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Sample records for numerical viscous solutions

  1. Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil

    Directory of Open Access Journals (Sweden)

    Slouka Martin

    2016-01-01

    Full Text Available This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.

  2. Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

    Science.gov (United States)

    Keslerová, Radka; Trdlička, David

    2015-09-01

    This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

  3. Numerical optimization of conical flow waveriders including detailed viscous effects

    Science.gov (United States)

    Bowcutt, Kevin G.; Anderson, John D., Jr.; Capriotti, Diego

    1987-01-01

    A family of optimized hypersonic waveriders is generated and studied wherein detailed viscous effects are included within the optimization process itself. This is in contrast to previous optimized waverider work, wherein purely inviscid flow is used to obtain the waverider shapes. For the present waveriders, the undersurface is a streamsurface of an inviscid conical flowfield, the upper surface is a streamsurface of the inviscid flow over a tapered cylinder (calculated by the axisymmetric method of characteristics), and the viscous effects are treated by integral solutions of the boundary layer equations. Transition from laminar to turbulent flow is included within the viscous calculations. The optimization is carried out using a nonlinear simplex method. The resulting family of viscous hypersonic waveriders yields predicted high values of lift/drag, high enough to break the L/D barrier based on experience with other hypersonic configurations. Moreover, the numerical optimization process for the viscous waveriders results in distinctly different shapes compared to previous work with inviscid-designed waveriders. Also, the fine details of the viscous solution, such as how the shear stress is distributed over the surface, and the location of transition, are crucial to the details of the resulting waverider geometry. Finally, the moment coefficient variations and heat transfer distributions associated with the viscous optimized waveriders are studied.

  4. Shallow water equations: viscous solutions and inviscid limit

    Science.gov (United States)

    Chen, Gui-Qiang; Perepelitsa, Mikhail

    2012-12-01

    We establish the inviscid limit of the viscous shallow water equations to the Saint-Venant system. For the viscous equations, the viscosity terms are more degenerate when the shallow water is close to the bottom, in comparison with the classical Navier-Stokes equations for barotropic gases; thus, the analysis in our earlier work for the classical Navier-Stokes equations does not apply directly, which require new estimates to deal with the additional degeneracy. We first introduce a notion of entropy solutions to the viscous shallow water equations and develop an approach to establish the global existence of such solutions and their uniform energy-type estimates with respect to the viscosity coefficient. These uniform estimates yield the existence of measure-valued solutions to the Saint-Venant system generated by the viscous solutions. Based on the uniform energy-type estimates and the features of the Saint-Venant system, we further establish that the entropy dissipation measures of the viscous solutions for weak entropy-entropy flux pairs, generated by compactly supported C 2 test-functions, are confined in a compact set in H -1, which yields that the measure-valued solutions are confined by the Tartar-Murat commutator relation. Then, the reduction theorem established in Chen and Perepelitsa [5] for the measure-valued solutions with unbounded support leads to the convergence of the viscous solutions to a finite-energy entropy solution of the Saint-Venant system with finite-energy initial data, which is relative with respect to the different end-states of the bottom topography of the shallow water at infinity. The analysis also applies to the inviscid limit problem for the Saint-Venant system in the presence of friction.

  5. Mathematical theory of compressible viscous fluids analysis and numerics

    CERN Document Server

    Feireisl, Eduard; Pokorný, Milan

    2016-01-01

    This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...

  6. Numerical solution of non-linear diffusion problems

    International Nuclear Information System (INIS)

    Carmen, A. del; Ferreri, J.C.

    1998-01-01

    This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

  7. Similar solutions for viscous hypersonic flow over a slender three-fourths-power body of revolution

    Science.gov (United States)

    Lin, Chin-Shun

    1987-01-01

    For hypersonic flow with a shock wave, there is a similar solution consistent throughout the viscous and inviscid layers along a very slender three-fourths-power body of revolution The strong pressure interaction problem can then be treated by the method of similarity. Numerical calculations are performed in the viscous region with the edge pressure distribution known from the inviscid similar solutions. The compressible laminar boundary-layer equations are transformed into a system of ordinary differential equations. The resulting two-point boundary value problem is then solved by the Runge-Kutta method with a modified Newton's method for the corresponding boundary conditions. The effects of wall temperature, mass bleeding, and body transverse curvature are investigated. The induced pressure, displacement thickness, skin friction, and heat transfer due to the previously mentioned parameters are estimated and analyzed.

  8. Numerical simulations of a family of the coupled viscous Burgers, equation using the lattice Boltzmann method

    International Nuclear Information System (INIS)

    He, Y B; Tang, X H

    2016-01-01

    In this paper, in order to extend the lattice Boltzmann method (LBM) to deal with more nonlinear systems, a one-dimensional and five-velocity lattice Boltzmann scheme with an amending function for a family of the coupled viscous Burgers’ equation (CVBE) is proposed. With the Taylor and Chapman–Enskog expansion, a family of the CVBE is recovered correctly from the lattice Boltzmann equation through selecting the equilibrium distribution functions and amending functions properly. The method is applied to some test examples with an analytical solution. The results are compared with those obtained by the finite difference method (FDM); it is shown that the numerical solutions agree well with the analytical solutions and the errors obtained by the present method are smaller than the FDM. Furthermore, some problems without analytical solutions are numerically studied by the present method and the FDM. The results show that the numerical solutions of the LBM are in good agreement with those obtained by the FDM, which can validate the effectiveness and stability of the LBM. (paper: classical statistical mechanics, equilibrium and non-equilibrium)

  9. Shear-Induced Membrane Fusion in Viscous Solutions

    KAUST Repository

    Kogan, Maxim

    2014-05-06

    Large unilamellar lipid vesicles do not normally fuse under fluid shear stress. They might deform and open pores to relax the tension to which they are exposed, but membrane fusion occurring solely due to shear stress has not yet been reported. We present evidence that shear forces in a viscous solution can induce lipid bilayer fusion. The fusion of 1,2-dioleoyl-sn-glycero-3- phosphocholine (DOPC) liposomes is observed in Couette flow with shear rates above 3000 s-1 provided that the medium is viscous enough. Liposome samples, prepared at different viscosities using a 0-50 wt % range of sucrose concentration, were studied by dynamic light scattering, lipid fusion assays using Förster resonance energy transfer (FRET), and linear dichroism (LD) spectroscopy. Liposomes in solutions with 40 wt % (or more) sucrose showed lipid fusion under shear forces. These results support the hypothesis that under suitable conditions lipid membranes may fuse in response to mechanical-force- induced stress. © 2014 American Chemical Society.

  10. Thermal-diffusion and diffusion-thermo effects on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation

    Directory of Open Access Journals (Sweden)

    S. Srinivas

    2016-01-01

    Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.

  11. Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

    Directory of Open Access Journals (Sweden)

    Yu Bai

    2017-12-01

    Full Text Available This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

  12. Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

    Science.gov (United States)

    Bai, Yu; Jiang, Yuehua; Liu, Fawang; Zhang, Yan

    2017-12-01

    This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

  13. Efficient self-consistent viscous-inviscid solutions for unsteady transonic flow

    Science.gov (United States)

    Howlett, J. T.

    1985-01-01

    An improved method is presented for coupling a boundary layer code with an unsteady inviscid transonic computer code in a quasi-steady fashion. At each fixed time step, the boundary layer and inviscid equations are successively solved until the process converges. An explicit coupling of the equations is described which greatly accelerates the convergence process. Computer times for converged viscous-inviscid solutions are about 1.8 times the comparable inviscid values. Comparison of the results obtained with experimental data on three airfoils are presented. These comparisons demonstrate that the explicitly coupled viscous-inviscid solutions can provide efficient predictions of pressure distributions and lift for unsteady two-dimensional transonic flows.

  14. Numerical Investigation of Damping of Torsional Beam Vibrations by Viscous Bimoments

    DEFF Research Database (Denmark)

    Hoffmeyer, David; Høgsberg, Jan Becker

    2017-01-01

    Damping of torsional beam vibrations of slender beam–structures with thin–walled cross–sections is investigated. Analytical results from solving the differential equation governing torsion with viscous bimoments imposed at the boundary, are compared with a numerical approach with three...

  15. The effects of plastic waves on the numerical convergence of the viscous-plastic and elastic-viscous-plastic sea-ice models

    Science.gov (United States)

    Williams, James; Tremblay, L. Bruno; Lemieux, Jean-François

    2017-07-01

    The plastic wave speed is derived from the linearized 1-D version of the widely used viscous-plastic (VP) and elastic-viscous-plastic (EVP) sea-ice models. Courant-Friedrichs-Lewy (CFL) conditions are derived using the propagation speed of the wave. 1-D numerical experiments of the VP, EVP and EVP* models successfully recreate a reference solution when the CFL conditions are satisfied, in agreement with the theory presented. The IMplicit-EXplicit (IMEX) method is shown to effectively alleviate the plastic wave CFL constraint on the timestep in the implicitly solved VP model in both 1-D and 2-D. In 2-D, the EVP and EVP* models show first order error in the simulated velocity field when the plastic wave is not resolved. EVP simulations are performed with various advective timestep, number of subcycles, and elastic-wave damping timescales. It is found that increasing the number of subcycles beyond that needed to resolve the elastic wave does not improve the quality of the solution. It is found that reducing the elastic wave damping timescale reduces the spatial extent of first order errors cause by the unresolved plastic wave. Reducing the advective timestep so that the plastic wave is resolved also reduces the velocity error in terms of magnitude and spatial extent. However, the parameter set required for convergence to within the error bars of satellite (RGPS) deformation fields is impractical for use in climate model simulations. The behavior of the EVP* method is analogous to that of the EVP method except that it is not possible to reduce the damping timescale with α = β.

  16. Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

    Directory of Open Access Journals (Sweden)

    Valášek J.

    2016-01-01

    Full Text Available The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE is used. The whole problem is solved by the finite element method (FEM based solver. Results of numerical experiments with different boundary conditions are presented.

  17. Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

    Science.gov (United States)

    Valášek, J.; Sváček, P.; Horáček, J.

    2016-03-01

    The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

  18. Numerical investigation of interaction between rising bubbles in a viscous liquid

    Energy Technology Data Exchange (ETDEWEB)

    Yoon, Ik Roh [Korea Institute of Marine Science and Technology Promotion, Seoul (Korea, Republic of); Shin Seung Won [Hongik University, Seoul (Korea, Republic of)

    2016-07-15

    The rising behavior of bubbles undergoing bubble-bubble interaction in a viscous liquid is studied using a two-dimensional direct numerical simulation. Level contour reconstruction method (LCRM), one of the connectivity-free front tracking methods, is applied to describe a moving interface accurately under highly deformable conditions. This work focuses on the effects of bubble size on the interaction of two bubbles rising side-by-side in a stagnant liquid. Several characteristics of bubble-bubble interaction are analyzed quantitatively as supported by energy analysis. The results showed clear differences between small and large bubbles with respect to their interaction behavior in terms of lateral movement, vortex intensity, suppression of surface deformation, and viscous dissipation rate. Distributions of vorticity and viscous dissipation rate near the bubble interfaces also differed depending on the size of the bubbles. Strong vortices from large bubbles triggered oscillation in bubble-bubble interaction and played a dominant role in the interaction process as the size of bubbles increases.

  19. Thermodynamic characteristics of viscous flow activation in aqueous solutions of alkali metal iodides

    International Nuclear Information System (INIS)

    Renskij, I.A.; Rudnitskaya, A.A.; Fialkov, Yu.A.

    2003-01-01

    The Gibbs activation energy of the viscous flow of the alkali metal iodides aqueous solutions MI (M = Li, Na, K, Cs) and from its temperature dependence - the enthalpy and entropy of this process are calculated by the Eyring modified equation. The kinetic compensation effects, related to the viscous flow of the unbound water and to the ion-hydrate complexes are established. The relative contribution of the enthalpy and entropy constituents for these solution components is analyzed [ru

  20. Aerosols generated by spills of viscous solutions and slurries

    International Nuclear Information System (INIS)

    Ballinger, M.Y.; Hodgson, W.H.

