the Hall magnetohydrodynamics. The propagation characteristics of the waves are studied in a reference frame moving with the mass flow outside the tube. In general, the flows change the waves' phase velocities compared with their magnitudes in a static MHD flux tube and the Hall effect extends the number of the possible wave dispersion curves. It turns out that while the kink waves, considered in the context of the standard magnetohydrodynamics, are unstable against the Kelvin-Helmholtz instability, they become stable when the Hall term in the generalized Ohm's law is taken into account. The sausage waves are stable in both considerations. All results concerning the waves' propagation and their stability/instability status are obtained on the basis of the linearized Hall-magnetohydrodynamic equations and are applicable mainly to the solar wind plasmas.

From Augmentation Media to Meme Media.

Science.gov (United States)

Tanaka, Yuzuru

Computers as meta media are now evolving from augmentation media vehicles to meme media vehicles. While an augmentation media system provides a seamlessly integrated environment of various tools and documents, meme media system provides further functions to edit and distribute tools and documents. Documents and tools on meme media can easily…

On the self-similar solution to the Euler equations for an incompressible fluid in three dimensions

Science.gov (United States)

Pomeau, Yves

2018-03-01

The equations for a self-similar solution to an inviscid incompressible fluid are mapped into an integral equation that hopefully can be solved by iteration. It is argued that the exponents of the similarity are ruled by Kelvin's theorem of conservation of circulation. The end result is an iteration with a nonlinear term entering a kernel given by a 3D integral for a swirling flow, likely within reach of present-day computational power. Because of the slow decay of the similarity solution at large distances, its kinetic energy diverges, and some mathematical results excluding non-trivial solutions of the Euler equations in the self-similar case do not apply. xml:lang="fr"

Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations

KAUST Repository

Bessaih, Hakima

2016-01-27

We study a modified three-dimensional incompressible anisotropic Navier−Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy−Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier−Stokes equations.

Social media management and media environment

Directory of Open Access Journals (Sweden)

Šiđanin Iva

2012-01-01

Full Text Available The paper deals with the system of services that social media management can offer to a variety of users. As social media systems are emerging, social media management can strengthen teams in social media and help to manage numerous social channels and distribution of social information from one place. Social media management is a system of procedures that are used to manage the flow of information in the environment of social media. This involves connecting with social media like Facebook, Twitter, LinkedIn, Plaxo, Ecademy, YouTube and many others, then the aggregation and management of social data. Social media management services are analysed through various fields, such as managing multiple social media profiles, mail scheduling and filtering, reporting and analytics. Social media management enables managing personal business through social media, which contributes to a significant reduction in expenditures. The paper also discusses the importance of social media management in marketing activities and various forms of social promotion, which allow companies to easily reach their customers.

Static black hole and vacuum energy: thin shell and incompressible fluid

Science.gov (United States)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

With the back reaction of the vacuum energy-momentum tensor consistently taken into account, we study static spherically symmetric black-hole-like solutions to the semi-classical Einstein equation. The vacuum energy is assumed to be given by that of 2-dimensional massless scalar fields, as a widely used model in the literature for black holes. The solutions have no horizon. Instead, there is a local minimum in the radius. We consider thin shells as well as incompressible fluid as the matter content of the black-hole-like geometry. The geometry has several interesting features due to the back reaction of vacuum energy. In particular, Buchdahl's inequality can be violated without divergence in pressure, even if the surface is below the Schwarzschild radius. At the same time, the surface of the star can not be far below the Schwarzschild radius for a density not much higher than the Planck scale, and the proper distance from its surface to the origin can be very short even for very large Schwarzschild radius. The results also imply that, contrary to the folklore, in principle the Boulware vacuum can be physical for black holes.

A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition

Directory of Open Access Journals (Sweden)

Mitsuteru Asai

2012-01-01

Full Text Available A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.

Remapping HELENA to incompressible plasma rotation parallel to the magnetic field

Energy Technology Data Exchange (ETDEWEB)

Poulipoulis, G.; Throumoulopoulos, G. N. [Physics Department, University of Ioannina, Ioannina 451 10 (Greece); Konz, C. [Max-Planck Institut für Plasma Physics, 85748 Garching bei München (Germany)

2016-07-15

Plasma rotation in connection to both zonal and mean (equilibrium) flows can play a role in the transitions to the advanced confinement regimes in tokamaks, as the L-H transition and the formation of internal transport barriers (ITBs). For incompressible rotation, the equilibrium is governed by a generalised Grad-Shafranov (GGS) equation and a decoupled Bernoulli-type equation for the pressure. For parallel flow, the GGS equation can be transformed to one identical in form with the usual Grad-Shafranov equation. In the present study on the basis of the latter equation, we have extended HELENA, an equilibrium fixed boundary solver. The extended code solves the GGS equation for a variety of the two free-surface-function terms involved for arbitrary Alfvén Mach number and density functions. We have constructed diverted-boundary equilibria pertinent to ITER and examined their characteristics, in particular, as concerns the impact of rotation on certain equilibrium quantities. It turns out that the rotation and its shear affect noticeably the pressure and toroidal current density with the impact on the current density being stronger in the parallel direction than in the toroidal one.

A form of MHD universal equations of unsteady incompressible fluid flow with variable elctroconductivity on heated moving plate

Directory of Open Access Journals (Sweden)

Boričić Zoran

2005-01-01

Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.

Safety in online media – freedom of the media; safety of media actors and media education

OpenAIRE

Moeller, Ch

2013-01-01

In this paper, prepared for the international conference ‘Mass Media – Society – Education: Media Safety Problems’ at the Chelyabinsk State University’s Department for Journalism and Media Education from September 30 – October 3, 2013, I would like to address three dimensions of media safety and security in online media.

Spike-like solitary waves in incompressible boundary layers driven by a travelling wave.

Science.gov (United States)

Feng, Peihua; Zhang, Jiazhong; Wang, Wei

2016-06-01

Nonlinear waves produced in an incompressible boundary layer driven by a travelling wave are investigated, with damping considered as well. As one of the typical nonlinear waves, the spike-like wave is governed by the driven-damped Benjamin-Ono equation. The wave field enters a completely irregular state beyond a critical time, increasing the amplitude of the driving wave continuously. On the other hand, the number of spikes of solitary waves increases through multiplication of the wave pattern. The wave energy grows in a sequence of sharp steps, and hysteresis loops are found in the system. The wave energy jumps to different levels with multiplication of the wave, which is described by winding number bifurcation of phase trajectories. Also, the phenomenon of multiplication and hysteresis steps is found when varying the speed of driving wave as well. Moreover, the nature of the change of wave pattern and its energy is the stability loss of the wave caused by saddle-node bifurcation.

Solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

International Nuclear Information System (INIS)

Rosenfeld, M.; Kwak, D.; Vinokur, M.

1988-01-01

A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.

2016-02-11

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Simulations of incompressible Navier Stokes equations on curved surfaces using discrete exterior calculus

Science.gov (United States)

Samtaney, Ravi; Mohamed, Mamdouh; Hirani, Anil

2015-11-01

We present examples of numerical solutions of incompressible flow on 2D curved domains. The Navier-Stokes equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. A conservative discretization of Navier-Stokes equations on simplicial meshes is developed based on discrete exterior calculus (DEC). The discretization is then carried out by substituting the corresponding discrete operators based on the DEC framework. By construction, the method is conservative in that both the discrete divergence and circulation are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step. Numerical examples include Taylor vortices on a sphere, Stuart vortices on a sphere, and flow past a cylinder on domains with varying curvature. Supported by the KAUST Office of Competitive Research Funds under Award No. URF/1/1401-01.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

Science.gov (United States)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

Energy Technology Data Exchange (ETDEWEB)

Snider, D.M. [SAIC, Albuquerque, NM (United States); O`Rourke, P.J. [Los Alamos National Lab., NM (United States); Andrews, M.J. [Texas A and M Univ., College Station, TX (United States). Dept. of Mechanical Engineering

1997-06-01

A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.

Fast pressure-correction method for incompressible Navier-Stokes equations in curvilinear coordinates

Science.gov (United States)

Aithal, Abhiram; Ferrante, Antonino

2017-11-01

In order to perform direct numerical simulations (DNS) of turbulent flows over curved surfaces and axisymmetric bodies, we have developed the numerical methodology to solve the incompressible Navier-Stokes (NS) equations in curvilinear coordinates for orthogonal meshes. The orthogonal meshes are generated by solving a coupled system of non-linear Poisson equations. The NS equations in orthogonal curvilinear coordinates are discretized in space on a staggered mesh using second-order central-difference scheme and are solved with an FFT-based pressure-correction method. The momentum equation is integrated in time using the second-order Adams-Bashforth scheme. The velocity field is advanced in time by applying the pressure correction to the approximate velocity such that it satisfies the divergence free condition. The novelty of the method stands in solving the variable coefficient Poisson equation for pressure using an FFT-based Poisson solver rather than the slower multigrid methods. We present the verification and validation results of the new numerical method and the DNS results of transitional flow over a curved axisymmetric body.

Media Literacy in Times of Media Divides

Directory of Open Access Journals (Sweden)

Kaja Žuran

2013-12-01

Full Text Available We live in a post-modern society, an information society, a society based around knowledge and participation, and above all in a media society. In a media culture where media holds a dominant position, we cannot overlook the emerging idea of a ‘media divide’ within the frame of media education, media literate individuals and the expansion of the traditional concept of media literacy. Firstly, we are in an era of technological revolution, and it is time to consider the meaning and function of media and how we experience it in our everyday life. Secondly, as a society we are subject to intense media invasion and we all need to learn how to use it to our benefit and apply a critical and autonomous perspective towards selecting media content. Otherwise the media divide between the media literate and illiterate will widen; but is there even a chance to overcome the supposed divide between those who are formally media educated and those who are not?

A cellular automaton simulation of contaminant transport in porous media

International Nuclear Information System (INIS)

Freed, D.M.; Simonson, S.A.