    1986-12-01

    Safety assessments and environmental impact statements for nuclear fuel cycle facilities require an estimate of potential airborne releases caused by accidents. Aerosols generated by accidents are being investigated by Pacific Northwest Laboratory to develop methods for estimating source terms from these accidents. Experiments were run by spilling viscous solutions and slurries to determine the mass and particle-size distribution of the material made airborne. In all cases, 1 L of solution was spilled from a height of 3 m. Aqueous solutions of sucrose (0 to 56%) gave a range of viscosities from 1.3 to 46 cp. The percent of spill mass made airborne from the spills of these solutions ranged from 0.001 to 0.0001. The mass of particles made airborne decreased as solution viscosity increased. Slurry loading ranged from 25 to 51% total solids. The maximum source airborne (0.0046 wt %) occurred with the slurry that had the lightest loading of soluble solids. The viscosity of the carrying solution also had an impact on the source term from spilling slurries. The effect of surface tension on the source term was examined in two experiments. Surface tension was halved in these spills by adding a surfactant. The maximum weight percent airborne from these spills was 0.0045, compared to 0.003 for spills with twice the surface tension. The aerodynamic mass medium diameters for the aerosols produced by spills of the viscous solutions, slurries, and low surface tension liquids ranged from 0.6 to 8.4 μm, and the geometric standard deviation ranged from 3.8 to 28.0

  1. Visualization of Solution Gas Drive in Viscous Oil, SUPRI TR-126

    Energy Technology Data Exchange (ETDEWEB)

    George, D.S.; Kovscek, A.R.

    2001-07-23

    Several experimental studies of solution gas drive are available in this report. Almost all of the studies have used light oil. Solution gas drive behavior, especially in heavy oil reservoirs, is poorly understood. Experiments were performed in which pore-scale solution gas drive phenomena were viewed in water/carbon dioxide and viscous oil/carbon dioxide systems. A new pressure vessel was designed and constructed to house silicon-wafer micromodels that previously operated at low (<3 atm) pressure. The new apparatus is used for the visual studies. Several interesting phenomena were viewed. The repeated nucleation of gas bubbles was observed at a gas-wet site occupied by dirt. Interestingly, the dissolution of a gas bubble into the liquid phase was previously recorded at the same nucleation site. Gas bubbles in both systems grew to span one ore more pore bodies before mobilization. Liquid viscosity affected the ease with which gas bubbles coalesced. More viscous solutions result in slower rates of coalescence. The transport of solid particles on gas-liquid interfaces was also observed.

  2. Viscous flows the practical use of theory

    CERN Document Server

    Brenner, Howard

    1988-01-01

    Representing a unique approach to the study of fluid flows, Viscous Flows demonstrates the utility of theoretical concepts and solutions for interpreting and predicting fluid flow in practical applications. By critically comparing all relevant classes of theoretical solutions with experimental data and/or general numerical solutions, it focuses on the range of validity of theoretical expressions rather than on their intrinsic character.This book features extensive use of dimensional analysis on both models and variables, and extensive development of theoretically based correlating equations.

  3. A semi-elliptic analysis of internal viscous flows

    International Nuclear Information System (INIS)

    Ghia, U.; Ramamurti, R.; Ghia, K.N.

    1986-01-01

    The increased demands placed presently on the performance of compressors and turbines of gas-turbine engines have, for some time, pointed the need for accurate analysis of viscous flows in turbomachinery. With the recent developments of advanced computational facilities, much effort has been made to respond to this need. Various mathematical formulations, grid systems and numerical techniques have been developed for the numerical solution of the viscous flow equations (Refs. 1-4). The full Navier-Stokes equations as well as their corresponding thin-layer approximate form have been employed in H- as well as C-grids, using explicit or implicit methods, including convergence enhancement techniques based on multi-grid methodology. Nevertheless, obtaining converged solutions for general geometries on acceptably refined grids remains a computationally demanding task. The present paper discusses a reduced form on the governing equations which can capture much of the physics, while requiring less computer resources than the full Navier-Stokes equations

  4. A Level-set based framework for viscous simulation of particle-laden supersonic flows

    Science.gov (United States)

    Das, Pratik; Sen, Oishik; Jacobs, Gustaaf; Udaykumar, H. S.

    2017-06-01

    Particle-laden supersonic flows are important in natural and industrial processes, such as, volcanic eruptions, explosions, pneumatic conveyance of particle in material processing etc. Numerical study of such high-speed particle laden flows at the mesoscale calls for a numerical framework which allows simulation of supersonic flow around multiple moving solid objects. Only a few efforts have been made toward development of numerical frameworks for viscous simulation of particle-fluid interaction in supersonic flow regime. The current work presents a Cartesian grid based sharp-interface method for viscous simulations of interaction between supersonic flow with moving rigid particles. The no-slip boundary condition is imposed at the solid-fluid interfaces using a modified ghost fluid method (GFM). The current method is validated against the similarity solution of compressible boundary layer over flat-plate and benchmark numerical solution for steady supersonic flow over cylinder. Further validation is carried out against benchmark numerical results for shock induced lift-off of a cylinder in a shock tube. 3D simulation of steady supersonic flow over sphere is performed to compare the numerically obtained drag co-efficient with experimental results. A particle-resolved viscous simulation of shock interaction with a cloud of particles is performed to demonstrate that the current method is suitable for large-scale particle resolved simulations of particle-laden supersonic flows.

  5. Applications of Operator-Splitting Methods to the Direct Numerical Simulation of Particulate and Free-Surface Flows and to the Numerical Solution of the Two-Dimensional Elliptic Monge--Ampère Equation

    OpenAIRE

    Glowinski, R.; Dean, E.J.; Guidoboni, G.; Juárez, L.H.; Pan, T.-W.

    2008-01-01

    The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various areas in Mechanics, Physics and Differential Geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and the elliptic real Monge--Ampère equation. The results of numerical ...

  6. Numerical Study on Mass Transfer of a Vapor Bubble Rising in Very High Viscous Fluid

    Directory of Open Access Journals (Sweden)

    T. Kunugi

    2014-09-01

    Full Text Available This study focused on a bubble rising behavior in a molten glass because it is important to improve the efficiency of removal of bubbles from the molten glass. On the other hand, it is expected that some gas species which exists in a bubble are transferred into the molten glass through the bubble interface, i.e., the mass transfer, subsequently, it may cause a bubble contraction in the molten glass. In this paper, in order to understand the bubble rising behavior with its contraction caused by the mass transfer through the bubble interface in the very high viscous fluid such as the molten glass, a bubble contraction model has been developed. The direct numerical simulations based on the MARS (Multi-interface Advection and Reconstruction Solver coupled with the mass transfer equation and the bubble contraction model regarding the mass transfer from the rising bubble in very high viscous fluid have been performed. Here, the working fluids were water vapor as the gas species and the molten glass as the very high viscous fluid. Also, the jump conditions at the bubble interface for the mass transfer were examined. Furthermore, the influence of the bubble contraction for the bubble rising compared to that in the water as a normal viscous fluid was investigated. From the result of the numerical simulations, it was found that the bubble rising behavior was strongly affected not only by the viscosity of the working fluid but also by the bubble contraction due to the mass transfer through the bubble interface.

  7. Viscous wing theory development. Volume 1: Analysis, method and results

    Science.gov (United States)

    Chow, R. R.; Melnik, R. E.; Marconi, F.; Steinhoff, J.

    1986-01-01

    Viscous transonic flows at large Reynolds numbers over 3-D wings were analyzed using a zonal viscid-inviscid interaction approach. A new numerical AFZ scheme was developed in conjunction with the finite volume formulation for the solution of the inviscid full-potential equation. A special far-field asymptotic boundary condition was developed and a second-order artificial viscosity included for an improved inviscid solution methodology. The integral method was used for the laminar/turbulent boundary layer and 3-D viscous wake calculation. The interaction calculation included the coupling conditions of the source flux due to the wing surface boundary layer, the flux jump due to the viscous wake, and the wake curvature effect. A method was also devised incorporating the 2-D trailing edge strong interaction solution for the normal pressure correction near the trailing edge region. A fully automated computer program was developed to perform the proposed method with one scalar version to be used on an IBM-3081 and two vectorized versions on Cray-1 and Cyber-205 computers.

  8. A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

    Science.gov (United States)

    Veerapaneni, Shravan K.; Gueyffier, Denis; Biros, George; Zorin, Denis

    2009-10-01

    We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

  9. Multidomain spectral solution of compressible viscous flows

    International Nuclear Information System (INIS)

    Kopriva, D.A.

    1994-01-01

    We develop a nonoverlapping mutidomain spectral collocation method to solve compressible viscous flows. At the interfaces, the advection terms are treated with a characteristic correction method. The diffusion terms are treated with a penalty method. Spectral accuracy is demonstrated on linear model problems in one and two space dimensions. The method is applied to a subsonic and supersonic flow over a flat plate. The results are compared to solutions of the boundary-layer equations which show that two digit accuracy in the adiabatic plate temperature is obtained with 16 points in the boundary layer for a freestream Mach number of two. A second application is to a transonic flow in a two-dimensional converging-diverging nozzle, where the computed results are compared to experimental data

  10. Viscous dissipation effects on heat transfer in flow past a continuous moving plate

    Digital Repository Service at National Institute of Oceanography (India)

    Soundalgekar, V.M.; Murty, T.V.R.

    The study of thermal boundary layer on taking into account the viscous dissipative heat, on a continuously moving semi-infinite flat plate is presented here.Similarity solutions are derived and the resulting equations are integrated numerically...

  11. A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

    Energy Technology Data Exchange (ETDEWEB)

    Okamoto, Kazuhisa [Nagoya University, Department of Physics, Nagoya (Japan); Nonaka, Chiho [Nagoya University, Department of Physics, Nagoya (Japan); Nagoya University, Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya (Japan); Duke University, Department of Physics, Durham, NC (United States)

    2017-06-15

    We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions. (orig.)

  12. A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

    Science.gov (United States)

    Okamoto, Kazuhisa; Nonaka, Chiho

    2017-06-01

    We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

  13. Hydromagnetic flow of a Cu-water nanofluid past a moving wedge with viscous dissipation

    Science.gov (United States)

    M. Salem, A.; Galal, Ismail; Rania, Fathy

    2014-04-01

    A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper (Cu)-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das (Tiwari I K and Das M K 2007 Int. J. Heat Mass Transfer 50 2002). A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter λ, solid volume fraction φ, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

  14. Theory of viscous transonic flow over airfoils at high Reynolds number

    Science.gov (United States)

    Melnik, R. E.; Chow, R.; Mead, H. R.

    1977-01-01

    This paper considers viscous flows with unseparated turbulent boundary layers over two-dimensional airfoils at transonic speeds. Conventional theoretical methods are based on boundary layer formulations which do not account for the effect of the curved wake and static pressure variations across the boundary layer in the trailing edge region. In this investigation an extended viscous theory is developed that accounts for both effects. The theory is based on a rational analysis of the strong turbulent interaction at airfoil trailing edges. The method of matched asymptotic expansions is employed to develop formal series solutions of the full Reynolds equations in the limit of Reynolds numbers tending to infinity. Procedures are developed for combining the local trailing edge solution with numerical methods for solving the full potential flow and boundary layer equations. Theoretical results indicate that conventional boundary layer methods account for only about 50% of the viscous effect on lift, the remaining contribution arising from wake curvature and normal pressure gradient effects.

  15. Numerical study of Free Convective Viscous Dissipative flow along Vertical Cone with Influence of Radiation using Network Simulation method

    Science.gov (United States)

    Kannan, R. M.; Pullepu, Bapuji; Immanuel, Y.

    2018-04-01

    A two dimensional mathematical model is formulated for the transient laminar free convective flow with heat transfer over an incompressible viscous fluid past a vertical cone with uniform surface heat flux with combined effects of viscous dissipation and radiation. The dimensionless boundary layer equations of the flow which are transient, coupled and nonlinear Partial differential equations are solved using the Network Simulation Method (NSM), a powerful numerical technique which demonstrates high efficiency and accuracy by employing the network simulator computer code Pspice. The velocity and temperature profiles have been investigated for various factors, namely viscous dissipation parameter ε, Prandtl number Pr and radiation Rd are analyzed graphically.