1995-01-01

A simulation tool to investigate radionuclide transport in porous groundwater flow is described. The flow systems of interest are those important in determining the fate of radionuclides emplaced in an underground repository, such as saturated matrix flow, matrix and fracture flow in the unsaturated zone, and viscous fingering in porous fractures. The work discussed here is confined to consideration of saturated flow in porous media carrying a dilute, sorptive species. The simulation technique is based on a special class of cellular automata known as lattice gas automata (LGA) which are capable of predicting hydrodynamic behavior. The original two-dimensional scheme (that of Frisch et. al. known as the FHP model) used particles of unit mass traveling on a triangular lattice with unit velocity and undergoing simple collisions which conserve mass and momentum at each node. These microscopic rules go over to the incompressible Navier-Stokes equations in the macroscopic limit. One of the strengths of this technique is the natural way that heterogeneities, such as boundaries, are accommodated. Complex geometries such as those associated with porous microstructures can be modeled effectively. Several constructions based on the FHP model have been devised, including techniques to eliminate statistical noise, extension to three dimensions, and the addition of surface tension which leads to multiphase flow

From Suitable Weak Solutions to Entropy Viscosity

KAUST Repository

Guermond, Jean-Luc

2010-12-16

This paper focuses on the notion of suitable weak solutions for the three-dimensional incompressible Navier-Stokes equations and discusses the relevance of this notion to Computational Fluid Dynamics. The purpose of the paper is twofold (i) to recall basic mathematical properties of the three-dimensional incompressible Navier-Stokes equations and to show how they might relate to LES (ii) to introduce an entropy viscosity technique based on the notion of suitable weak solution and to illustrate numerically this concept. © 2010 Springer Science+Business Media, LLC.

[Chronic otitis mediaChronic Otitis Media].

Science.gov (United States)

Kohles, N; Schulz, T; Eßer, D

2015-11-01

There are 2 different kinds of chronic otitis media: Otitis media chronica mesotympanalis and otitis media chronica epitympanalis (cholesteatoma). The incidence of chronic otitis media as reported in literature differs in a wide range. The incidence rates vary between 0.45 and 46%. Both, otitis media chronica mesotympanalis and cholesteatoma, lead to eardrum perforation due to lengthy and recurring inflammations. Furthermore, chronic otitis media is characterized by frequently recurring otorrhea and conductive hearing loss. Georg Thieme Verlag KG Stuttgart · New York.

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

Science.gov (United States)

Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

2000-01-01

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

Iterative methods for the detection of Hopf bifurcations in finite element discretisation of incompressible flow problems

International Nuclear Information System (INIS)

Cliffe, K.A.; Garratt, T.J.; Spence, A.

1992-03-01

This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection. (author)

Parallelization of pressure equation solver for incompressible N-S equations

International Nuclear Information System (INIS)

Ichihara, Kiyoshi; Yokokawa, Mitsuo; Kaburaki, Hideo.

1996-03-01

A pressure equation solver in a code for 3-dimensional incompressible flow analysis has been parallelized by using red-black SOR method and PCG method on Fujitsu VPP500, a vector parallel computer with distributed memory. For the comparison of scalability, the solver using the red-black SOR method has been also parallelized on the Intel Paragon, a scalar parallel computer with a distributed memory. The scalability of the red-black SOR method on both VPP500 and Paragon was lost, when number of processor elements was increased. The reason of non-scalability on both systems is increasing communication time between processor elements. In addition, the parallelization by DO-loop division makes the vectorizing efficiency lower on VPP500. For an effective implementation on VPP500, a large scale problem which holds very long vectorized DO-loops in the parallel program should be solved. PCG method with red-black SOR method applied to incomplete LU factorization (red-black PCG) has more iteration steps than normal PCG method with forward and backward substitution, in spite of same number of the floating point operations in a DO-loop of incomplete LU factorization. The parallelized red-black PCG method has less merits than the parallelized red-black SOR method when the computational region has fewer grids, because the low vectorization efficiency is obtained in red-black PCG method. (author)

Sur le volume élémentaire représentatif de la loi de perte de charge d'Ergun On the Representative Elementary Volume of the Ergun's Law

Directory of Open Access Journals (Sweden)

Herrmann H. J.

2006-12-01

Full Text Available Diverses expressions permettent de calculer la perte de charge occasionnée par le passage d'un fluide visqueux incompressible en écoulement à travers un milieu granulaire. Ces lois ont toutes une origine phénoménologique et sont obtenues à partir d'expériences réalisées à une échelle macroscopique. L'une d'entre elles, la loi d'Ergun, est couramment utilisée sous une forme locale dans des modèles de couplage fluide-solide pour réaliser le transfert de quantité de mouvement entre les deux phases sans réelle justification. Dans cet article, la simulation numérique directe des équations de Navier-Stokes est utilisée pour calculer les pertes de charge de fluide visqueux incompressible en écoulement à travers un milieu granulaire. Des simulations effectuées pour différents volumes de matériau granulaire permettent de retrouver la loi de perte de charge d'Ergun, de définir un volume élémentaire représentatif et de prouver le caractère local de cette loi. Several expressions can be used to predict the pressure drop caused by a viscous incompressible fluid flow through a granular media. These laws are empiricals and are obtained at macroscopic scale. One of these, Ergun's law, is currently used in a local form to modelling the momentum transfer between fluid and solid. There is not a real justification. In these study, the direct simulation of Navier-Stokes Equation is used to calculate pressure drop caused by viscous incompressible fluid flow through a granular media. Some simulations realised for different volume of granular media allow to find a representative elementary volume and prove the local character of the Ergun's law.

Surface wave propagation in a fluid-saturated incompressible ...

Indian Academy of Sciences (India)

dilatational and one rotational elastic waves in fluid-saturated porous solids. Biot theory ..... If the pore liquid is absent or gas is filled in the pores, then ρF ..... Biot M A (1962) Mechanics of deformation and acoustic propagation in porous media.

A model to analyse the flow of an incompressible Newtonian fluid through a rigid, homogeneous, isotropic and infinite porous medium

International Nuclear Information System (INIS)

Gama, R.M.S. da; Sampaio, R.

1985-01-01

The flow of an incompressible Newtonian fluid through a rigid, homogeneous, isotropic and infinite porous medium which has a given inicial distribuition of the mentioned fluid, is analyzed. It is proposed a model that assumes that the motion is caused by concentration gradient, but it does not consider the friction between the porous medium and the fluid. We solve an onedimensional case where the mathematical problem is reduced to the solution of a non-linear hyperbolic system of differential equations, subjected to an inicial condition given by a step function, called 'Riemann Problem'. (Author) [pt

A linearized system describing stationary incompressible viscous flow around rotating and translating bodies: improved decay estimates of the velocity and its gradient

Czech Academy of Sciences Publication Activity Database

Deuring, P.; Kračmar, S.; Nečasová, Šárka

2011-01-01

Roč. 2011, - (2011), s. 351-361 ISSN 1078-0947. [8th AIMS International Conference. Dresden, 25.05.2010-28.05.2010] R&D Projects: GA AV ČR IAA100190804; GA ČR(CZ) GAP201/11/1304 Institutional research plan: CEZ:AV0Z10190503 Keywords : viscous incompressible flow * rotating body * fundamental solution Subject RIV: BA - General Mathematics Impact factor: 0.913, year: 2011 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6978

Dissipation, intermittency, and singularities in incompressible turbulent flows

Science.gov (United States)

Debue, P.; Shukla, V.; Kuzzay, D.; Faranda, D.; Saw, E.-W.; Daviaud, F.; Dubrulle, B.

2018-05-01

We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation. In the presence of a singularity in the velocity field, this formulation yields a nonzero dissipation (inertial dissipation) in the limit of an infinite resolution. Moreover, at finite resolutions, it provides an expression for local interscale energy transfers down to the scale where the energy is dissipated by viscosity. In the presence of a quasisingularity that is regularized by viscosity, the formulation provides the contribution to the viscous dissipation due to the presence of the quasisingularity. Therefore, our formulation provides a concrete support to the general multifractal description of the intermittency. We present the maps and statistics of the interscale energy transfer and show that the extreme events of this transfer govern the intermittency corrections and are compatible with a refined similarity hypothesis based on this transfer. We characterize the probability distribution functions of these extreme events via generalized Pareto distribution analysis and find that the widths of the tails are compatible with a similarity of the second kind. Finally, we make a connection between the topological and the statistical properties of the extreme events of the interscale energy transfer field and its multifractal properties.

A GPU-based incompressible Navier-Stokes solver on moving overset grids

Science.gov (United States)

Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.

2013-07-01

In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.

Quantifying the Micromechanical Effects of Variable Cement in Granular Porous Media

Energy Technology Data Exchange (ETDEWEB)

Goodwin, Laurel B.; Boutt David F.

2010-02-18

The mechanical and hydrologic behavior of clastic rocks and sediments is fundamentally controlled by variables such as grain size and shape, sorting, grain and cement mineralogy, porosity, and %cement - parameters that are not used directly in field-scale models of coupled flow and deformation. To improve our understanding of the relationship between these micromechanical properties and bulk behavior we focused on (1) relating detailed, quantitative characterization of the grain-pore systems to both hydrologic and mechanical properties of a suite of variably quartz-cemented quartz arenite samples and (2) the use of a combination of discrete element method (DEM) and poroelastic models parameterized by data from the natural samples to isolate and compare the influence of changes in the mechanical and hydrologic properties of granular porous media due to changes in degree of cementation. Quartz overgrowths, the most common form of authigenic cements in sandstones, are responsible for significant porosity and permeability reduction. The distribution of quartz overgrowths is controlled by available pore space and the crystallographic orientations of individual quartz grains. Study of the St. Peter Sandstone allowed evaluation of the relative effects of quartz cementation and compaction on final grain and pore morphology, showing that progressive quartz cementation modifies the grain framework in consistent, predictable ways. Detailed microstructural characterization and multiple regression analyses show that with progressive diagenesis, the number and length of grain contacts increases as the number of pores increases, the number of large, well-connected pores decreases, and pores become rounder. These changes cause a decrease in pore size variability that leads to a decrease in bulk permeability and both stiffening and strengthening of the grain framework. The consistent nature of these changes allows us to predict variations in hydrologic and mechanical properties

A high-resolution code for large eddy simulation of incompressible turbulent boundary layer flows

KAUST Repository

Cheng, Wan

2014-03-01

We describe a framework for large eddy simulation (LES) of incompressible turbulent boundary layers over a flat plate. This framework uses a fractional-step method with fourth-order finite difference on a staggered mesh. We present several laminar examples to establish the fourth-order accuracy and energy conservation property of the code. Furthermore, we implement a recycling method to generate turbulent inflow. We use the stretched spiral vortex subgrid-scale model and virtual wall model to simulate the turbulent boundary layer flow. We find that the case with Reθ ≈ 2.5 × 105 agrees well with available experimental measurements of wall friction, streamwise velocity profiles and turbulent intensities. We demonstrate that for cases with extremely large Reynolds numbers (Reθ = 1012), the present LES can reasonably predict the flow with a coarse mesh. The parallel implementation of the LES code demonstrates reasonable scaling on O(103) cores. © 2013 Elsevier Ltd.