  16. Study of the motion of a vertically falling sphere in a viscous fluid

    International Nuclear Information System (INIS)

    Soares, A A; Caramelo, L; Andrade, M A P M

    2012-01-01

    This paper aims at contributing to a better understanding of the motion of spherical particles in viscous fluids. The classical problem of spheres falling through viscous fluids for small Reynolds numbers was solved taking into account the effects of added mass. The analytical solution for the motion of a falling sphere, from the beginning to the end of the fall, was combined with an iterative numerical method to determine the fluid viscosity coefficient, diameter of the sphere and terminal velocity. The proposed solution was validated with experimental literature data. The study presented may also help understanding the fluid-particle interactions from both theoretical and educational standpoints. (paper)

  17. Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube

    Science.gov (United States)

    Zhou, Guangzhao; Xu, Kun; Liu, Feng

    2018-01-01

    The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics are of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru and Tenaud ["Evaluation of TVD high resolution schemes for unsteady viscous shocked flows," Comput. Fluids 30, 89-113 (2001)] proposed a two-dimensional model problem as a numerical test case for high-resolution schemes to simulate the flow field in a square closed shock tube. Though many researchers attempted this problem using a variety of computational methods, there is not yet an agreed-upon grid-converged solution of the problem at the Reynolds number of 1000. This paper presents a rigorous grid-convergence study and the resulting grid-converged solutions for this problem by using a newly developed, efficient, and high-order gas-kinetic scheme. Critical data extracted from the converged solutions are documented as benchmark data. The complex fluid dynamics of the flow at Re = 1000 are discussed and analyzed in detail. Major phenomena revealed by the numerical computations include the downward concentration of the fluid through the curved shock, the formation of the vortices, the mechanism of the shock wave bifurcation, the structure of the jet along the bottom wall, and the Kelvin-Helmholtz instability near the contact surface. Presentation and analysis of those flow processes provide important physical insight into the complex flow physics occurring in a shock tube.

  18. Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary

    International Nuclear Information System (INIS)

    Mahanthesh, B.; Gireesha, B.J.; Gorla, R.S. Reddy; Abbasi, F.M.; Shehzad, S.A.

    2016-01-01

    Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al 2 O3 and TiO 2 types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.

  19. A numerical method for the solution of three-dimensional incompressible viscous flow using the boundary-fitted curvilinear coordinate transformation and domain decomposition technique

    International Nuclear Information System (INIS)

    Umegaki, Kikuo; Miki, Kazuyoshi

    1990-01-01

    A numerical method is developed to solve three-dimensional incompressible viscous flow in complicated geometry using curvilinear coordinate transformation and domain decomposition technique. In this approach, a complicated flow domain is decomposed into several subdomains, each of which has an overlapping region with neighboring subdomains. Curvilinear coordinates are numerically generated in each subdomain using the boundary-fitted coordinate transformation technique. The modified SMAC scheme is developed to solve Navier-Stokes equations in which the convective terms are discretized by the QUICK method. A fully vectorized computer program is developed on the basis of the proposed method. The program is applied to flow analysis in a semicircular curved, 90deg elbow and T-shape branched pipes. Computational time with the vector processor of the HITAC S-810/20 supercomputer system, is reduced to 1/10∼1/20 of that with a scalar processor. (author)

  20. Numerical method for calculation of 3D viscous turbomachine flow taking into account stator/rotor unsteady interaction

    Energy Technology Data Exchange (ETDEWEB)

    Rusanov, A V; Yershov, S V [Institute of Mechanical Engineering Problems of National Academy of Sciences of Ukraine Kharkov (Ukraine)

    1998-12-31

    The numerical method is suggested for the calculation of the 3D periodically unsteady viscous cascade flow evoked by the aerodynamics interaction of blade rows. Such flow is described by the thin-layer Reynolds-averaged unsteady Navier-Stokes equations. The turbulent effects are simulated with the modified Baldwin-Lomax turbulence model. The problem statement allows to consider an unsteady flow through either a single turbo-machine stage or a multi stage turbomachine. The sliding mesh techniques and the time-space non-oscillatory square interpolation are used in axial spacings to calculate the flow in a computational domain that contains the reciprocally moving elements. The gasdynamical equations are integrated numerically with the implicit quasi-monotonous Godunov`s type ENO scheme of the second or third order of accuracy. The suggested numerical method is incorporated in the FlowER code developed by authors for calculations of the 3D viscous compressible flows through multi stage turbomachines. The numerical results are presented for unsteady turbine stage throughflows. The method suggested is shown to simulate qualitatively properly the main unsteady cascade effects in particular the periodically blade loadings, the propagation of stator wakes through rotor blade passage and the unsteady temperature flowfields for stages with cooled stator blades. (author) 21 refs.

  1. Numerical method for calculation of 3D viscous turbomachine flow taking into account stator/rotor unsteady interaction

    Energy Technology Data Exchange (ETDEWEB)

    Rusanov, A.V.; Yershov, S.V. [Institute of Mechanical Engineering Problems of National Academy of Sciences of Ukraine Kharkov (Ukraine)

    1997-12-31

    The numerical method is suggested for the calculation of the 3D periodically unsteady viscous cascade flow evoked by the aerodynamics interaction of blade rows. Such flow is described by the thin-layer Reynolds-averaged unsteady Navier-Stokes equations. The turbulent effects are simulated with the modified Baldwin-Lomax turbulence model. The problem statement allows to consider an unsteady flow through either a single turbo-machine stage or a multi stage turbomachine. The sliding mesh techniques and the time-space non-oscillatory square interpolation are used in axial spacings to calculate the flow in a computational domain that contains the reciprocally moving elements. The gasdynamical equations are integrated numerically with the implicit quasi-monotonous Godunov`s type ENO scheme of the second or third order of accuracy. The suggested numerical method is incorporated in the FlowER code developed by authors for calculations of the 3D viscous compressible flows through multi stage turbomachines. The numerical results are presented for unsteady turbine stage throughflows. The method suggested is shown to simulate qualitatively properly the main unsteady cascade effects in particular the periodically blade loadings, the propagation of stator wakes through rotor blade passage and the unsteady temperature flowfields for stages with cooled stator blades. (author) 21 refs.

  2. Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

    Science.gov (United States)

    Anderson, E. C.; Moss, J. N.

    1975-01-01

    The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

  3. Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

    Science.gov (United States)

    Anderson, E. C.; Moss, J. N.

    1975-01-01

    The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

  4. Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary

    Energy Technology Data Exchange (ETDEWEB)

    Mahanthesh, B., E-mail: bmanths@gmail.com [Department of Mathematics, AIMS Institutes, Peenya, 560058 Bangalore (India); Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Gireesha, B.J., E-mail: bjgireesu@rediffmail.com [Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Gorla, R.S. Reddy, E-mail: r.gorla@csuohio.edu [Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)

    2016-11-01

    Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al{sub 2}O3 and TiO{sub 2} types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.

  5. Large-scale thermal convection of viscous fluids in a faulted system: 3D test case for numerical codes

    Science.gov (United States)

    Magri, Fabien; Cacace, Mauro; Fischer, Thomas; Kolditz, Olaf; Wang, Wenqing; Watanabe, Norihiro

    2017-04-01

    In contrast to simple homogeneous 1D and 2D systems, no appropriate analytical solutions exist to test onset of thermal convection against numerical models of complex 3D systems that account for variable fluid density and viscosity as well as permeability heterogeneity (e.g. presence of faults). Owing to the importance of thermal convection for the transport of energy and minerals, the development of a benchmark test for density/viscosity driven flow is crucial to ensure that the applied numerical models accurately simulate the physical processes at hands. The presented study proposes a 3D test case for the simulation of thermal convection in a faulted system that accounts for temperature dependent fluid density and viscosity. The linear stability analysis recently developed by Malkovsky and Magri (2016) is used to estimate the critical Rayleigh number above which thermal convection of viscous fluids is triggered. The numerical simulations are carried out using the finite element technique. OpenGeoSys (Kolditz et al., 2012) and Moose (Gaston et al., 2009) results are compared to those obtained using the commercial software FEFLOW (Diersch, 2014) to test the ability of widely applied codes in matching both the critical Rayleigh number and the dynamical features of convective processes. The methodology and Rayleigh expressions given in this study can be applied to any numerical model that deals with 3D geothermal processes in faulted basins as by example the Tiberas Basin (Magri et al., 2016). References Kolditz, O., Bauer, S., Bilke, L., Böttcher, N., Delfs, J. O., Fischer, T., U. J. Görke, T. Kalbacher, G. Kosakowski, McDermott, C. I., Park, C. H., Radu, F., Rink, K., Shao, H., Shao, H.B., Sun, F., Sun, Y., Sun, A., Singh, K., Taron, J., Walther, M., Wang,W., Watanabe, N., Wu, Y., Xie, M., Xu, W., Zehner, B., 2012. OpenGeoSys: an open-source initiative for numerical simulation of thermo-hydro-mechanical/chemical (THM/C) processes in porous media. Environmental

  6. Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid

    Science.gov (United States)

    Gupta, Sumeet; Poulikakos, Dimos; Kurtcuoglu, Vartan

    2008-09-01

    We present here the analytical solution of transient, laminar, viscous flow of an incompressible, Newtonian fluid driven by a harmonically oscillating pressure gradient in a straight elliptic annulus. The analytical formulation is based on the exact solution of the governing fluid flow equations known as Navier-Stokes equations. We validate the analytical solution using a finite-volume computational fluid dynamics approach. As the analytical solution includes Mathieu and modified Mathieu functions, we also present a stepwise procedure for their evaluation for large complex arguments typically associated with viscous flows. We further outline the procedure for evaluating the associated Fourier coefficients and their eigenvalues. We finally apply the analytical solution to investigate the cerebrospinal fluid flow in the human spinal cavity, which features a shape similar to an elliptic annulus.

  7. Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

    International Nuclear Information System (INIS)

    Glowinski, R.; Le Tallec, P.

    1984-01-01

    The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

  8. Bulk viscous cosmology with causal transport theory

    International Nuclear Information System (INIS)

    Piattella, Oliver F.; Fabris, Júlio C.; Zimdahl, Winfried

    2011-01-01

    We consider cosmological scenarios originating from a single imperfect fluid with bulk viscosity and apply Eckart's and both the full and the truncated Müller-Israel-Stewart's theories as descriptions of the non-equilibrium processes. Our principal objective is to investigate if the dynamical properties of Dark Matter and Dark Energy can be described by a single viscous fluid and how such description changes when a causal theory (Müller-Israel-Stewart's, both in its full and truncated forms) is taken into account instead of Eckart's non-causal one. To this purpose, we find numerical solutions for the gravitational potential and compare its behaviour with the corresponding ΛCDM case. Eckart's and the full causal theory seem to be disfavoured, whereas the truncated theory leads to results similar to those of the ΛCDM model for a bulk viscous speed in the interval 10 −11 || cb 2 ∼ −8

  9. Numerical Asymptotic Solutions Of Differential Equations

    Science.gov (United States)

    Thurston, Gaylen A.

    1992-01-01

    Numerical algorithms derived and compared with classical analytical methods. In method, expansions replaced with integrals evaluated numerically. Resulting numerical solutions retain linear independence, main advantage of asymptotic solutions.

  10. New lidocaine lozenge as topical anesthesia compared to lidocaine viscous oral solution before upper gastrointestinal endoscopy

    DEFF Research Database (Denmark)

    Mogensen, Stine; Treldal, Charlotte; Feldager, Erik

    2012-01-01

    To evaluate the effect and acceptance of a new lidocaine lozenge compared with a lidocaine viscous oral solution as a pharyngeal anesthetic before upper gastrointestinal endoscopy (UGE), a diagnostic procedure commonly performed worldwide during which many patients experience severe discomfort...

  11. Algebraic mesh generation for large scale viscous-compressible aerodynamic simulation

    International Nuclear Information System (INIS)

    Smith, R.E.