A meshless local radial basis function method for two-dimensional incompressible Navier-Stokes equations

KAUST Repository

Wang, Zhiheng

2014-12-10

A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.

Self-organization phenomena and decaying self-similar state in two-dimensional incompressible viscous fluids

International Nuclear Information System (INIS)

Kondoh, Yoshiomi; Serizawa, Shunsuke; Nakano, Akihiro; Takahashi, Toshiki; Van Dam, James W.

2004-01-01

The final self-similar state of decaying two-dimensional (2D) turbulence in 2D incompressible viscous flow is analytically and numerically investigated for the case with periodic boundaries. It is proved by theoretical analysis and simulations that the sinh-Poisson state cω=-sinh(βψ) is not realized in the dynamical system of interest. It is shown by an eigenfunction spectrum analysis that a sufficient explanation for the self-organization to the decaying self-similar state is the faster energy decay of higher eigenmodes and the energy accumulation to the lowest eigenmode for given boundary conditions due to simultaneous normal and inverse cascading by nonlinear mode couplings. The theoretical prediction is demonstrated to be correct by simulations leading to the lowest eigenmode of {(1,0)+(0,1)} of the dissipative operator for the periodic boundaries. It is also clarified that an important process during nonlinear self-organization is an interchange between the dominant operators, which leads to the final decaying self-similar state

A two pressure-velocity approach for immersed boundary methods in three dimensional incompressible flows

International Nuclear Information System (INIS)

Sabir, O; Ahmad, Norhafizan; Nukman, Y; Tuan Ya, T M Y S

2013-01-01

This paper describes an innovative method for computing fluid solid interaction using Immersed boundary methods with two stage pressure-velocity corrections. The algorithm calculates the interactions between incompressible viscous flows and a solid shape in three-dimensional domain. The fractional step method is used to solve the Navier-Stokes equations in finite difference schemes. Most of IBMs are concern about exchange of the momentum between the Eulerian variables (fluid) and the Lagrangian nodes (solid). To address that concern, a new algorithm to correct the pressure and the velocity using Simplified Marker and Cell method is added. This scheme is applied on staggered grid to simulate the flow past a circular cylinder and study the effect of the new stage on calculations cost. To evaluate the accuracy of the computations the results are compared with the previous software results. The paper confirms the capacity of new algorithm for accurate and robust simulation of Fluid Solid Interaction with respect to pressure field

Lattice Boltzmann simulations of heat transfer in fully developed periodic incompressible flows

Science.gov (United States)

Wang, Zimeng; Shang, Helen; Zhang, Junfeng

2017-06-01

Flow and heat transfer in periodic structures are of great interest for many applications. In this paper, we carefully examine the periodic features of fully developed periodic incompressible thermal flows, and incorporate them in the lattice Boltzmann method (LBM) for flow and heat transfer simulations. Two numerical approaches, the distribution modification (DM) approach and the source term (ST) approach, are proposed; and they can both be used for periodic thermal flows with constant wall temperature (CWT) and surface heat flux boundary conditions. However, the DM approach might be more efficient, especially for CWT systems since the ST approach requires calculations of the streamwise temperature gradient at all lattice nodes. Several example simulations are conducted, including flows through flat and wavy channels and flows through a square array with circular cylinders. Results are compared to analytical solutions, previous studies, and our own LBM calculations using different simulation techniques (i.e., the one-module simulation vs. the two-module simulation, and the DM approach vs. the ST approach) with good agreement. These simple, however, representative simulations demonstrate the accuracy and usefulness of our proposed LBM methods for future thermal periodic flow simulations.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

Science.gov (United States)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Managing Media: Segmenting Media Through Consumer Expectancies

Directory of Open Access Journals (Sweden)

Matt Eastin

2014-04-01

Full Text Available It has long been understood that consumers are motivated to media differently. However, given the lack of comparative model analysis, this assumption is without empirical validation, and thus, the orientation of segmentation from a media management perspective is without motivational grounds. Thus, evolving the literature on media consumption, the current study develops and compares models of media segmentation within the context of use. From this study, six models of media expectancies were constructed so that motivational differences between media (i.e., local and national newspapers, network and cable television, radio, and Internet could be observed. Utilizing higher order statistical analyses the data indicates differences across a model comparison approach for media motivations. Furthermore, these differences vary across numerous demographic factors. Results afford theoretical advancement within the literature of consumer media consumption as well as provide media planners’ insight into consumer choices.

Calculation of laminar incompressible fluid flow and heat transfer during spherical annulus filling

International Nuclear Information System (INIS)

Tuft, D.B.

1979-04-01

A method of computing laminar incompressible fluid-flow and heat transfer during the filling of a spherical annulus is presented. Transient fluid temperatures and heat flux rates in the spherical annulus are calculated for an insulated outer sphere and a constant temperature inner sphere with heated water filling the annulus from the bottom. To achieve a solution, laminar axially symmetric flow is assumed and the Marker-and-Cell (MAC) free surface computational method is applied to this problem in spherical coordinates. Changes in the standard MAC treatment are incorporated and special methods for handling the free surface are introduced. A variable mesh is used to improve resolution near the inner sphere where temperature and velocity gradients are steep and the governing equations are derived for variable fluid properties to allow an eddy viscosity turbulence model to be applied later. Calculations of velocity, temperature, and inner sphere heat flux in a spherical annulus of 139.7 mm inner radius, and 168.3 mm outer radius within an inlet tube diameter of 38.1 mm are presented

Unified theory of damping of linear surface Alfven waves in inhomogeneous incompressible plasmas

International Nuclear Information System (INIS)

Ruderman, M.S.; Goossens, M.

1996-01-01

The viscous damping of surface Alfven waves in a non-uniform plasma is studied in the context of linear and incompressible MHD. It is shown that damping due to resonant absorption and damping on a true discontinuity are two limiting cases of the continuous variation of the damping rate with respect to the dimensionless number Rg = Δλ 2 Re, where Δ is the relative variation of the local Alfven velocity, λ is the ratio of the thickness of the inhomogeneous layer to the wavelength, and Re is the viscous Reynolds number. The analysis is restricted to waves with wavelengths that are long in comparison with the extent of the non-uniform layer (λ '' >'' 1) values of Rg. For very small values of Rg, the damping rate agrees with that found for a true discontinuity, while for very large values of Rg, it agrees with the damping rate due to resonant absorption. The dispersion relation is subsequently studied numerically over a wide range of values of Rg, revealing a continuous but non-monotonic variation of the damping rate with respect to Rg. (Author)

Tensor formulation of the model equations on strong conservation form for an incompressible flow in general coordinates

DEFF Research Database (Denmark)

Jørgensen, Bo Hoffmann

2003-01-01

This brief report expresses the basic equations of an incompressible flow model in a form which can be translated easily into the form used by a numerical solver. The application of tensor notation makes is possible to effectively address the issue ofnumerical robustness and stating the model...... 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...... form of the equations is included which allows for special solutions to be developed in the transformedcoordinate system. Examples of applications are atmospheric flows over complex terrain, aerodynamically flows, industrial flows and environmental flows....

Media relations after the introduction of social media

OpenAIRE

Mesila, Helin

2010-01-01

In the light of the popularity of social media on one hand, and the contradictive relationships between journalists and public relations practitioners on the other hand, the thesis studies media relations after the introduction of social media. The study focuses on media relations in Estonian public relations scenery. The research answers to the questions: - What are media relations today? - What are the functions of social media and media relations in organizational communication? ...

A Navier-Stokes/Cahn-Hilliard model for the simulation of three phase immiscible incompressible flows

International Nuclear Information System (INIS)

Celine Lapuerta; Bruno Piar; Franck Boyer; Philippe Angot; Michel Quintard

2005-01-01

This paper presents a Navier-Stokes/Cahn-Hilliard model designed for incompressible flows of three immiscible phases, characterized by different surface tensions and without phase change. This physical context is relevant to study the late phase of a hypothetical severe accident in a nuclear pressurized water reactor. Thanks to a suitable choice of a free energy and a particular form of the Cahn-Hilliard equation, the evolution of the three phases is described by only two order parameters. Moreover, this model allows the simulation of purely two phase flows as a limiting case: no artificial apparition of the third phase occurs if this later is physically absent which contrasts with others models of the literature. We examine the spreading of a liquid lens at the interface between two stratified phases. We present results showing that the method gives correct contact angles and pressure jumps, at equilibrium. (authors)

Comparative analysis of different variants of the Uzawa algorithm in problems of the theory of elasticity for incompressible materials

Directory of Open Access Journals (Sweden)

Nikita E. Styopin

2016-09-01

Full Text Available Different variants of the Uzawa algorithm are compared with one another. The comparison is performed for the case in which this algorithm is applied to large-scale systems of linear algebraic equations. These systems arise in the finite-element solution of the problems of elasticity theory for incompressible materials. A modification of the Uzawa algorithm is proposed. Computational experiments show that this modification improves the convergence of the Uzawa algorithm for the problems of solid mechanics. The results of computational experiments show that each variant of the Uzawa algorithm considered has its advantages and disadvantages and may be convenient in one case or another.