    1984-01-01

    Viscous-compressible aerodynamic simulation is the numerical solution of the compressible Navier-Stokes equations and associated boundary conditions. Boundary-fitted coordinate systems are well suited for the application of finite difference techniques to the Navier-Stokes equations. An algebraic approach to boundary-fitted coordinate systems is one where an explicit functional relation describes a mesh on which a solution is obtained. This approach has the advantage of rapid-precise mesh control. The basic mathematical structure of three algebraic mesh generation techniques is described. They are transfinite interpolation, the multi-surface method, and the two-boundary technique. The Navier-Stokes equations are transformed to a computational coordinate system where boundary-fitted coordinates can be applied. Large-scale computation implies that there is a large number of mesh points in the coordinate system. Computation of viscous compressible flow using boundary-fitted coordinate systems and the application of this computational philosophy on a vector computer are presented

  12. Numerical Investigation of Thermal Radiation and Viscous Effects on Entropy Generation in Forced Convection Blood Flow over an Axisymmetric Stretching Sheet

    Directory of Open Access Journals (Sweden)

    Mohammad Yaghoub Abdollahzadeh Jamalabadi

    2016-05-01

    Full Text Available Numerical and analytical investigation of the effects of thermal radiation and viscous heating on a convective flow of a non-Newtonian, incompressible fluid in an axisymmetric stretching sheet with constant temperature wall is performed. The power law model of the blood is used for the non-Newtonian model of the fluid and the Rosseland model for the thermal radiative heat transfer in an absorbing medium and viscous heating are considered as the heat sources. The non-dimensional governing equations are transformed to similarity form and solved numerically. A parameter study on entropy generation in medium is presented based on the Second Law of Thermodynamics by considering various parameters such as the thermal radiation parameter, the Brinkman number, Prandtl number, Eckert number.

  13. On the thermal stability for a model reactive flow with viscous dissipation

    International Nuclear Information System (INIS)

    Okoya, S.S.

    2006-12-01

    We study the thermal stability of a reactive flow of a third-grade fluid with viscous heating and chemical reaction between two horizontal flat plates, where the top is moving with a uniform speed and the bottom plate is fixed in the presence of an imposed pressure gradient. This study is a natural continuation of earlier work on rectilinear shear flows. The governing equations are non-dimensionalized and the resulting system of equations are not coupled. An approximate explicit solution is found for the flow velocity using homotopy - perturbation technique and the range of validity is determined. After the velocity is known, the heat transport may be analyzed. It is found that the temperature solution depends on the non-Newtonian material parameter of the fluid, Λ, viscous heating parameter, Γ, and an exponent, m. Attention is focused upon the disappearance of criticality of the solution set {β, δ, θ max } for various values of Λ, Γ and m, and the numerical computations are presented graphically to show salient features of the solution set. (author)

  14. Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation

    Directory of Open Access Journals (Sweden)

    Javad Alinejad

    2012-01-01

    Full Text Available The flow and heat transfer characteristics of incompressible viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation is investigated numerically. The similarity transformation reduces the time-independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear equation for the velocity field and differential equation by variable coefficient for the temperature field , are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. The effect of various values of Prandtl number, Eckert number and nonlinear stretching parameter are studied. The results presented graphically show some behaviors such as decrease in dimensionless temperature due to increase in Pr number, and curve relocations are observed when heat dissipation is considered.

  15. Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

    Science.gov (United States)

    Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

    2014-01-01

    Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

  16. Numerical simulation of energy equation with viscous dissipation for compressible flow over cones

    International Nuclear Information System (INIS)

    Asif, M.; Chughtai, I.R.

    1998-01-01

    A finite volume discretization technique has been used to solve the energy equation with viscous dissipation. The effects of viscous heat dissipation for Mach numbers 1.5 and 2.0, at an angle of attack of 0 degree, over sharp and blunt cones have been studied. Algebraic equations have been solved using line-by-line Tda method. Supersonic flow over cones has been analyzed and discussed with and without considering the viscous dissipation effects. It has been found that the effects of viscous dissipation increase with the increase in Mach number. Viscous dissipation affects the temperature distribution of the body. However, the temperature difference in these cases was insignificant. This may be due to the fact that these analysis have been done at 0 km altitude. (author)

  17. Hydromagnetic flow of third grade nanofluid with viscous dissipation and flux conditions

    Energy Technology Data Exchange (ETDEWEB)

    Hussain, T. [Faculty of Computing, Mohammad Ali Jinnah University, Islamabad 44000 (Pakistan); Shehzad, S. A., E-mail: ali-qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia); Alsaedi, A. [Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)

    2015-08-15

    This article investigates the magnetohydrodynamic flow of third grade nanofluid with thermophoresis and Brownian motion effects. Energy equation is considered in the presence of thermal radiation and viscous dissipation. Rosseland’s approximation is employed for thermal radiation. The heat and concentration flux conditions are taken into account. The governing nonlinear mathematical expressions of velocity, temperature and concentration are converted into dimensionless expressions via transformations. Series solutions of the dimensionless velocity, temperature and concentration are developed. Convergence of the constructed solutions is checked out both graphically and numerically. Effects of interesting physical parameters on the temperature and concentration are plotted and discussed in detail. Numerical values of skin-friction coefficient are computed for the hydrodynamic and hydromagnetic flow cases.

  18. Spurious Numerical Solutions Of Differential Equations

    Science.gov (United States)

    Lafon, A.; Yee, H. C.

    1995-01-01

    Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

  19. Periodic folding of viscous sheets

    Science.gov (United States)

    Ribe, Neil M.

    2003-09-01

    The periodic folding of a sheet of viscous fluid falling upon a rigid surface is a common fluid mechanical instability that occurs in contexts ranging from food processing to geophysics. Asymptotic thin-layer equations for the combined stretching-bending deformation of a two-dimensional sheet are solved numerically to determine the folding frequency as a function of the sheet’s initial thickness, the pouring speed, the height of fall, and the fluid properties. As the buoyancy increases, the system bifurcates from “forced” folding driven kinematically by fluid extrusion to “free” folding in which viscous resistance to bending is balanced by buoyancy. The systematics of the numerically predicted folding frequency are in good agreement with laboratory experiments.

  20. Diffusion on Viscous Fluids, Existence and Asymptotic Properties of Solutions,

    Science.gov (United States)

    1983-09-01

    Matematica - Politecuico di Milano (1982). 11.* P. Secchi "On the Initial Value ProbleM for the Nquations of Notion of Viscous Incompressible Fluids In...of two viscous Incompressible Fluids’, preprint DepartLmento dl matematica - Politecuico di Milano (1982). -15- 11. P. Secchi 00n the XnitiaI Value

  1. Newton solution of inviscid and viscous problems

    International Nuclear Information System (INIS)

    Venkatakrishnan, V.

    1988-01-01

    The application of Newton iteration to inviscid and viscous airfoil calculations is examined. Spatial discretization is performed using upwind differences with split fluxes. The system of linear equations which arises as a result of linearization in time is solved directly using either a banded matrix solver or a sparse matrix solver. In the latter case, the solver is used in conjunction with the nested dissection strategy, whose implementation for airfoil calculations is discussed. The boundary conditions are also implemented in a fully implicit manner, thus yielding quadratic convergence. Complexities such as the ordering of cell nodes and the use of a far field vortex to correct freestream for a lifting airfoil are addressed. Various methods to accelerate convergence and improve computational efficiency while using Newton iteration are discussed. Results are presented for inviscid, transonic nonlifting and lifting airfoils and also for laminar viscous cases. 17 references

  2. Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension

    Science.gov (United States)

    Bland, Michael T.; McKinnon, William B.

    2018-05-01

    Ganymede's bright terrain formed during a near-global resurfacing event (or events) that produced both heavily tectonized and relatively smooth terrains. The mechanism(s) by which resurfacing occurred on Ganymede (e.g., cryovolcanic or tectonic), and the relationship between the older, dark and the younger, bright terrain are fundamental to understanding the geological evolution of the satellite. Using a two-dimensional numerical model of lithospheric extension that has previously been used to successfully simulate surface deformation consistent with grooved terrain morphologies, we investigate whether large-amplitude preexisting topography can be resurfaced (erased) by extension (i.e., tectonic resurfacing). Using synthetically produced initial topography, we show that when the total relief of the initial topography is larger than 25-50 m, periodic groove-like structures fail to form. Instead, extension is localized in a few individual, isolated troughs. These results pose a challenge to the tectonic resurfacing hypothesis. We further investigate the effects of preexisting topography by performing suites of simulations initialized with topography derived from digital terrain models of Ganymede's surface. These include dark terrain, fresh (relatively deep) impact craters, smooth bright terrain, and a viscously relaxed impact crater. The simulations using dark terrain and fresh impact craters are consistent with our simulations using synthetic topography: periodic groove-like deformation fails to form. In contrast, when simulations were initialized with bright smooth terrain topography, groove-like deformation results from a wide variety of heat flow and surface temperature conditions. Similarly, when a viscously relaxed impact crater was used, groove-like structures were able to form during extension. These results suggest that tectonic resurfacing may require that the amplitude of the initial topography be reduced before extension begins. We emphasize that viscous

  3. A numerical study of viscous vortex rings using a spectral method

    Science.gov (United States)

    Stanaway, S. K.; Cantwell, B. J.; Spalart, Philippe R.

    1988-01-01

    Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass.

  4. 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.

  5. Modified rational Legendre approach to laminar viscous flow over a semi-infinite flat plate

    International Nuclear Information System (INIS)

    Tajvidi, T.; Razzaghi, M.; Dehghan, M.

    2008-01-01

    A numerical method for solving the classical Blasius' equation is proposed. The Blasius' equation is a third order nonlinear ordinary differential equation , which arises in the problem of the two-dimensional laminar viscous flow over a semi-infinite flat plane. The approach is based on a modified rational Legendre tau method. The operational matrices for the derivative and product of the modified rational Legendre functions are presented. These matrices together with the tau method are utilized to reduce the solution of Blasius' equation to the solution of a system of algebraic equations. A numerical evaluation is included to demonstrate the validity and applicability of the method and a comparison is made with existing results

  6. A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

    Science.gov (United States)

    Das, Pratik; Sen, Oishik; Jacobs, Gustaaf; Udaykumar, H. S.

    2017-09-01

    A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid-fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid-fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.

  7. Highly-viscous microjet induced by an impact

    Science.gov (United States)

    Onuki, Hajime; Tagawa, Yoshiyuki

    2017-11-01

    Ejection of a liquid microjet with high viscosity is essential for various novel technologies such as 3D printers, printed electronics and bio printers. To generate such a microjet, we focus on utilizing an impulsive force. Thanks to a short-time impact, the viscous dissipation in the liquid can be suppressed, resulting in the ejection of viscous microjets. In this study, we investigate ejection mechanism of the viscous jet experimentally and numerically. The jet velocity decreases with increasing the viscosity of a liquid. Remarkably it is found that all the data of jet velocities normalized by initial velocities of the liquid as a function of Reynolds number, the balance between the inertia force and the viscous force, collapse onto a single master curve.

  8. A least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line

    KAUST Repository

    He, Qiaolin

    2011-06-01

    In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.

  9. Efficient Simulation of Compressible, Viscous Fluids using Multi-rate Time Integration

    Science.gov (United States)

    Mikida, Cory; Kloeckner, Andreas; Bodony, Daniel

    2017-11-01

    In the numerical simulation of problems of compressible, viscous fluids with single-rate time integrators, the global timestep used is limited to that of the finest mesh point or fastest physical process. This talk discusses the application of multi-rate Adams-Bashforth (MRAB) integrators to an overset mesh framework to solve compressible viscous fluid problems of varying scale with improved efficiency, with emphasis on the strategy of timescale separation and the application of the resulting numerical method to two sample problems: subsonic viscous flow over a cylinder and a viscous jet in crossflow. The results presented indicate the numerical efficacy of MRAB integrators, outline a number of outstanding code challenges, demonstrate the expected reduction in time enabled by MRAB, and emphasize the need for proper load balancing through spatial decomposition in order for parallel runs to achieve the predicted time-saving benefit. This material is based in part upon work supported by the Department of Energy, National Nuclear Security Administration, under Award Number DE-NA0002374.

  10. Numerical Solution of the Blasius Viscous Flow Problem by Quartic B-Spline Method

    Directory of Open Access Journals (Sweden)

    Hossein Aminikhah

    2016-01-01

    Full Text Available A numerical method is proposed to study the laminar boundary layer about a flat plate in a uniform stream of fluid. The presented method is based on the quartic B-spline approximations with minimizing the error L2-norm. Theoretical considerations are discussed. The computed results are compared with some numerical results to show the efficiency of the proposed approach.

  11. Self-consistent viscous heating of rapidly compressed turbulence

    Science.gov (United States)

    Campos, Alejandro; Morgan, Brandon

    2017-11-01

    Given turbulence subjected to infinitely rapid deformations, linear terms representing interactions between the mean flow and the turbulence dictate the evolution of the flow, whereas non-linear terms corresponding to turbulence-turbulence interactions are safely ignored. For rapidly deformed flows where the turbulence Reynolds number is not sufficiently large, viscous effects can't be neglected and tend to play a prominent role, as shown in the study of Davidovits & Fisch (2016). For such a case, the rapid increase of viscosity in a plasma-as compared to the weaker scaling of viscosity in a fluid-leads to the sudden viscous dissipation of turbulent kinetic energy. As shown in Davidovits & Fisch, increases in temperature caused by the direct compression of the plasma drive sufficiently large values of viscosity. We report on numerical simulations of turbulence where the increase in temperature is the result of both the direct compression (an inviscid mechanism) and the self-consistent viscous transfer of energy from the turbulent scales towards the thermal energy. A comparison between implicit large-eddy simulations against well-resolved direct numerical simulations is included to asses the effect of the numerical and subgrid-scale dissipation on the self-consistent viscous This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  12. MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect

    Science.gov (United States)

    Zokri, S. M.; Arifin, N. S.; Salleh, M. Z.; Kasim, A. R. M.; Mohammad, N. F.; Yusoff, W. N. S. W.

    2017-09-01

    This study investigates the influence of viscous dissipation on magnetohydrodynamic (MHD) flow of Jeffrey nanofluid over a stretching sheet with convective boundary conditions. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by utilizing the similarity transformation variables. The Runge-Kutta Fehlberg method is used to solve the problem numerically. The numerical solutions obtained are presented graphically for several dimensionless parameters such as Brownian motion, Lewis number and Eckert number on the specified temperature and concentration profiles. It is noted that the temperature profile is accelerated due to increasing values of Brownian motion parameter and Eckert number. In contrast, both the Brownian motion parameter and Lewis number have caused the deceleration in the concentration profiles.

  13. Viscous, Resistive Magnetorotational Modes

    DEFF Research Database (Denmark)

    Pessah, Martin Elias; Chan, Chi-kwan

    2008-01-01

    We carry out a comprehensive analysis of the behavior of the magnetorotational instability (MRI) in viscous, resistive plasmas. We find exact, non-linear solutions of the non-ideal magnetohydrodynamic (MHD) equations describing the local dynamics of an incompressible, differentially rotating...

  14. Sensitivity analysis of numerical solutions for environmental fluid problems

    International Nuclear Information System (INIS)

    Tanaka, Nobuatsu; Motoyama, Yasunori

    2003-01-01

    In this study, we present a new numerical method to quantitatively analyze the error of numerical solutions by using the sensitivity analysis. If a reference case of typical parameters is one calculated with the method, no additional calculation is required to estimate the results of the other numerical parameters such as more detailed solutions. Furthermore, we can estimate the strict solution from the sensitivity analysis results and can quantitatively evaluate the reliability of the numerical solution by calculating the numerical error. (author)

  15. Qualitative analysis of cosmological models in Brans-Dicke theory, solutions from non-minimal coupling and viscous universe

    International Nuclear Information System (INIS)

    Romero Filho, C.A.

    1988-01-01

    Using dynamical system theory we investigate homogeneous and isotropic models in Brans-Dicke theory for perfect fluids with general equation of state and arbitrary ω. Phase diagrams are drawn on the Poincare sphere which permits a qualitative analysis of the models. Based on this analysis we construct a method for generating classes of solutions in Brans-Dicke theory. The same technique is used for studying models arising from non-minimal coupling of electromagnetism with gravity. In addition, viscous fluids are considered and non-singular solutions with bulk viscosity are found. (author)

  16. Exact solutions, numerical relativity and gravitational radiation

    International Nuclear Information System (INIS)

    Winicour, J.

    1986-01-01

    In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

  17. Mixed convection boundary layer flow over a moving vertical flat plate in an external fluid flow with viscous dissipation effect.

    Directory of Open Access Journals (Sweden)

    Norfifah Bachok

    Full Text Available The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.

  18. Analysis of numerical solutions for Bateman equations

    International Nuclear Information System (INIS)

    Loch, Guilherme G.; Bevilacqua, Joyce S.

    2013-01-01

    The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)

  19. 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

  20. One-dimensional reduction of viscous jets. II. Applications

    Science.gov (United States)

    Pitrou, Cyril

    2018-04-01

    In a companion paper [Phys. Rev. E 97, 043115 (2018), 10.1103/PhysRevE.97.043115], a formalism allowing to describe viscous fibers as one-dimensional objects was developed. We apply it to the special case of a viscous fluid torus. This allows to highlight the differences with the basic viscous string model and with its viscous rod model extension. In particular, an elliptic deformation of the torus section appears because of surface tension effects, and this cannot be described by viscous string nor viscous rod models. Furthermore, we study the Rayleigh-Plateau instability for periodic deformations around the perfect torus, and we show that the instability is not sufficient to lead to the torus breakup in several droplets before it collapses to a single spherical drop. Conversely, a rotating torus is dynamically attracted toward a stationary solution, around which the instability can develop freely and split the torus in multiple droplets.

  1. 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)

  2. On the homogenization of the acoustic wave propagation in perforated ducts of finite length for an inviscid and a viscous model.

    Science.gov (United States)

    Semin, Adrien; Schmidt, Kersten

    2018-02-01

    The direct numerical simulation of the acoustic wave propagation in multiperforated absorbers with hundreds or thousands of tiny openings would result in a huge number of basis functions to resolve the microstructure. One is, however, primarily interested in effective and so homogenized transmission and absorption properties and how they are influenced by microstructure and its endpoints. For this, we introduce the surface homogenization that asymptotically decomposes the solution in a macroscopic part, a boundary layer corrector close to the interface and a near-field part close to its ends. The effective transmission and absorption properties are expressed by transmission conditions for the macroscopic solution on an infinitely thin interface and corner conditions at its endpoints to ensure the correct singular behaviour, which are intrinsic to the microstructure. We study and give details on the computation of the effective parameters for an inviscid and a viscous model and show their dependence on geometrical properties of the microstructure for the example of Helmholtz equation. Numerical experiments indicate that with the obtained macroscopic solution representation one can achieve an high accuracy for low and high porosities as well as for viscous boundary conditions while using only a small number of basis functions.

  3. Simultaneous viscous-inviscid coupling via transpiration

    International Nuclear Information System (INIS)

    Yiu, K.F.C.; Giles, M.B.

    1995-01-01

    In viscous-inviscid coupling analysis, the direct coupling technique and the inverse coupling technique are commonly adopted. However, stability and convergence of the algorithms derived are usually very unsatisfactory. Here, by using the transpiration technique to simulate the effect of the displacement thickness, a new simultaneous coupling method is derived. The integral boundary layer equations and the full potential equation are chosen to be the viscous-inviscid coupled system. After discretization, the Newton-Raphson technique is proposed to solve the coupled nonlinear system. Several numerical results are used to demonstrate the accuracy and efficiency of the proposed method. 15 refs., 23 figs

  4. Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions

    Science.gov (United States)

    Fang, Tiegang

    2014-05-01

    In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.

  5. Quasiadiabatic modes from viscous inhomogeneities

    CERN Document Server

    Giovannini, Massimo

    2016-04-20

    The viscous inhomogeneities of a relativistic plasma determine a further class of entropic modes whose amplitude must be sufficiently small since curvature perturbations are observed to be predominantly adiabatic and Gaussian over large scales. When the viscous coefficients only depend on the energy density of the fluid the corresponding curvature fluctuations are shown to be almost adiabatic. After addressing the problem in a gauge-invariant perturbative expansion, the same analysis is repeated at a non-perturbative level by investigating the nonlinear curvature inhomogeneities induced by the spatial variation of the viscous coefficients. It is demonstrated that the quasiadiabatic modes are suppressed in comparison with a bona fide adiabatic solution. Because of its anomalously large tensor to scalar ratio the quasiadiabatic mode cannot be a substitute for the conventional adiabatic paradigm so that, ultimately, the present findings seems to exclude the possibility of a successful accelerated dynamics solely...

  6. Numerical integration of asymptotic solutions of ordinary differential equations

    Science.gov (United States)

    Thurston, Gaylen A.

    1989-01-01

    Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

  7. Diffusivity measurements of volatile organics in levitated viscous aerosol particles

    Science.gov (United States)

    Bastelberger, Sandra; Krieger, Ulrich K.; Luo, Beiping; Peter, Thomas

    2017-07-01

    Field measurements indicating that atmospheric secondary organic aerosol (SOA) particles can be present in a highly viscous, glassy state have spurred numerous studies addressing low diffusivities of water in glassy aerosols. The focus of these studies is on kinetic limitations of hygroscopic growth and the plasticizing effect of water. In contrast, much less is known about diffusion limitations of organic molecules and oxidants in viscous matrices. These may affect atmospheric chemistry and gas-particle partitioning of complex mixtures with constituents of different volatility. In this study, we quantify the diffusivity of a volatile organic in a viscous matrix. Evaporation of single particles generated from an aqueous solution of sucrose and small amounts of volatile tetraethylene glycol (PEG-4) is investigated in an electrodynamic balance at controlled relative humidity (RH) and temperature. The evaporative loss of PEG-4 as determined by Mie resonance spectroscopy is used in conjunction with a radially resolved diffusion model to retrieve translational diffusion coefficients of PEG-4. Comparison of the experimentally derived diffusivities with viscosity estimates for the ternary system reveals a breakdown of the Stokes-Einstein relationship, which has often been invoked to infer diffusivity from viscosity. The evaporation of PEG-4 shows pronounced RH and temperature dependencies and is severely depressed for RH ≲ 30 %, corresponding to diffusivities pollutant molecules such as polycyclic aromatic hydrocarbons (PAHs).

  8. Existence and Stability of Viscous Shock Profiles for 2-D Isentropic MHD with Infinite Electrical Resistivity

    International Nuclear Information System (INIS)

    Blake, B.; Zumbrun, K.; Lafitte, O.

    2010-01-01

    For the two-dimensional Navier Stokes equations of isentropic magnetohydrodynamics (MHD) with γ-law gas equation of state, γ≥1, and infinite electrical resistivity, we carry out a global analysis categorizing all possible viscous shock profiles. Precisely, we show that the phase portrait of the Crave ling-wave ODE generically consists of either two rest points connected by a viscous Lax profile, or else four rest points, two saddles and two nodes. In the latter configuration, which rest points are connected by profiles depends on the ratio of viscosities, and can involve Lax, over-compressive, or under-compressive shock profiles. Considered as three-dimensional solutions, under-compressive shocks are Lax-type (Alfven) waves. For the monatomic and diatomic cases γ=5/3 and γ=7/5, with standard viscosity ratio for a nonmagnetic gas, we find numerically that the the nodes are connected by a family of over-compressive profiles bounded by Lax profiles connecting saddles to nodes, with no under-compressive shocks occurring. We carry out a systematic numerical Evans function analysis indicating that all of these two-dimensional shock profiles are linearly and nonlinearly stable, both with respect to two- and three-dimensional perturbations. For the same gas constants, but different viscosity ratios, we investigate also cases for which under-compressive shocks appear; these are seen numerically to be stable as well, both with respect to two-dimensional and (in the neutral sense of convergence to nearby Riemann solutions) three-dimensional perturbations. (authors)

  9. Free-surface viscous flow solution methods for ship hydrodynamics

    NARCIS (Netherlands)

    Wackers, J.; Koren, B.; Raven, H.C.; Ploeg, van der A.; Starke, A.R.; Deng, G.; Queutey, P.; Visonneau, M.; Hino, T.; Ohashi, K.