SOCIAL MEDIA

Science.gov (United States)

RESPONSIBILITY CENTCOM COALITION MEDIA SOCIAL MEDIA NEWS ARTICLES PRESS RELEASES IMAGERY VIDEOS TRANSCRIPTS VISITORS AND PERSONNEL FAMILY CENTER FAMILY READINESS CENTCOM WEBMAIL SOCIAL MEDIA SECURITY ACCOUNTABILITY HomeMEDIASOCIAL MEDIA Social Media CENTCOM'S ENGLISH SOCIAL MEDIA ACCOUNTS There are many U.S. military commands

Coupled, parabolic-marching method for the prediction of three-dimensional viscous incompressible turbomachinery flows. Doctoral thesis

Energy Technology Data Exchange (ETDEWEB)

Kirtley, K.R.

1988-10-01

A new coupled parabolic-marching method was developed to solve the three-dimensional incompressible Navier-Stokes equation for turbulent turbomachinery flows. Earlier space-marching methods were analyzed to determine their global stability during multiple passes of the computational domain. The methods were found to be unconditionally unstable even when an extra equation for the pressure, namely the Poisson equation for the pressure, was used between passes of the domain. Relaxation of one constraint during the solution process was found to be necessary for the successful calculation of a complex flow.Thus, the method of pseudocompressibility was introduced into the partially parabolized Navier-Stokes equation to relax the mass flow constraint during a forward-marching integration as well as globally stable during successive passes of the domain. With consistent discretization, the new method was found to be convergent.

Non-linear dynamo waves in an incompressible medium when the turbulence dissipative coefficients depend on temperature

Directory of Open Access Journals (Sweden)

A. D. Pataraya

1997-01-01

Full Text Available Non-linear α-ω; dynamo waves existing in an incompressible medium with the turbulence dissipative coefficients depending on temperature are studied in this paper. We investigate of α-ω solar non-linear dynamo waves when only the first harmonics of magnetic induction components are included. If we ignore the second harmonics in the non-linear equation, the turbulent magnetic diffusion coefficient increases together with the temperature, the coefficient of turbulent viscosity decreases, and for an interval of time the value of dynamo number is greater than 1. In these conditions a stationary solution of the non-linear equation for the dynamo wave's amplitude exists; meaning that the magnetic field is sufficiently excited. The amplitude of the dynamo waves oscillates and becomes stationary. Using these results we can explain the existence of Maunder's minimum.

Linearized stationary incompressible flow around rotating and translating bodies: Asymptotic profile of the velocity gradient and decay estimate of the second derivatives of the velocity

Czech Academy of Sciences Publication Activity Database

Deuring, P.; Kračmar, S.; Nečasová, Šárka

2012-01-01

Roč. 252, č. 1 (2012), s. 459-476 ISSN 0022-0396 R&D Projects: GA AV ČR IAA100190804; GA ČR(CZ) GAP201/11/1304 Institutional research plan: CEZ:AV0Z10190503 Keywords : viscous incompressible flow * rotating body * rundamental solution * decay * asymptotic profile * Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 1.480, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022039611003573

Dual plane problems for creeping flow of power-law incompressible medium

Directory of Open Access Journals (Sweden)

Dmitriy S. Petukhov

2016-09-01

Full Text Available In this paper, we consider the class of solutions for a creeping plane flow of incompressible medium with power-law rheology, which are written in the form of the product of arbitrary power of the radial coordinate by arbitrary function of the angular coordinate of the polar coordinate system covering the plane. This class of solutions represents the asymptotics of fields in the vicinity of singular points in the domain occupied by the examined medium. We have ascertained the duality of two problems for a plane with wedge-shaped notch, at which boundaries in one of the problems the vector components of the surface force vanish, while in the other—the vanishing components are the vector components of velocity, We have investigated the asymptotics and eigensolutions of the dual nonlinear eigenvalue problems in relation to the rheological exponent and opening angle of the notch for the branch associated with the eigenvalue of the Hutchinson–Rice–Rosengren problem learned from the problem of stress distribution over a notched plane for a power law medium. In the context of the dual problem we have determined the velocity distribution in the flow of power-law medium at the vertex of a rigid wedge, We have also found another two eigenvalues, one of which was determined by V. V. Sokolovsky for the problem of power-law fluid flow in a convergent channel.

CLASSICAL MEDIA RELATIONS AND NEW MEDIA RELATIONS IN SPORT

Directory of Open Access Journals (Sweden)

Alexandru Lucian MIHAI

2014-06-01

Full Text Available Media relations in sport mean maintenance of networks and positive relationships with people in the media to obtain positive media exposure for a sport product (informal and formal information sessions with media representatives. Because of the pervasive influence the media has on marketing success, sport marketers must make concerted efforts to create a positive relationship between their sport event and the media. They may accomplish this by providing the media with press releases, having news conferences, having media-day events (in which the media are invited to interact with the players, coaches, and administrators, providing media guides for the respective sport events and so on. Each of these activities promotes active involvement from the media, which will subsequently contribute to relationship building with the community.

Media education and media influence on youth

OpenAIRE

LILÁK, Karel

2011-01-01

Bachelor´s work is focused on the questions of the medial education and the medias themselves. This work also investigate with the influence of the action of medias to the students of apprenticeship. The first part of the theoretical work has generally explains what is media education, what is its significance for society and for the benefit of education in school. They are given functions, types and objectives of media education and communications capabilities via the media. The second part ...

A large-scale layered stationary convection of a incompressible viscous fluid under the action of shear stresses at the upper boundary. Temperature and presure field investigation

Directory of Open Access Journals (Sweden)

Natal'ya V. Burmasheva

2017-12-01

Full Text Available In this paper a new exact solution of an overdetermined system of Oberbeck–Boussinesq equations that describes a stationary shear flow of a viscous incompressible fluid in an infinite layer is under study. The given exact solution is a generalization of the Ostroumov–Birich class for a layered unidirectional flow. In the proposed solution, the horizontal velocities depend only on the transverse coordinate z. The temperature field and the pressure field are three-dimensional. In contradistinction to the Ostroumov–Birich solution, in the solution presented in the paper the horizontal temperature gradients are linear functions of the $z$ coordinate. This structure of the exact solution allows us to find a nontrivial solution of the Oberbeck–Boussinesq equations by means of the identity zero of the incompressibility equation. This exact solution is suitable for investigating large-scale flows of a viscous incompressible fluid by quasi-two-dimensional equations. Convective fluid motion is caused by the setting of tangential stresses on the free boundary of the layer. Inhomogeneous thermal sources are given on both boundaries. The pressure in the fluid at the upper boundary coincides with the atmospheric pressure. The paper focuses on the study of temperature and pressure fields, which are described by polynomials of three variables. The features of the distribution of the temperature and pressure profiles, which are polynomials of the seventh and eighth degree, respectively, are discussed in detail. To analyze the properties of temperature and pressure, algebraic methods are used to study the number of roots on a segment. It is shown that the background temperature and the background pressure are nonmonotonic functions. The temperature field is stratified into zones that form the thermocline and the thermal boundary layer near the boundaries of the fluid layer. Investigation of the properties of the pressure field showed that it is stratified

A steady weak solution of the equations of motion of a viscous incompressible fluid through porous media in a domain with a non-compact boundary

Czech Academy of Sciences Publication Activity Database

Akyildiz, F.T.; Neustupa, Jiří; Siginer, D.

2012-01-01

Roč. 119, č. 1 (2012), s. 23-42 ISSN 0167-8019 R&D Projects: GA AV ČR IAA100190905 Institutional research plan: CEZ:AV0Z10190503 Keywords : flows in porous media * steady-state problems * inhomogeneous boundary data Subject RIV: BA - General Mathematics Impact factor: 0.985, year: 2012 http://www.springerlink.com/content/t8n71p67w2282t96/

Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier--Stokes Equations

KAUST Repository

Tamellini, L.; Le Maî tre, O.; Nouy, A.

2014-01-01

In this paper we consider a proper generalized decomposition method to solve the steady incompressible Navier-Stokes equations with random Reynolds number and forcing term. The aim of such a technique is to compute a low-cost reduced basis approximation of the full stochastic Galerkin solution of the problem at hand. A particular algorithm, inspired by the Arnoldi method for solving eigenproblems, is proposed for an efficient greedy construction of a deterministic reduced basis approximation. This algorithm decouples the computation of the deterministic and stochastic components of the solution, thus allowing reuse of preexisting deterministic Navier-Stokes solvers. It has the remarkable property of only requiring the solution of m uncoupled deterministic problems for the construction of an m-dimensional reduced basis rather than M coupled problems of the full stochastic Galerkin approximation space, with m l M (up to one order of magnitudefor the problem at hand in this work). © 2014 Society for Industrial and Applied Mathematics.

Development of a Front Tracking Method for Two-Phase Micromixing of Incompressible Viscous Fluids with Interfacial Tension in Solvent Extraction

Energy Technology Data Exchange (ETDEWEB)

Zhou, Yijie [ORNL; Lim, Hyun-Kyung [ORNL; de Almeida, Valmor F [ORNL; Navamita, Ray [State University of New York, Stony Brook; Wang, Shuqiang [State University of New York, Stony Brook; Glimm, James G [ORNL; Li, Xiao-lin [State University of New York, Stony Brook; Jiao, Xiangmin [ORNL

2012-06-01

This progress report describes the development of a front tracking method for the solution of the governing equations of motion for two-phase micromixing of incompressible, viscous, liquid-liquid solvent extraction processes. The ability to compute the detailed local interfacial structure of the mixture allows characterization of the statistical properties of the two-phase mixture in terms of droplets, filaments, and other structures which emerge as a dispersed phase embedded into a continuous phase. Such a statistical picture provides the information needed for building a consistent coarsened model applicable to the entire mixing device. Coarsening is an undertaking for a future mathematical development and is outside the scope of the present work. We present here a method for accurate simulation of the micromixing dynamics of an aqueous and an organic phase exposed to intense centrifugal force and shearing stress. The onset of mixing is the result of the combination of the classical Rayleigh- Taylor and Kelvin-Helmholtz instabilities. A mixing environment that emulates a sector of the annular mixing zone of a centrifugal contactor is used for the mathematical domain. The domain is small enough to allow for resolution of the individual interfacial structures and large enough to allow for an analysis of their statistical distribution of sizes and shapes. A set of accurate algorithms for this application requires an advanced front tracking approach constrained by the incompressibility condition. This research is aimed at designing and implementing these algorithms. We demonstrate verification and convergence results for one-phase and unmixed, two-phase flows. In addition we report on preliminary results for mixed, two-phase flow for realistic operating flow parameters.