    2011-01-01

    The simulation of viscous free-surface water flow is a subject that has reached a certain maturity and is nowadays used in industrial applications, like the simulation of the flow around ships. While almost all methods used are based on the Navier-Stokes equations, the discretisation methods for the

  10. Effects of Second-Order Slip and Viscous Dissipation on the Analysis of the Boundary Layer Flow and Heat Transfer Characteristics of a Casson Fluid

    Directory of Open Access Journals (Sweden)

    Mohammad M. Rahman

    2016-11-01

    Full Text Available The aim of the present study is to analyze numerically the steady boundary layer flow and heat transfer characteristics of Casson fluid with variable temperature and viscous dissipation past a permeable shrinking sheet with second order slip velocity. Using appropriate similarity transformations, the basic nonlinear partial differential equations have been transformed into ordinary differential equations. These equations have been solved numerically for different values of the governing parameters namely: shrinking parametersuction parameterCasson parameterfirst order slip parametersecond order slip parameter  Prandtl number  and the Eckert number  using the bvp4c function from MATLAB. A stability analysis has also been performed. Numerical results have been obtained for the reduced skin-friction, heat transfer and the velocity and temperature profiles. The results indicate that dual solutions exist for the shrinking surface for certain values of the parameter space. The stability analysis indicates that the lower solution branch is unstable, while the upper solution branch is stable and physically realizable. In addition, it is shown that for a viscous fluida very good agreement exists between the present numerical results and those reported in the open literature. The present results are original and new for the boundary-layer flow and heat transfer past a shrinking sheet in a Casson fluid. Therefore, this study has importance for researchers working in the area of non-Newtonian fluids, in order for them to become familiar with the flow behavior and properties of such fluids.

  11. A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings

    Science.gov (United States)

    Yates, John E.

    1991-01-01

    A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.

  12. Motion of two spheres translating and rotating through a viscous fluid with slip surfaces

    International Nuclear Information System (INIS)

    Saad, E I

    2012-01-01

    The axisymmetrical motion of two spherical particles translating along and rotating about a common line that joins their centers in viscous fluid with slip flow boundary conditions on their surfaces has been studied numerically. The particles may differ in radius and in translational and angular velocities. Under the Stokesian approximation, a general solution is constructed from the superposition of the basic functions in the two spherical coordinate systems based on the centers of the particles. The boundary conditions at their surfaces are satisfied by the collocation technique. Numerical results for the normalized drag force and couple acting on each sphere are obtained for various values of the slip coefficients, size ratio, separation parameter, and velocity ratio of the particles. The normalized force and couple on each particle reach the single particle limit as the distance between the centers grows large enough and each particle may then be translated and rotated independently of each other. The accuracy of the numerical technique has been tested against the known analytical solution for two spheres with no-slip surfaces. (paper)

  13. Viscous entrainment on hairy surfaces

    Science.gov (United States)

    Nasto, Alice; Brun, P.-T.; Hosoi, A. E.

    2018-02-01

    Nectar-drinking bats and honeybees have tongues covered with hairlike structures, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory, we explore the physical mechanisms that govern viscous entrainment in a hairy texture. Hairy surfaces are fabricated using laser cut molds and casting samples with polydimethylsiloxane (PDMS) elastomer. We model the liquid trapped within the texture using a Darcy-Brinkmann-like approach and derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both experiments and theory reveal an optimal hair density to maximize fluid uptake.

  14. The effect of diffusion in a new viscous continuum traffic model

    International Nuclear Information System (INIS)

    Yu Lei; Li Tong; Shi Zhongke

    2010-01-01

    In this Letter, we propose a new continuum traffic model with a viscous term. The linear stability condition for viscous shock waves is derived. We derive the Korteweg-de Vries (KdV) equation near the neutral stability line. Then we investigate the effect of the viscous term by numerical simulations. The results show that viscosity may induce oscillations and the amplitude of the oscillation increases as the viscosity coefficient increases. This agrees with the linear stability condition. The local clusters are compressed by increasing the viscosity coefficient in the cluster study.

  15. The effect of diffusion in a new viscous continuum traffic model

    Energy Technology Data Exchange (ETDEWEB)

    Yu Lei, E-mail: yuleijk@126.co [College of Automation, Northwestern Polytechnical University, Xi' an, ShaanXi (China); Li Tong [Department of Mathematics, University of Iowa, Iowa City, IA (United States); Shi Zhongke [College of Automation, Northwestern Polytechnical University, Xi' an, ShaanXi (China)

    2010-05-10

    In this Letter, we propose a new continuum traffic model with a viscous term. The linear stability condition for viscous shock waves is derived. We derive the Korteweg-de Vries (KdV) equation near the neutral stability line. Then we investigate the effect of the viscous term by numerical simulations. The results show that viscosity may induce oscillations and the amplitude of the oscillation increases as the viscosity coefficient increases. This agrees with the linear stability condition. The local clusters are compressed by increasing the viscosity coefficient in the cluster study.

  16. An Algorithm for the Numerical Solution of the Pseudo Compressible Navier-stokes Equations Based on the Experimenting Fields Approach

    KAUST Repository

    Salama, Amgad; Sun, Shuyu; Amin, Mohamed F. El

    2015-01-01

    In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.

  17. An Algorithm for the Numerical Solution of the Pseudo Compressible Navier-stokes Equations Based on the Experimenting Fields Approach

    KAUST Repository

    Salama, Amgad

    2015-06-01

    In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.

  18. On the application of reynolds theory to thermo-piezo-viscous lubrication in oil hydraulics

    DEFF Research Database (Denmark)

    Johansen, Per; Roemer, Daniel Beck; Andersen, Torben O.

    2015-01-01

    The efficiency of fluid power motors and pumps is a subject to research, which has generated numerous publications during the last three decades. The main incentives for this research are optimization of reliability and efficiency through the study of loss and wear mechanisms, which are very....... In this paper the derivation of Reynolds equation from the continuum assumption is reviewed and it is shown that the validity of Reynolds theory based pressure field solutions in oil hydraulic thermo-piezo-viscous lubrication models are subject to maximum bounds on the pressure and temperature field gradients...

  19. USE OF POLYMERS TO RECOVER VISCOUS OIL FROM UNCONVENTIONAL RESERVOIRS

    Energy Technology Data Exchange (ETDEWEB)

    Randall Seright

    2011-09-30

    This final technical progress report summarizes work performed the project, 'Use of Polymers to Recover Viscous Oil from Unconventional Reservoirs.' The objective of this three-year research project was to develop methods using water soluble polymers to recover viscous oil from unconventional reservoirs (i.e., on Alaska's North Slope). The project had three technical tasks. First, limits were re-examined and redefined for where polymer flooding technology can be applied with respect to unfavorable displacements. Second, we tested existing and new polymers for effective polymer flooding of viscous oil, and we tested newly proposed mechanisms for oil displacement by polymer solutions. Third, we examined novel methods of using polymer gels to improve sweep efficiency during recovery of unconventional viscous oil. This report details work performed during the project. First, using fractional flow calculations, we examined the potential of polymer flooding for recovering viscous oils when the polymer is able to reduce the residual oil saturation to a value less than that of a waterflood. Second, we extensively investigated the rheology in porous media for a new hydrophobic associative polymer. Third, using simulation and analytical studies, we compared oil recovery efficiency for polymer flooding versus in-depth profile modification (i.e., 'Bright Water') as a function of (1) permeability contrast, (2) relative zone thickness, (3) oil viscosity, (4) polymer solution viscosity, (5) polymer or blocking-agent bank size, and (6) relative costs for polymer versus blocking agent. Fourth, we experimentally established how much polymer flooding can reduce the residual oil saturation in an oil-wet core that is saturated with viscous North Slope crude. Finally, an experimental study compared mechanical degradation of an associative polymer with that of a partially hydrolyzed polyacrylamide. Detailed results from the first two years of the project may be

  20. Osmosis-driven viscous fingering of oil-in-water emulsions

    Science.gov (United States)

    Liu, Ying; Rallabandi, Bhargav; Baskaran, Mrudhula; Stone, Howard

    2017-11-01

    Viscous fingering occurs when a low viscosity fluid invades a more viscous fluid. Fingering of two miscible fluids is more complicated than that of immiscible fluids in that there is no sharp fluid-fluid interface and diffusion occurs between the phases. We experimentally studied the fingering of two miscible fluids: an oil-in-water emulsion and a sodium chloride solution. When the concentration of sodium chloride in the water phase in the emulsion exceeds that in the sodium chloride solution, the consequent osmotic flow automatically facilitates the occurrence of the fingering. On the contrary, when the sodium chloride solution has higher concentration, the spreading of emulsion is more uniform than the case without the concentration difference. We provide a model to rationalize and quantify these observations.

  1. Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction

    NARCIS (Netherlands)

    Veldman, AEP

    The paper presents a personal view on the history of viscous-inviscid interaction methods, a history closely related to the evolution of the method of matched asymptotic expansions. The main challenge in solving Prandtl's boundary-layer equations has been to overcome the singularity at a point of

  2. MHD stagnation point flow and heat transfer of a nanofluid over a permeable nonlinear stretching/shrinking sheet with viscous dissipation effect

    Science.gov (United States)

    Jusoh, Rahimah; Nazar, Roslinda

    2018-04-01

    The magnetohydrodynamic (MHD) stagnation point flow and heat transfer of an electrically conducting nanofluid over a nonlinear stretching/shrinking sheet is studied numerically. Mathematical modelling and analysis are attended in the presence of viscous dissipation. Appropriate similarity transformations are used to reduce the boundary layer equations for momentum, energy and concentration into a set of ordinary differential equations. The reduced equations are solved numerically using the built in bvp4c function in Matlab. The numerical and graphical results on the effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are analyzed and discussed in this paper. The study discovers the existence of dual solutions for a certain range of the suction parameter. The conducted stability analysis reveals that the first solution is stable and feasible, while the second solution is unstable.

  3. 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.

  4. Diffusivity measurements of volatile organics in levitated viscous aerosol particles

    Directory of Open Access Journals (Sweden)

    S. Bastelberger

    2017-07-01

    Full Text Available Field measurements indicating that atmospheric secondary organic aerosol (SOA particles can be present in a highly viscous, glassy state have spurred numerous studies addressing low diffusivities of water in glassy aerosols. The focus of these studies is on kinetic limitations of hygroscopic growth and the plasticizing effect of water. In contrast, much less is known about diffusion limitations of organic molecules and oxidants in viscous matrices. These may affect atmospheric chemistry and gas–particle partitioning of complex mixtures with constituents of different volatility. In this study, we quantify the diffusivity of a volatile organic in a viscous matrix. Evaporation of single particles generated from an aqueous solution of sucrose and small amounts of volatile tetraethylene glycol (PEG-4 is investigated in an electrodynamic balance at controlled relative humidity (RH and temperature. The evaporative loss of PEG-4 as determined by Mie resonance spectroscopy is used in conjunction with a radially resolved diffusion model to retrieve translational diffusion coefficients of PEG-4. Comparison of the experimentally derived diffusivities with viscosity estimates for the ternary system reveals a breakdown of the Stokes–Einstein relationship, which has often been invoked to infer diffusivity from viscosity. The evaporation of PEG-4 shows pronounced RH and temperature dependencies and is severely depressed for RH ≲ 30 %, corresponding to diffusivities < 10−14 cm2 s−1 at temperatures < 15 °C. The temperature dependence is strong, suggesting a diffusion activation energy of about 300 kJ mol−1. We conclude that atmospheric volatile organic compounds can be subject to severe diffusion limitations in viscous organic aerosol particles. This may enable an important long-range transport mechanism for organic material, including pollutant molecules such as polycyclic aromatic hydrocarbons (PAHs.

  5. The equivalence of perfect fluid space-times and viscous magnetohydrodynamic space-times in general relativity

    International Nuclear Information System (INIS)

    Tupper, B.O.J.

    1983-01-01

    The work of a previous article is extended to show that space-times which are the exact solutions of the field equations for a perfect fluid also may be exact solutions of the field equations for a viscous magnetohydrodynamic fluid. Conditions are found for this equivalence to exist and viscous magnetohydrodynamic solutions are found for a number of known perfect fluid space-times. (author)

  6. Numerical simulation of fire vortex

    Science.gov (United States)

    Barannikova, D. D.; Borzykh, V. E.; Obukhov, A. G.

    2018-05-01

    The article considers the numerical simulation of the swirling flow of air around the smoothly heated vertical cylindrical domain in the conditions of gravity and Coriolis forces action. The solutions of the complete system of Navie-Stocks equations are numerically solved at constant viscosity and heat conductivity factors. Along with the proposed initial and boundary conditions, these solutions describe the complex non-stationary 3D flows of viscous compressible heat conducting gas. For various instants of time of the initial flow formation stage using the explicit finite-difference scheme the calculations of all gas dynamics parameters, that is density, temperature, pressure and three velocity components of gas particles, have been run. The current instant lines corresponding to the trajectories of the particles movement in the emerging flow have been constructed. A negative direction of the air flow swirling occurred in the vertical cylindrical domain heating has been defined.

  7. Numerical simulation of steady cavitating flow of viscous fluid in a Francis hydroturbine

    Science.gov (United States)

    Panov, L. V.; Chirkov, D. V.; Cherny, S. G.; Pylev, I. M.; Sotnikov, A. A.

    2012-09-01

    Numerical technique was developed for simulation of cavitating flows through the flow passage of a hydraulic turbine. The technique is based on solution of steady 3D Navier—Stokes equations with a liquid phase transfer equation. The approch for setting boundary conditions meeting the requirements of cavitation testing standard was suggested. Four different models of evaporation and condensation were compared. Numerical simulations for turbines of different specific speed were compared with experiment.

  8. Viscous-inviscid interaction using the parabolized Navier-Stokes equations

    DEFF Research Database (Denmark)

    Filippone, Antonino; Sørensen, Jens Nørkær

    1997-01-01

    adaptive grid is used.The interaction is achieved by iterative updatingof the boundary conditions, through the wall transpiration concept. The Navier-Stokes equationsare discretized on a semi-staggered grid.Space-marching integration is performed starting from the stagnation streamline ontwo independent......A numerical model for the calculation of incompressible viscous flows past airfoils andwings has been developed. The approach is based on a strong viscous-inviscid coupling of aboundary element method with the Navier-Stokesequations in vorticity-streamfunction formulation.A semi-adaptive or fully...

  9. Numerical solution of singularity-perturbed two-point boundary-value problems

    International Nuclear Information System (INIS)

    Masenge, R.W.P.

    1993-07-01

    Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab

  10. Viscous modes, isocurvature perturbations and CMB initial conditions

    CERN Document Server

    Giovannini, Massimo

    2015-01-01

    When the predecoupling plasma is thermodinamically reversible its fluctuations are classified in terms of the adiabatic and entropic modes. A different category of physical solutions, so far unexplored, arises when the inhomogeneities of the viscosity coefficients induce computable curvature perturbations. The viscous modes are explicitly illustrated and compared with the conventional isocurvature solutions.

  11. A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools

    International Nuclear Information System (INIS)

    McHugh, P.R.; Ramshaw, J.D.

    1991-11-01

    MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equation voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs

  12. A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools

    Energy Technology Data Exchange (ETDEWEB)

    McHugh, P.R.; Ramshaw, J.D.

    1991-11-01

    MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equation voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.

  13. Research on the porous flow of the mechanism of viscous-elastic fluids displacing residual oil droplets in micro pores

    Science.gov (United States)

    Dong, Guanyu

    2018-03-01

    In order to analyze the microscopic stress field acting on residual oil droplets in micro pores, calculate its deformation, and explore the hydrodynamic mechanism of viscous-elastic fluids displacing oil droplets, the viscous-elastic fluid flow equations in micro pores are established by choosing the Upper Convected Maxwell constitutive equation; the numerical solutions of the flow field are obtained by volume control and Alternate Direction Implicit methods. From the above, the velocity field and microscopic stress field; the forces acting on residual oil droplets; the deformations of residual oil droplets by various viscous-elastic displacing fluids and at various Wiesenberg numbers are calculated and analyzed. The result demonstrated that both the normal stress and horizontal force acting on the residual oil droplets by viscous-elastic fluids are much larger compared to that of inelastic fluid; the distribution of normal stress changes abruptly; under the condition of the same pressure gradient in the system under investigation, the ratio of the horizontal forces acting on the residual oil droplets by different displacing fluids is about 1:8:20, which means that under the above conditions, the driving force on a oil droplet is 20 times higher for a viscous-elastic fluid compared to that of a Newtonian Fluid. The conclusions are supportive of the mechanism that viscous-elastic driving fluids can increase the Displacement Efficiency. This should be of help in designing new chemicals and selecting Enhanced Oil Recovery systems.

  14. Spatiotemporal resonances in mixing of open viscous fluids

    DEFF Research Database (Denmark)

    Okkels, Fridolin; Tabeling, Patrick

    2004-01-01

    In this Letter, we reveal a new dynamical phenomenon, called "spatiotemporal resonance," which is expected to take place in a broad range of viscous, periodically forced, open systems. The observation originates from a numerical and theoretical analysis of a micromixer, and is supported...

  15. Numerical investigation of heat and mass transfer processes in a spherical layer of viscous incompressible liquid with free boundaries

    Directory of Open Access Journals (Sweden)

    Zakurdaeva Alia

    2016-01-01

    Full Text Available The results of mathematical modelling of the dynamics of a mixture of the viscous incompressible liquid and gas, which fills a spherical layer with free boundaries and contains a gas bubble within itself, are presented in this paper. Spherical symmetry is assumed, and it is considered that the dynamics of the layer is determined by thermal, diffusive and inertial factors. On the basis of constructed numerical algorithm the studies of the formation of the liquid glass layers, which contain the carbon dioxide gas within themselves, have been conducted. The impact of the external thermal regime, external pressure and the density of gas in the bubble at the initial time on the dynamics of the layer, diffusion and heat-and-mass processes inside it is investigated. The results of numerical investigation of the full and simplified thermal problem statement, without consideration of gas diffusion, are compared.

  16. 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.

  17. Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows

    Science.gov (United States)

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

    2016-08-01

    The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.

  18. A simple and effective approach to prepare injectable macroporous calcium phosphate cement for bone repair: Syringe-foaming using a viscous hydrophilic polymeric solution.

    Science.gov (United States)

    Zhang, Jingtao; Liu, Weizhen; Gauthier, Olivier; Sourice, Sophie; Pilet, Paul; Rethore, Gildas; Khairoun, Khalid; Bouler, Jean-Michel; Tancret, Franck; Weiss, Pierre

    2016-02-01

    In this study, we propose a simple and effective strategy to prepare injectable macroporous calcium phosphate cements (CPCs) by syringe-foaming via hydrophilic viscous polymeric solution, such as using silanized-hydroxypropyl methylcellulose (Si-HPMC) as a foaming agent. The Si-HPMC foamed CPCs demonstrate excellent handling properties such as injectability and cohesion. After hardening the foamed CPCs possess hierarchical macropores and their mechanical properties (Young's modulus and compressive strength) are comparable to those of cancellous bone. Moreover, a preliminary in vivo study in the distal femoral sites of rabbits was conducted to evaluate the biofunctionality of this injectable macroporous CPC. The evidence of newly formed bone in the central zone of implantation site indicates the feasibility and effectiveness of this foaming strategy that will have to be optimized by further extensive animal experiments. A major challenge in the design of biomaterial-based injectable bone substitutes is the development of cohesive, macroporous and self-setting calcium phosphate cement (CPC) that enables rapid cell invasion with adequate initial mechanical properties without the use of complex processing and additives. Thus, we propose a simple and effective strategy to prepare injectable macroporous CPCs through syringe-foaming using a hydrophilic viscous polymeric solution (silanized-hydroxypropyl methylcellulose, Si-HPMC) as a foaming agent, that simultaneously meets all the aforementioned aims. Evidence from our in vivo studies shows the existence of newly formed bone within the implantation site, indicating the feasibility and effectiveness of this foaming strategy, which could be used in various CPC systems using other hydrophilic viscous polymeric solutions. Copyright © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

  19. 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.

  20. Inhibition of ice crystallisation in highly viscous aqueous organic acid droplets

    Directory of Open Access Journals (Sweden)

    B. J. Murray

    2008-09-01

    Full Text Available Homogeneous nucleation of ice within aqueous solution droplets and their subsequent crystallisation is thought to play a significant role in upper tropospheric ice cloud formation. It is normally assumed that homogeneous nucleation will take place at a threshold supersaturation, irrespective of the identity of the solute, and that rapid growth of ice particles will follow immediately after nucleation. However, it is shown here through laboratory experiments that droplets may not readily freeze in the very cold tropical tropopause layer (TTL, typical temperatures of 186–200 K. In these experiments ice crystal growth in citric acid solution droplets did not occur when ice nucleated below 197±6 K. Citric acid, 2-hydroxypropane-1,2,3-tricarboxyllic acid, is a molecule with similar functionality to oxygenated organic compounds which are ubiquitous in atmospheric aerosol. It is therefore thought to be a sensible proxy for atmospheric organic material. Evidence is presented that suggests citric acid solution droplets become ultra-viscous and form glassy solids under atmospherically relevant conditions. Diffusion of liquid water molecules to ice nuclei is expected to be very slow in ultra-viscous solution droplets and nucleation is negligible in glassy droplets; this most likely provides an explanation for the experimentally observed inhibition of ice crystallisation. The implications of ultra-viscous and glassy solution droplets for ice cloud formation and supersaturations in the TTL are discussed.

  1. Numerically satisfactory solutions of Kummer recurrence relations

    NARCIS (Netherlands)

    J. Segura (Javier); N.M. Temme (Nico)

    2008-01-01

    textabstractPairs of numerically satisfactory solutions as $n\\rightarrow \\infty$ for the three-term recurrence relations satisfied by the families of functions $_1\\mbox{F}_1(a+\\epsilon_1 n; b +\\epsilon_2 n;z)$, $\\epsilon_i \\in {\\mathbb Z}$, are given. It is proved that minimal solutions always

  2. Constructing exact symmetric informationally complete measurements from numerical solutions

    Science.gov (United States)

    Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

    2018-04-01

    Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

  3. Axisymmetric capillary-gravity waves at the interface of two viscous, immiscible fluids - Initial value problem

    Science.gov (United States)

    Farsoiya, Palas Kumar; Dasgupta, Ratul

    2017-11-01

    When the interface between two radially unbounded, viscous fluids lying vertically in a stable configuration (denser fluid below) at rest, is perturbed, radially propagating capillary-gravity waves are formed which damp out with time. We study this process analytically using a recently developed linearised theory. For small amplitude initial perturbations, the analytical solution to the initial value problem, represented as a linear superposition of Bessel modes at time t = 0 , is found to agree very well with results obtained from direct numerical simulations of the Navier-Stokes equations, for a range of initial conditions. Our study extends the earlier work by John W. Miles who studied this initial value problem analytically, taking into account, a single viscous fluid only. Implications of this study for the mechanistic understanding of droplet impact into a deep pool, will be discussed. Some preliminary, qualitative comparison with experiments will also be presented. We thank SERB Dept. Science & Technology, Govt. of India, Grant No. EMR/2016/000830 for financial support.

  4. 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.

  5. Calculation of viscous effects on transonic flow for oscillating airfoils and comparisons with experiment

    Science.gov (United States)

    Howlett, James T.; Bland, Samuel R.

    1987-01-01

    A method is described for calculating unsteady transonic flow with viscous interaction by coupling a steady integral boundary-layer code with an unsteady, transonic, inviscid small-disturbance computer code in a quasi-steady fashion. Explicit coupling of the equations together with viscous -inviscid iterations at each time step yield converged solutions with computer times about double those required to obtain inviscid solutions. The accuracy and range of applicability of the method are investigated by applying it to four AGARD standard airfoils. The first-harmonic components of both the unsteady pressure distributions and the lift and moment coefficients have been calculated. Comparisons with inviscid calcualtions and experimental data are presented. The results demonstrate that accurate solutions for transonic flows with viscous effects can be obtained for flows involving moderate-strength shock waves.

  6. Bulk viscous matter and recent acceleration of the universe based on causal viscous theory

    Energy Technology Data Exchange (ETDEWEB)

    Mohan, N.D.J.; Sasidharan, Athira; Mathew, Titus K. [Cochin University of Science and Technology, Department of Physics, Kochi (India)

    2017-12-15

    The evolution of the bulk viscous matter dominated universe has been analysed using the full causal theory for the evolution of the viscous pressure in the context of the recent acceleration of the universe. The form of the viscosity is taken as ξ = αρ{sup 1/2}. We obtained analytical solutions for the Hubble parameter and scale factor of the universe. The model parameters have been computed using the observational data. The evolution of the prominent cosmological parameters was obtained. The age of the universe for the best estimated model parameters is found to be less than observational value. The viscous matter behaves like a stiff fluid in the early phase and evolves to a negative pressure fluid in the later phase. The equation of state is found to be stabilised with value ω > -1. The local as well as generalised second law of thermodynamics is satisfied. The statefinder diagnostic shows that this model is distinct from the standard ΛCDM. One of the marked deviations seen in this model to be compared with the corresponding model using the Eckart approach is that in this model the bulk viscosity decreases with the expansion of the universe, while in the Eckart formalism it increases from negative values in the early universe towards positive values. (orig.)