Compact stars with a small electric charge: the limiting radius to mass relation and the maximum mass for incompressible matter

Energy Technology Data Exchange (ETDEWEB)

Lemos, Jose P.S.; Lopes, Francisco J.; Quinta, Goncalo [Universidade de Lisboa, UL, Departamento de Fisica, Centro Multidisciplinar de Astrofisica, CENTRA, Instituto Superior Tecnico, IST, Lisbon (Portugal); Zanchin, Vilson T. [Universidade Federal do ABC, Centro de Ciencias Naturais e Humanas, Santo Andre, SP (Brazil)

2015-02-01

One of the stiffest equations of state for matter in a compact star is constant energy density and this generates the interior Schwarzschild radius to mass relation and the Misner maximum mass for relativistic compact stars. If dark matter populates the interior of stars, and this matter is supersymmetric or of some other type, some of it possessing a tiny electric charge, there is the possibility that highly compact stars can trap a small but non-negligible electric charge. In this case the radius to mass relation for such compact stars should get modifications. We use an analytical scheme to investigate the limiting radius to mass relation and the maximum mass of relativistic stars made of an incompressible fluid with a small electric charge. The investigation is carried out by using the hydrostatic equilibrium equation, i.e., the Tolman-Oppenheimer-Volkoff (TOV) equation, together with the other equations of structure, with the further hypothesis that the charge distribution is proportional to the energy density. The approach relies on Volkoff and Misner's method to solve the TOV equation. For zero charge one gets the interior Schwarzschild limit, and supposing incompressible boson or fermion matter with constituents with masses of the order of the neutron mass one finds that the maximum mass is the Misner mass. For a small electric charge, our analytical approximating scheme, valid in first order in the star's electric charge, shows that the maximum mass increases relatively to the uncharged case, whereas the minimum possible radius decreases, an expected effect since the new field is repulsive, aiding the pressure to sustain the star against gravitational collapse. (orig.)

Simulation of incompressible flows with heat and mass transfer using parallel finite element method

Directory of Open Access Journals (Sweden)

Jalal Abedi

2003-02-01

Full Text Available The stabilized finite element formulations based on the SUPG (Stream-line-Upwind/Petrov-Galerkin and PSPG (Pressure-Stabilization/Petrov-Galerkin methods are developed and applied to solve buoyancy-driven incompressible flows with heat and mass transfer. The SUPG stabilization term allows us to solve flow problems at high speeds (advection dominant flows and the PSPG term eliminates instabilities associated with the use of equal order interpolation functions for both pressure and velocity. The finite element formulations are implemented in parallel using MPI. In parallel computations, the finite element mesh is partitioned into contiguous subdomains using METIS, which are then assigned to individual processors. To ensure a balanced load, the number of elements assigned to each processor is approximately equal. To solve nonlinear systems in large-scale applications, we developed a matrix-free GMRES iterative solver. Here we totally eliminate a need to form any matrices, even at the element levels. To measure the accuracy of the method, we solve 2D and 3D example of natural convection flows at moderate to high Rayleigh numbers.

A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

KAUST Repository

Xie, Yu; Wodo, Olga; Ganapathysubramanian, Baskar

2016-01-01

In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.

A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

KAUST Repository

Xie, Yu

2016-10-04

In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.

Magnetohydrodynamics effect on three-dimensional viscous incompressible flow between two horizontal parallel porous plates and heat transfer with periodic injection/suction

Directory of Open Access Journals (Sweden)

R. C. Chaudhary

2004-11-01

Full Text Available We investigate the hydromagnetic effect on viscous incompressible flow between two horizontal parallel porous flat plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by periodic suction through the plate in uniform motion. The flow becomes three dimensional due to this injection/suction velocity. Approximate solutions are obtained for the flow field, the pressure, the skin-friction, the temperature field, and the rate of heat transfer. The dependence of solution on M (Hartmann number and λ (injection/suction is investigated by the graphs and tables.

Media identities and media-influenced indentifications Visibility and identity recognition in the media

Directory of Open Access Journals (Sweden)

Víctor Fco. Sampedro Blanco

2004-10-01

Full Text Available The media establish, in large part, the patterns of visibility and public recognition of collective identities. We define media identities as those that are the object of production and diffusion by the media. From this discourse, the communities and individuals elaborate media-influenced identifications; that is, processes of recognition or banishment; (rearticulating the identity markers that the media offer with other cognitive and emotional sources. The generation and appropriation of the identities are subjected to a media hierarchisation that influences their normalisation or marginalisation. The identities presented by the media and assumed by the audience as part of the official, hegemonic discourse are normalised, whereas the identities and identifications formulated in popular and minority terms are marginalised. After presenting this conceptual and analytical framework, this study attempts to outline the logics that condition the presentation, on the one hand, andthe public recognition, on the other hand, of contemporary identities.

On the convergence of a fully discrete scheme of LES type to physically relevant solutions of the incompressible Navier-Stokes

Science.gov (United States)

Berselli, Luigi C.; Spirito, Stefano

2018-06-01

Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The large eddy simulation (LES) models are efficient tools to approximate turbulent fluids, and an important step in the validation of these models is the ability to reproduce relevant properties of the flow. In this paper, we consider a fully discrete approximation of the Navier-Stokes-Voigt model by an implicit Euler algorithm (with respect to the time variable) and a Fourier-Galerkin method (in the space variables). We prove the convergence to weak solutions of the incompressible Navier-Stokes equations satisfying the natural local entropy condition, hence selecting the so-called physically relevant solutions.

Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2004-01-01

We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least

Komunikasi Krisis di Era New Media dan Social Media

OpenAIRE

Prastya, Narayana Mahendra

2016-01-01

New media and social media have changed the practice of public relations. One area that changed is crisis communication. Because of these new technologies, crisis can be more complex. The pace of information, the uncertainty, and the rumors, are increasing. Public relations practitioners should include the new media and social media use in their crisis communication plan. Before doing that, public relations practitioners should change their mindset about social media and new media. The first ...

Media education and media enlightenment as attributes of information society

Directory of Open Access Journals (Sweden)

Лилия Борисовна Белоглазова

2014-12-01

Full Text Available The article deals with the problem of the functioning of media-education and media-enlightenment in modern society. Focuses on the impact of this socio-cultural phenomenon on consciousness of members of the Information Society. Are the main characteristics of media-education and media-education and media-enlightenment. Concludes that media-education and media-enlightenment forms unscientific and anti-scientific thinking and style speech.

Weakly nonlinear incompressible Rayleigh-Taylor instability growth at cylindrically convergent interfaces

International Nuclear Information System (INIS)

Wang, L. F.; He, X. T.; Wu, J. F.; Zhang, W. Y.; Ye, W. H.

2013-01-01

A weakly nonlinear (WN) model has been developed for the incompressible Rayleigh-Taylor instability (RTI) in cylindrical geometry. The transition from linear to nonlinear growth is analytically investigated via a third-order solutions for the cylindrical RTI initiated by a single-mode velocity perturbation. The third-order solutions can depict the early stage of the interface asymmetry due to the bubble-spike formation, as well as the saturation of the linear (exponential) growth of the fundamental mode. The WN results in planar RTI [Wang et al., Phys. Plasmas 19, 112706 (2012)] are recovered in the limit of high-mode number perturbations. The difference between the WN growth of the RTI in cylindrical geometry and in planar geometry is discussed. It is found that the interface of the inward (outward) development spike/bubble is extruded (stretched) by the additional inertial force in cylindrical geometry compared with that in planar geometry. For interfaces with small density ratios, the inward growth bubble can grow fast than the outward growth spike in cylindrical RTI. Moreover, a reduced formula is proposed to describe the WN growth of the RTI in cylindrical geometry with an acceptable precision, especially for small-amplitude perturbations. Using the reduced formula, the nonlinear saturation amplitude of the fundamental mode and the phases of the Fourier harmonics are studied. Thus, it should be included in applications where converging geometry effects play an important role, such as the supernova explosions and inertial confinement fusion implosions.

Sensitive Media

Directory of Open Access Journals (Sweden)

Malinowska Anna

2017-12-01

Full Text Available The paper engages with what we refer to as “sensitive media,” a concept associated with developments in the overall media environment, our relationships with media devices, and the quality of the media themselves. Those developments point to the increasing emotionality of the media world and its infrastructures. Mapping the trajectories of technological development and impact that the newer media exert on human condition, our analysis touches upon various forms of emergent affect, emotion, and feeling in order to trace the histories and motivations of the sensitization of “the media things” as well as the redefinition of our affective and emotional experiences through technologies that themselves “feel.”

Social Media Sites

Science.gov (United States)

Media Sites Site Registration Contact Us Search AF.mil: Home > AF Sites > Social Media Sites Social Media Welcome to the Air Force social media directory! The directory is a one-stop shop of official Air Force social media pages across various social media sites. Social media is all about

Stereotypes in media and media literacy among young people

Directory of Open Access Journals (Sweden)

Đerić Ivana

2006-01-01

Full Text Available Young people, the most common consumers of media content, bear out the view that media shapes people’s lives. Therefore we must not underestimate the effect media exerts on young people’s values and behavioral patterns. Television is the medium which draws children and young people for the greatest part of their free time. Regardless whether television programs are described as positive or negative, whether they abound with stereotypes or not, it is important that young people develop a critical attitude towards them so that they may resist different forms of media manipulation. The paper discusses how stereotypes are generated and used by media and the manners in which stereotypical concepts affect young people’s attitudes. It highlights the importance of the development of media literacy which implies a critical attitude towards media images and discourses, the development of criteria for the selection and evaluation of information broadcast by media, the development of skills in interpreting and understanding stereotypical concepts and familiarity with alternative forms of media culture. The paper draws special attention to the issue of media education. The conclusion is that schools should offer media literacy as part of their curriculum and in it possible solutions to the problems discussed. .

Isotopic Dependence of the Giant Monopole Resonance in the Even-A 112-124Sn Isotopes and the Asymmetry Term in Nuclear Incompressibility

International Nuclear Information System (INIS)

Li, T.; Garg, U.; Liu, Y.; Marks, R.; Nayak, B. K.; Rao, P. V. Madhusudhana; Fujiwara, M.; Hashimoto, H.; Kawase, K.; Nakanishi, K.; Okumura, S.; Yosoi, M.; Itoh, M.; Ichikawa, M.; Matsuo, R.; Terazono, T.; Uchida, M.; Kawabata, T.; Akimune, H.; Iwao, Y.

2007-01-01

The strength distributions of the giant monopole resonance (GMR) have been measured in the even-A Sn isotopes (A=112-124) with inelastic scattering of 400-MeV α particles in the angular range 0 deg. - 8.5 deg. We find that the experimentally observed GMR energies of the Sn isotopes are lower than the values predicted by theoretical calculations that reproduce the GMR energies in 208 Pb and 90 Zr very well. From the GMR data, a value of K τ =-550±100 MeV is obtained for the asymmetry term in the nuclear incompressibility

Isotopic Dependence of the Giant Monopole Resonance in the Even-A Sn112 124 Isotopes and the Asymmetry Term in Nuclear Incompressibility

Science.gov (United States)

Li, T.; Garg, U.; Liu, Y.; Marks, R.; Nayak, B. K.; Rao, P. V. Madhusudhana; Fujiwara, M.; Hashimoto, H.; Kawase, K.; Nakanishi, K.; Okumura, S.; Yosoi, M.; Itoh, M.; Ichikawa, M.; Matsuo, R.; Terazono, T.; Uchida, M.; Kawabata, T.; Akimune, H.; Iwao, Y.; Murakami, T.; Sakaguchi, H.; Terashima, S.; Yasuda, Y.; Zenihiro, J.; Harakeh, M. N.

2007-10-01

The strength distributions of the giant monopole resonance (GMR) have been measured in the even-A Sn isotopes (A=112 124) with inelastic scattering of 400-MeV α particles in the angular range 0° 8.5°. We find that the experimentally observed GMR energies of the Sn isotopes are lower than the values predicted by theoretical calculations that reproduce the GMR energies in Pb208 and Zr90 very well. From the GMR data, a value of Kτ=-550±100MeV is obtained for the asymmetry term in the nuclear incompressibility.

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

Energy Technology Data Exchange (ETDEWEB)

Sidler, Rolf, E-mail: rsidler@gmail.com [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland); Carcione, José M. [Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010 Sgonico, Trieste (Italy); Holliger, Klaus [Center for Research of the Terrestrial Environment, University of Lausanne, CH-1015 Lausanne (Switzerland)

2013-02-15

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

Science.gov (United States)

Faghih Shojaei, Mostafa; Yavari, Arash

2018-05-01

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

Media evolution and ‘epi-technic’ digital media: Media as cultural selection mechanisms

DEFF Research Database (Denmark)

Olesen, Mogens

2016-01-01

The explosive development of new digital media technologies is often described as a media evolution but hardly ever is the concept of ‘media evolution’ taken at face value. This article takes up that challenge by combining cultural evolution theories with medium theory. The article argues that bi...

Flow of miscible and immiscible hydrocarbons in heterogeneous porous media

Energy Technology Data Exchange (ETDEWEB)

Butts, M.B.

1996-12-31

A series of large-scale two-dimensional physical model studies has been carried out in order to better understand and predict the multiphase flow of hydrocarbon contaminants and the release of the water-soluble fraction of such contaminants into the groundwater stream. The detailed measurements of the fluid saturations within the bulk hydrocarbon plume as well as the aqueous concentrations recorded downstream should provide a useful data set for testing and improving numerical models of both multiphase flow and transport. Predictions of a numerical model of immiscible multiphase flow developed in the petroleum industry were found to compare favourably with the observed oil plume for the case of an immiscible oil spill. Nevertheless, subtle layering within the experimental flume altered the long-term development of the oil plume in a manner not predicted by the numerical model. A stochastic model for three-dimensional, two-phase incompressible flow in heterogeneous soil and rock formations is developed. Analytical solutions for the resulting stochastic differential equations are derived for asymptotic flows using a perturbation approach. These solutions were used to derive general expressions for the large-scale (effective) properties for large-scale two-phase flow in porous media. An important observation from this analysis is that general large-scale flow in heterogeneous soils cannot be predicted on the basis of simple averages of the soil hydraulic properties alone. The large-scale capillary pressure saturation relation is evaluated for imbibition into a wet soil or rock formation. (EG) 194 refs.

Flow of miscible and immiscible hydrocarbons in heterogeneous porous media

Energy Technology Data Exchange (ETDEWEB)

Butts, M B

1997-12-31

A series of large-scale two-dimensional physical model studies has been carried out in order to better understand and predict the multiphase flow of hydrocarbon contaminants and the release of the water-soluble fraction of such contaminants into the groundwater stream. The detailed measurements of the fluid saturations within the bulk hydrocarbon plume as well as the aqueous concentrations recorded downstream should provide a useful data set for testing and improving numerical models of both multiphase flow and transport. Predictions of a numerical model of immiscible multiphase flow developed in the petroleum industry were found to compare favourably with the observed oil plume for the case of an immiscible oil spill. Nevertheless, subtle layering within the experimental flume altered the long-term development of the oil plume in a manner not predicted by the numerical model. A stochastic model for three-dimensional, two-phase incompressible flow in heterogeneous soil and rock formations is developed. Analytical solutions for the resulting stochastic differential equations are derived for asymptotic flows using a perturbation approach. These solutions were used to derive general expressions for the large-scale (effective) properties for large-scale two-phase flow in porous media. An important observation from this analysis is that general large-scale flow in heterogeneous soils cannot be predicted on the basis of simple averages of the soil hydraulic properties alone. The large-scale capillary pressure saturation relation is evaluated for imbibition into a wet soil or rock formation. (EG) 194 refs.

Trolling new media: violent extremist groups recruiting through social media

OpenAIRE

Chang, Mark D.

2015-01-01

Approved for public release; distribution is unlimited With the advent and subsequent growth of several new media technologies, violent extremist groups have incorporated social media into recruiting strategies. How are violent extremist groups using social media for recruiting? This thesis explores several new media technologies—websites, blogs, social media, mobile phones, and online gaming—to determine if violent extremist groups rely on social media for recruiting. By comparing the com...

A Note on an Analytic Solution for an Incompressible Fluid-Conveying Pipeline System

Directory of Open Access Journals (Sweden)

Vincent O. S. Olunloyo

2017-01-01

Full Text Available This paper presents an integral transform analytic solution to the equations governing a fluid-conveying pipeline segment where a gyroscopic or Coriolis force effect is taken into consideration. The mathematical model idealizes a segment of the pipeline as an elastic beam conveying an incompressible fluid. It is clearly shown that when such a system is supported at both ends and in a free motion, the Coriolis force dissipates no energy (or simply does not work as it generates conjugate complex vibratory components for all flow velocities. It is demonstrated that the modal natural frequencies can be computed from the algebraic products of the complex frequency pairs. Clearly, the patterns of the characteristics of the system’s natural frequencies are seen partly when the real and imaginary components are plotted, as widely seen in the literature. Nonetheless, results from this study revealed that a continuity profile exists to connect the subcritical, critical, and postcritical vibratory behaviours when the absolute values are plotted for any velocity. In the meantime, the efficacy and versatility of this method against the usual assumed spatial or temporal modal solutions are demonstrated by confirming the predictions and validity of results of earlier workers such as Paidoussis, Ziegler, and others where pre- and postdivergence behaviours are exhibited.

Exact integration of the unsteady incompressible Navier-Stokes equations, gauge criteria, and applications

Science.gov (United States)

Scholle, M.; Gaskell, P. H.; Marner, F.

2018-04-01

An exact first integral of the full, unsteady, incompressible Navier-Stokes equations is achieved in its most general form via the introduction of a tensor potential and parallels drawn with Maxwell's theory. Subsequent to this gauge freedoms are explored, showing that when used astutely they lead to a favourable reduction in the complexity of the associated equation set and number of unknowns, following which the inviscid limit case is discussed. Finally, it is shown how a change in gauge criteria enables a variational principle for steady viscous flow to be constructed having a self-adjoint form. Use of the new formulation is demonstrated, for different gauge variants of the first integral as the starting point, through the solution of a hierarchy of classical three-dimensional flow problems, two of which are tractable analytically, the third being solved numerically. In all cases the results obtained are found to be in excellent accord with corresponding solutions available in the open literature. Concurrently, the prescription of appropriate commonly occurring physical and necessary auxiliary boundary conditions, incorporating for completeness the derivation of a first integral of the dynamic boundary condition at a free surface, is established, together with how the general approach can be advantageously reformulated for application in solving unsteady flow problems with periodic boundaries.

Media education.

Science.gov (United States)

Strasburger, Victor C

2010-11-01

The American Academy of Pediatrics recognizes that exposure to mass media (eg, television, movies, video and computer games, the Internet, music lyrics and videos, newspapers, magazines, books, advertising) presents health risks for children and adolescents but can provide benefits as well. Media education has the potential to reduce the harmful effects of media and accentuate the positive effects. By understanding and supporting media education, pediatricians can play an important role in reducing harmful effects of media on children and adolescents.

Numerical simulations of natural or mixed convection in vertical channels: comparisons of level-set numerical schemes for the modeling of immiscible incompressible fluid flows

International Nuclear Information System (INIS)

Li, R.

2012-01-01

The aim of this research dissertation is at studying natural and mixed convections of fluid flows, and to develop and validate numerical schemes for interface tracking in order to treat incompressible and immiscible fluid flows, later. In a first step, an original numerical method, based on Finite Volume discretizations, is developed for modeling low Mach number flows with large temperature gaps. Three physical applications on air flowing through vertical heated parallel plates were investigated. We showed that the optimum spacing corresponding to the peak heat flux transferred from an array of isothermal parallel plates cooled by mixed convection is smaller than those for natural or forced convections when the pressure drop at the outlet keeps constant. We also proved that mixed convection flows resulting from an imposed flow rate may exhibit unexpected physical solutions; alternative model based on prescribed total pressure at inlet and fixed pressure at outlet sections gives more realistic results. For channels heated by heat flux on one wall only, surface radiation tends to suppress the onset of re-circulations at the outlet and to unify the walls temperature. In a second step, the mathematical model coupling the incompressible Navier-Stokes equations and the Level-Set method for interface tracking is derived. Improvements in fluid volume conservation by using high order discretization (ENO-WENO) schemes for the transport equation and variants of the signed distance equation are discussed. (author)

A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations

KAUST Repository

Guermond, J.L.

2011-06-01

We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier-Stokes equations. The main originality of the method consists of using the operator (I-∂xx)(I-∂yy)(I-∂zz) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. © 2011 Elsevier B.V.

Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids

KAUST Repository

Chen, Huangxin

2017-09-01

In this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.

INS3D - NUMERICAL SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN THREE-DIMENSIONAL GENERALIZED CURVILINEAR COORDINATES (DEC RISC ULTRIX VERSION)

Science.gov (United States)

Biyabani, S. R.

1994-01-01

INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far

Media Framing

DEFF Research Database (Denmark)

Pedersen, Rasmus T.

2017-01-01

The concept of media framing refers to the way in which the news media organize and provide meaning to a news story by emphasizing some parts of reality and disregarding other parts. These patterns of emphasis and exclusion in news coverage create frames that can have considerable effects on news...... consumers’ perceptions and attitudes regarding the given issue or event. This entry briefly elaborates on the concept of media framing, presents key types of media frames, and introduces the research on media framing effects....

An efficient algorithm for incompressible N-phase flows

International Nuclear Information System (INIS)

Dong, S.

2014-01-01

We present an efficient algorithm within the phase field framework for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids, with possibly very different physical properties such as densities, viscosities, and pairwise surface tensions. The algorithm employs a physical formulation for the N-phase system that honors the conservations of mass and momentum and the second law of thermodynamics. We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids. Our numerical algorithm has several attractive properties that make it computationally very efficient: (i) it has completely de-coupled the computations for different flow variables, and has also completely de-coupled the computations for the (N−1) phase field functions; (ii) the algorithm only requires the solution of linear algebraic systems after discretization, and no nonlinear algebraic solve is needed; (iii) for each flow variable the linear algebraic system involves only constant and time-independent coefficient matrices, which can be pre-computed during pre-processing, despite the variable density and variable viscosity of the N-phase mixture; (iv) within a time step the semi-discretized system involves only individual de-coupled Helmholtz-type (including Poisson) equations, despite the strongly-coupled phase–field system of fourth spatial order at the continuum level; (v) the algorithm is suitable for large density contrasts and large viscosity contrasts among the N fluids. Extensive numerical experiments have been presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts. In particular, we compare our simulations with the de Gennes theory, and demonstrate that our method produces physically accurate results for multiple fluid phases. We also demonstrate the significant and sometimes dramatic effects of the

The linearization method in hydrodynamical stability theory

CERN Document Server

Yudovich, V I

1989-01-01

This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

Media Entrepreneurship

DEFF Research Database (Denmark)

Khajeheian, Datis

2017-01-01

Media Entrepreneurship has been an ambiguous, unclear and controversial concept and despite of growing academic efforts in the last decade, it is still a poorly defined subject. This paper is an effort to fill this gap by providing a comprehensive definition of media entrepreneurship. Firstly......, a literature review conducted and entrepreneurship, media, opportunity and innovation as building blocks of media entrepreneurship explained. Then by using of a mixed of bibliographic method and a Delphi method with multi-stage analysis process, a consensual definition of media entrepreneurship proposed...... entrepreneurship....

New media technologies and mass media reform processes

Directory of Open Access Journals (Sweden)

Tomić Boban

2017-01-01

Full Text Available This paper reviews and assesses the chances for survival and development of the media in Serbia and ib the region, from the perspective of new information and communication technologies (ICT applied in media business. In the paper theoretical method is used and harmonized with the needs of describing the problems and the observed processes and phenomena, as well as empirical method which is used for collecting and interpreting concrete facts and data on the observed processes and phenomena. The starting point lies in the fact that modern media is definitely, more and more, dependent on new technologies. A part of the new technologies is used in the process of collecting, selecting and editing media content, while the other part of the technology is used in the process of dissemination and propulsion of media content to the mass audience, and also in the feedback function as well. The technology revolution, which we describe, started with mp3, jpg and avi files, and continues with internet broadcasting, social networks, cloud technologies and new digital platforms which are used by today's media for distribution of media content. The particularity of the media in the region lies in the fact that they operating in the societes with delay of political and economic transition, so all the productive resources of society, due to this backlog, are slower adapted to the new conditions of business in the digital era. The consequences that have arisen from such dynamics of development make many media in Serbia and the region quite dysfunctional, especially those who were exposed during this transition to long-standing legal, economic and program crises. That is why most of the existing media in Serbia, especially small ones, are unprepared for modernization and they are not ready for re-modeling in accordance with the new technological circumstances.

Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

KAUST Repository

Le Maitre, Olivier

2014-01-06

In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

Direct calibration framework of triple-hole pressure probes for incompressible flow

International Nuclear Information System (INIS)

Díaz, K M Argüelles; Oro, J M Fernández; Marigorta, E Blanco

2008-01-01

This paper carries out a mathematical analysis of the limits and data reduction techniques of three-hole pressure (THP) probes operating in a 'non-nulling' mode for incompressible flow. As a result of this analysis, a direct procedure is advanced, based on the distinction of several zones within the angular range, where different relations can be applied to obtain the flow variables. This proposal provides a considerable increment of the operative angular range of THP probes: about ±70° instead of the typical ±35° for a cylindrical probe. This may extend the application of these probes in highly unsteady flows, or reduce the acquisition and data reduction effort minimizing the necessity of probe reorientation. The influence of the data reduction technique on the uncertainty transmission is also presented in the paper. From detailed considerations, it is demonstrated that the results uncertainty depends on the specific probe, but it is unaffected by the mathematical procedure employed to calculate the flow variables. Validation measurements with pneumatic probes have been made for Reynolds numbers from 4 × 10 3 to 3.5 × 10 4 . In addition, a highly unsteady measurement in a low-speed axial flow fan is succinctly analysed. Taking into account both attainable angular range and uncertainty, it is determined that the optimal construction angle for the holes of a low frequency response THP probe lies between 30° and 60°, while for fast response probes, in order to avoid the separated flow region, the optimal construction angle is around 30°

Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

KAUST Repository

Le Maitre, Olivier

2014-01-01

In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

[Media for 21st century--towards human communication media].

Science.gov (United States)

Harashima, H

2000-05-01

Today, with the approach of the 21st century, attention is focused on multi-media communications combining computer, visual and audio technologies. This article discusses the communication media target and the technological problems constituting the nucleus of multi-media. The communication media is becoming an environment from which no one can escape. Since the media has such a great power, what is needed now is not to predict the future technologies, but to estimate the future world and take to responsibility for future environments.

Media Ecology

Directory of Open Access Journals (Sweden)

Marina Ašković

2015-05-01

Full Text Available Does the trend in which electronic media are gradually becoming extension of human body have to move towards full enslavement of a human and his personality, or the same human will unpredictably, with the aid of his personal media literacy, exit the whirls of media and technological censorships? Personality crisis is closely related to the crisis of language no matter how contradicted to global ideology of transnational transhumanism it may seem. Considering the fact that recent media presentations of the world are based on commercialization of environmentalism, philosophical and aesthetic thought appears as an important subject of ecology. As media mediates, the scenery of civilized living increasingly becomes more appealing even though it derives from commercial and political background. Consequently, the future of humanity depends by large on the philosophy of media. Media have to truly ecologise returning the humanum to its essence making it into the extension of the natural world.

Media Education and Media Criticism in the Educational Process in Russia

Science.gov (United States)

Fedorov, Alexander; Levitskaya, Anastasia

2017-01-01

Media criticism and media education have a lot in common. For example, both media education and media criticism attach great importance to the development of analytical thinking of the audience. Indeed, one of the most important tasks of media education is precisely to teach the audience not only to analyze media texts of any types, but also to…

Geographic Media Literacy

Science.gov (United States)

Lukinbeal, Chris

2014-01-01

While the use of media permeates geographic research and pedagogic practice, the underlying literacies that link geography and media remain uncharted. This article argues that geographic media literacy incorporates visual literacy, information technology literacy, information literacy, and media literacy. Geographic media literacy is the ability…

SOCIAL MEDIA SECURITY

Science.gov (United States)

RESPONSIBILITY CENTCOM COALITION MEDIA SOCIAL MEDIA NEWS ARTICLES PRESS RELEASES IMAGERY VIDEOS TRANSCRIPTS VISITORS AND PERSONNEL FAMILY CENTER FAMILY READINESS CENTCOM WEBMAIL SOCIAL MEDIA SECURITY ACCOUNTABILITY HomeVISITORS AND PERSONNELSOCIAL MEDIA SECURITY FAQ on Security for Social Media Due to the widespread use of

ANALISIS CATEGORY ADVERTISING EXPENDITURE DAN CONSUMER MEDIA HABIT DI MEDIA TELEVISI DAN MEDIA CETAK

Directory of Open Access Journals (Sweden)

Zifwen Zifwen

2011-08-01

Full Text Available Normal 0 false false false MicrosoftInternetExplorer4 The purpose of the study is to identify the category of advertising expenditure and media habit on media advertising, especially on television and print ad such as newspapers, magazines and tabloids. The Data were collected  from Nielsen Media Research (NMR data base from a number of cities in Indonesia, such as Jakarta,Surabaya, Bandung, Semarang, Surabaya, Yogyakarta, Bali, Medan,Palembang and Makassar. There are three different type of data used to acquire the secondary data for the study: (1  Telescope (data collected for rating analysis January 1st, 2005 to March 31st, 2005, (2 Print scope (data collected from the readership of magazines, tabloids and newspaper January 1st, 2004 to December 31st, 2004 and (3 Ad quest (data collected from advertising expenditure for all categories. The data were collected, calculated and analyzed from January 1st, 2002 to December 31st, 2004. The purpose of the study is to uncover the trend of advertising budget from all categories on the television and print ads, in order to describe the consumption tendency of the people within advertising media. Index analysis and Biplot were used to analyze the data. Based on the result of advertising expenditure analysis of data, showing that all categories were completely different in the utilization of the media for advertisement. Some categories used mix media to support their campaign and others used a single media. Characteristic of the categories were strongly involved in the decision making in way of choosing and using the advertising media. The result of consumer media analysis found that the people habit were completely different and unique in media consumption. Different of age, sex and social economic status can create a different habit in term of hobbies and desire within the channel, programme, newspaper, magazines and the tabloids. Finally, to create an effective and efficient advertising activity

Media Culture and Media Education in Modern School

Science.gov (United States)

Tolic, Mirela

2011-01-01

Culture is no longer conceivable without the media and/or new phenomena called. "Cyber" culture. The article discusses issues in what respect the different media, like TV, film and Internet are with different cultures, how it changes everyday life under influence of various forms of sophisticated communications media and what…

Coronal heating by Alfven waves dissipation in compressible nonuniform media

International Nuclear Information System (INIS)

Malara, Francesco; Primavera, Leonardo; Veltri, Pierluigi

1996-01-01

The possibility to produce small scales and then to efficiently dissipate energy has been studied by Malara et al. [1992b] in the case of MHD disturbances propagating in an weakly dissipative incompressible and inhomogeneous medium, for a strictly 2D geometry. We extend this work to include both compressibility and the third component for vector quantities. Numerical simulations show that, when an Alfven wave propagates in a compressible nonuniform medium, the two dynamical effects responsible for the small scales formation in the incompressible case are still at work: energy pinching and phase-mixing. These effects give rise to the formation of compressible perturbations (fast and slow waves or a static entropy wave). Some of these compressive fluctuations are subject to the steepening of the wave front and become shock waves, which are extremely efficient in dissipating their energy, their dissipation being independent of the Reynolds number. Rough estimates of the typical times the various dynamical processes take to produce small scales show that these times are consistent with those required to dissipate inside the solar corona the energy of Alfven waves of photospheric origin

Post Media Literacy: Menyaksikan Kuasa Media Bersama Michel Foucault

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Iswandi Syahputra

2017-01-01

Full Text Available This article would like to present Michel Foucault’s idea concerning Knowledge and Power in media industry. As a contemporary intellectual, Foucault’s thought has a unique style of postmodernism. His thought had gone beyond traditional critical theory whose trying to disclose the relation of power and economic behind the ideology of media. Foucault’s thought had given new perspective in understanding how the media produce truth under tightly control process into something that seems normal. With the assumption of media has the power to create mass culture, which has to be studied critically by media literacy approach, Foucault’s thought had given new space of discursive. An alternative thought on how to estimate the work of mass media as supervisor of truth and creator of information trough normalization practice.

Locative media

CERN Document Server

Wilken, Rowan

2014-01-01

Not only is locative media one of the fastest growing areas in digital technology, but questions of location and location-awareness are increasingly central to our contemporary engagements with online and mobile media, and indeed media and culture generally. This volume is a comprehensive account of the various location-based technologies, services, applications, and cultures, as media, with an aim to identify, inventory, explore, and critique their cultural, economic, political, social, and policy dimensions internationally. In particular, the collection is organized around the perception that the growth of locative media gives rise to a number of crucial questions concerning the areas of culture, economy, and policy.

Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem

Science.gov (United States)

Badia, Santiago; Martín, Alberto F.; Planas, Ramon

2014-10-01

The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.

Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

Science.gov (United States)

Tice, Ian

2018-04-01

This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which arises in modeling the motion of such a fluid down an inclined plane, after a coordinate change. We consider the problem both with and without surface tension for horizontally periodic flows. This problem gives rise to shear-flow equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of the equilibria in certain parameter regimes. We prove that there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t=0 give rise to global-in-time solutions that return to equilibrium exponentially in the case with surface tension and almost exponentially in the case without surface tension. We also establish a vanishing surface tension limit, which connects the solutions with and without surface tension.

A constitutive framework for modelling thin incompressible viscoelastic materials under plane stress in the finite strain regime

Science.gov (United States)

Kroon, M.

2011-11-01

Rubbers and soft biological tissues may undergo large deformations and are also viscoelastic. The formulation of constitutive models for these materials poses special challenges. In several applications, especially in biomechanics, these materials are also relatively thin, implying that in-plane stresses dominate and that plane stress may therefore be assumed. In the present paper, a constitutive model for viscoelastic materials in the finite strain regime and under the assumption of plane stress is proposed. It is assumed that the relaxation behaviour in the direction of plane stress can be treated separately, which makes it possible to formulate evolution laws for the plastic strains on explicit form at the same time as incompressibility is fulfilled. Experimental results from biomechanics (dynamic inflation of dog aorta) and rubber mechanics (biaxial stretching of rubber sheets) were used to assess the proposed model. The assessment clearly indicates that the model is fully able to predict the experimental outcome for these types of material.

On Media Education

Science.gov (United States)

Fedorov, Alexander

2008-01-01

This monograph analyzes the theory and practice of media education and media literacy. The book also includes the list of Russian media education literature and addresses of websites of the associations for media education.

More Media, More People—On Social & Multimodal Media Intelligence

OpenAIRE

Degerstedt, Lars; Pelle, Snickars

2017-01-01

The purpose of this article is to address some challenges facing media intelligence in general, and competitive intelligence in particular within an altered information landscape. To understand this new situation, the notion of social and multimodal media intelligence are introduced. With cases taken primarily from the Swedish media intelligence sector, we argue that data driven media intelligence today needs to pay increasing attention to new forms of (A.) crowd-oriented and (B.) multimedia-...

A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

KAUST Repository

Bourantas, Georgios

2013-12-01

A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a collocated or a semi-staggered "grid" configuration. The developed numerical scheme approximates the unknown field functions using the Moving Least Squares approximation. A velocity, along with a pressure correction scheme is applied in the context of the meshless point collocation method. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it is a truly meshless method, (ii) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (iii) it incorporates simplicity and accuracy, (iv) results can be obtained using collocated or semi-staggered "grids", (v) there is no need for the usage of a curvilinear system of coordinates and (vi) it can solve steady and unsteady flows. The lid-driven cavity flow problem, for Reynolds numbers up to 5000, has been considered, by using both staggered and collocated grid configurations. Following, the Backward-Facing Step (BFS) flow problem was considered for Reynolds numbers up to 800 using a staggered grid. As a final example, the case of a laminar flow in a two-dimensional tube with an obstacle was examined. © 2013 Elsevier Ltd.

A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations

Directory of Open Access Journals (Sweden)

Yibao Li

2017-01-01

Full Text Available Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier–Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity–pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes.

Active unsteady aerodynamic suppression of rotating stall in an incompressible flow centrifugal compressor with vaned diffuser

Science.gov (United States)

Lawless, Patrick B.; Fleeter, Sanford

1991-01-01

A mathematical model is developed to analyze the suppression of rotating stall in an incompressible flow centrifugal compressor with a vaned diffuser, thereby addressing the important need for centrifugal compressor rotating stall and surge control. In this model, the precursor to to instability is a weak rotating potential velocity perturbation in the inlet flow field that eventually develops into a finite disturbance. To suppress the growth of this potential disturbance, a rotating control vortical velocity disturbance is introduced into the impeller inlet flow. The effectiveness of this control is analyzed by matching the perturbation pressure in the compressor inlet and exit flow fields with a model for the unsteady behavior of the compressor. To demonstrate instability control, this model is then used to predict the control effectiveness for centrifugal compressor geometries based on a low speed research centrifugal compressor. These results indicate that reductions of 10 to 15 percent in the mean inlet flow coefficient at instability are possible with control waveforms of half the magnitude of the total disturbance at the inlet.

PENGEMBANGAN MEDIA PEMBELAJARAN FILM ANIMASI SEBAGAI MEDIA PEMBELAJARAN KONSEP FOTOSINTESIS

Directory of Open Access Journals (Sweden)

Umrotul Hasanah

2015-11-01

Full Text Available The research aims to develop animation film as a learning media in photosynthesis concept learning and to know the results of the assessment of the learning media expert test the concept of photosynthesis animated films. This research is Research and Development (R&D. The research used questionnaire  Aspects of assessment in terms of the media covering aspects of technical quality, narration, and music/sound effects. Aspects of the assessment of the suitability of the material terms covering the material aspects of the curriculum, the clarity of the material, the order of the material, communicative, suitability of the material with the purpose of learning, material relationship with the students’ critical thinking skill, and material relationship with motivation. Media expert test against “Cahaya dan Fotosintesis” animated film made by media experts with a percentage of 80,6% with the as good category, and  92,5% are material expert excellent category. Based on the “Cahaya dan Fotosintesis” animated film expert test to students can be tasted on a limited basis, after the media deficiencies corrected. Penelitian ini bertujuan untuk mengembangkan media pembelajaran film animasi pada konsep fotosintesis dan untuk mengetahui hasil penilaian uji ahli terhadap media pembelajaran film animasi pada konsep fotosintesis. Penelitian ini merupakan penelitian research and development (R & D. Teknik pengumpulan data dengan menggunakan angket. Aspek penilaian dari segi media meliputi aspek kualitas teknik, narasi dan musik/efek suara. Aspek penilaian dari segi materi meliputi aspek kesesuaian materi dengan kurikulum, kejelasan materi, urutan materi, komunikatif, kesesuaian soal evaluasi, kesesuaian materi dengan tujuan pembelajaran, hubungan materi dengan kemampuan berpikir kritis dan hubungan materi dengan motivasi. Uji ahli terhadap media film animasi “Cahaya dan Fotosintesis” dilakukan oleh ahli media dengan perolehan persentse 80,6% dengan

Electrokinetic and Poroelastic Characterization of Porous Media : Application to CO2 storage monitoring

NARCIS (Netherlands)

Kirichek, O.J.

2018-01-01

Monitoring the properties of a CO2 storage reservoir is important for two main reasons: firstly, to verify that the injected CO2 is safely contained in the reservoir rock as planned, and secondly, to provide data which can be used to update the existing reservoir models and support eventual