  7. Bulk viscous matter and recent acceleration of the universe based on causal viscous theory

    International Nuclear Information System (INIS)

    Mohan, N.D.J.; Sasidharan, Athira; Mathew, Titus K.

    2017-01-01

    The evolution of the bulk viscous matter dominated universe has been analysed using the full causal theory for the evolution of the viscous pressure in the context of the recent acceleration of the universe. The form of the viscosity is taken as ξ = αρ 1/2 . We obtained analytical solutions for the Hubble parameter and scale factor of the universe. The model parameters have been computed using the observational data. The evolution of the prominent cosmological parameters was obtained. The age of the universe for the best estimated model parameters is found to be less than observational value. The viscous matter behaves like a stiff fluid in the early phase and evolves to a negative pressure fluid in the later phase. The equation of state is found to be stabilised with value ω > -1. The local as well as generalised second law of thermodynamics is satisfied. The statefinder diagnostic shows that this model is distinct from the standard ΛCDM. One of the marked deviations seen in this model to be compared with the corresponding model using the Eckart approach is that in this model the bulk viscosity decreases with the expansion of the universe, while in the Eckart formalism it increases from negative values in the early universe towards positive values. (orig.)

  8. Numerical solution of Boltzmann's equation

    International Nuclear Information System (INIS)

    Sod, G.A.

    1976-04-01

    The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

  9. Modeling of brittle-viscous flow using discrete particles

    Science.gov (United States)

    Thordén Haug, Øystein; Barabasch, Jessica; Virgo, Simon; Souche, Alban; Galland, Olivier; Mair, Karen; Abe, Steffen; Urai, Janos L.

    2017-04-01

    Many geological processes involve both viscous flow and brittle fractures, e.g. boudinage, folding and magmatic intrusions. Numerical modeling of such viscous-brittle materials poses challenges: one has to account for the discrete fracturing, the continuous viscous flow, the coupling between them, and potential pressure dependence of the flow. The Discrete Element Method (DEM) is a numerical technique, widely used for studying fracture of geomaterials. However, the implementation of viscous fluid flow in discrete element models is not trivial. In this study, we model quasi-viscous fluid flow behavior using Esys-Particle software (Abe et al., 2004). We build on the methodology of Abe and Urai (2012) where a combination of elastic repulsion and dashpot interactions between the discrete particles is implemented. Several benchmarks are presented to illustrate the material properties. Here, we present extensive, systematic material tests to characterize the rheology of quasi-viscous DEM particle packing. We present two tests: a simple shear test and a channel flow test, both in 2D and 3D. In the simple shear tests, simulations were performed in a box, where the upper wall is moved with a constant velocity in the x-direction, causing shear deformation of the particle assemblage. Here, the boundary conditions are periodic on the sides, with constant forces on the upper and lower walls. In the channel flow tests, a piston pushes a sample through a channel by Poisseuille flow. For both setups, we present the resulting stress-strain relationships over a range of material parameters, confining stress and strain rate. Results show power-law dependence between stress and strain rate, with a non-linear dependence on confining force. The material is strain softening under some conditions (which). Additionally, volumetric strain can be dilatant or compactant, depending on porosity, confining pressure and strain rate. Constitutive relations are implemented in a way that limits the

  10. Microfluidic System Simulation Including the Electro-Viscous Effect

    Science.gov (United States)

    Rojas, Eileen; Chen, C. P.; Majumdar, Alok

    2007-01-01

    This paper describes a practical approach using a general purpose lumped-parameter computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels including electro-viscous effects due to the existence of electrical double layer (EDL). In this study, an empirical formulation for calculating an effective viscosity of ionic solutions based on dimensional analysis is described to account for surface charge and bulk fluid conductivity, which give rise to electro-viscous effect in microfluidics network. Two dimensional slit micro flow data was used to determine the model coefficients. Geometry effect is then included through a Poiseuille number correlation in GFSSP. The bi-power model was used to calculate flow distribution of isotropically etched straight channel and T-junction microflows involving ionic solutions. Performance of the proposed model is assessed against experimental test data.

  11. Numerical solution of one-dimensional transient, two-phase flows with temporal fully implicit high order schemes: Subcooled boiling in pipes

    Energy Technology Data Exchange (ETDEWEB)

    López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es

    2017-03-15

    Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.

  12. Viscous Corrections of the Time Incremental Minimization Scheme and Visco-Energetic Solutions to Rate-Independent Evolution Problems

    Science.gov (United States)

    Minotti, Luca; Savaré, Giuseppe

    2018-02-01

    We propose the new notion of Visco-Energetic solutions to rate-independent systems {(X, E,} d) driven by a time dependent energy E and a dissipation quasi-distance d in a general metric-topological space X. As for the classic Energetic approach, solutions can be obtained by solving a modified time Incremental Minimization Scheme, where at each step the dissipation quasi-distance d is incremented by a viscous correction {δ} (for example proportional to the square of the distance d), which penalizes far distance jumps by inducing a localized version of the stability condition. We prove a general convergence result and a typical characterization by Stability and Energy Balance in a setting comparable to the standard energetic one, thus capable of covering a wide range of applications. The new refined Energy Balance condition compensates for the localized stability and provides a careful description of the jump behavior: at every jump the solution follows an optimal transition, which resembles in a suitable variational sense the discrete scheme that has been implemented for the whole construction.

  13. Comparison of elastic-viscous-plastic and viscous-plastic dynamics models using a high resolution Arctic sea ice model

    Energy Technology Data Exchange (ETDEWEB)

    Hunke, E.C. [Los Alamos National Lab., NM (United States); Zhang, Y. [Naval Postgraduate School, Monterey, CA (United States)

    1997-12-31

    A nonlinear viscous-plastic (VP) rheology proposed by Hibler (1979) has been demonstrated to be the most suitable of the rheologies commonly used for modeling sea ice dynamics. However, the presence of a huge range of effective viscosities hinders numerical implementations of this model, particularly on high resolution grids or when the ice model is coupled to an ocean or atmosphere model. Hunke and Dukowicz (1997) have modified the VP model by including elastic waves as a numerical regularization in the case of zero strain rate. This modification (EVP) allows an efficient, fully explicit discretization that adapts well to parallel architectures. The authors present a comparison of EVP and VP dynamics model results from two 5-year simulations of Arctic sea ice, obtained with a high resolution sea ice model. The purpose of the comparison is to determine how differently the two dynamics models behave, and to decide whether the elastic-viscous-plastic model is preferable for high resolution climate simulations, considering its high efficiency in parallel computation. Results from the first year of this experiment (1990) are discussed in detail in Hunke and Zhang (1997).

  14. Introduction to the numerical solutions of Markov chains

    CERN Document Server

    Stewart, Williams J

    1994-01-01

    A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...

  15. Numerical methods for engine-airframe integration

    International Nuclear Information System (INIS)

    Murthy, S.N.B.; Paynter, G.C.

    1986-01-01

    Various papers on numerical methods for engine-airframe integration are presented. The individual topics considered include: scientific computing environment for the 1980s, overview of prediction of complex turbulent flows, numerical solutions of the compressible Navier-Stokes equations, elements of computational engine/airframe integrations, computational requirements for efficient engine installation, application of CAE and CFD techniques to complete tactical missile design, CFD applications to engine/airframe integration, and application of a second-generation low-order panel methods to powerplant installation studies. Also addressed are: three-dimensional flow analysis of turboprop inlet and nacelle configurations, application of computational methods to the design of large turbofan engine nacelles, comparison of full potential and Euler solution algorithms for aeropropulsive flow field computations, subsonic/transonic, supersonic nozzle flows and nozzle integration, subsonic/transonic prediction capabilities for nozzle/afterbody configurations, three-dimensional viscous design methodology of supersonic inlet systems for advanced technology aircraft, and a user's technology assessment

  16. Dual Solutions in a Boundary Layer Flow of a Power Law Fluid over a Moving Permeable Flat Plate with Thermal Radiation, Viscous Dissipation and Heat Generation/Absorption

    Directory of Open Access Journals (Sweden)

    Aftab Ahmed

    2018-01-01

    Full Text Available The aim of the present study is to investigate the combined effects of the thermal radiation, viscous dissipation, suction/injection and internal heat generation/absorption on the boundary layer flow of a non-Newtonian power law fluid over a semi infinite permeable flat plate moving in parallel or reversely to a free stream. The resulting system of partial differential equations (PDEs is first transformed into a system of coupled nonlinear ordinary differential equations (ODEs which are then solved numerically by using the shooting technique. It is found that the dual solutions exist when the flat plate and the free stream move in the opposite directions. Dimensionless boundary layer velocity and temperature distributions are plotted and discussed for various values of the emerging physical parameters. Finally, the tables of the relevant boundary derivatives are presented for some values of the governing physical parameters.

  17. Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

    KAUST Repository

    El-Beltagy, Mohamed A.

    2015-01-07

    Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

  18. Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

    KAUST Repository

    El-Beltagy, Mohamed A.; Al-Juhani, Amnah

    2015-01-01

    Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

  19. Rotationally symmetric numerical solutions to the sine-Gordon equation

    DEFF Research Database (Denmark)

    Olsen, O. H.; Samuelsen, Mogens Rugholm

    1981-01-01

    We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...

  20. On numerical solution of Burgers' equation by homotopy analysis method

    International Nuclear Information System (INIS)

    Inc, Mustafa

    2008-01-01

    In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions

  1. Computational fluid dynamics study of viscous fingering in supercritical fluid chromatography.

    Science.gov (United States)

    Subraveti, Sai Gokul; Nikrityuk, Petr; Rajendran, Arvind

    2018-01-26

    Axi-symmetric numerical simulations are carried out to study the dynamics of a plug introduced through a mixed-stream injection in supercritical fluid chromatographic columns. The computational fluid dynamics model developed in this work takes into account both the hydrodynamics and adsorption equilibria to describe the phenomena of viscous fingering and plug effect that contribute to peak distortions in mixed-stream injections. The model was implemented into commercial computational fluid dynamics software using user-defined functions. The simulations describe the propagation of both the solute and modifier highlighting the interplay between the hydrodynamics and plug effect. The simulated peaks showed good agreement with experimental data published in the literature involving different injection volumes (5 μL, 50 μL, 1 mL and 2 mL) of flurbiprofen on Chiralpak AD-H column using a mobile phase of CO 2 and methanol. The study demonstrates that while viscous fingering is the main source of peak distortions for large-volume injections (1 mL and 2 mL) it has negligible impact on small-volume injections (5 μL and 50 μL). Band broadening in small-volume injections arise mainly due to the plug effect. Crown Copyright © 2017. Published by Elsevier B.V. All rights reserved.

  2. Numerical Investigation on MHD Flow and Heat Transfer over an Exponentially Stretching Sheet with Viscous Dissipation and Radiation Effects

    Directory of Open Access Journals (Sweden)

    Çilingir Süngü İnci

    2017-01-01

    Full Text Available This study is to examine the steady two dimensional laminar flow of a viscous incompressible electrically conducting fluid over a continuous surface. In this study DTM-Padé method is used to solve which is a combination of differential transform method (DTM and Padé approximant. Comparisons between the solutions obtained by DTM and DTM-Padé and are shown that DTM-Padé is the completely powerful method then DTM for solving the problems in which boundary conditions at infinity. Also in this study the effect of Magnetic and Radiation parameters, Prandtl number and Eckert number for velocity and temperature distributions are investigated.

  3. Microjet Generator for Highly Viscous Fluids

    Science.gov (United States)

    Onuki, Hajime; Oi, Yuto; Tagawa, Yoshiyuki

    2018-01-01

    This paper describes a simple system for generating a highly viscous microjet. The jet is produced inside a wettable thin tube partially submerged in a liquid. The gas-liquid interface inside the tube, which is initially concave, is kept much deeper than that outside the tube. An impulsive force applied at the bottom of a liquid container leads to significant acceleration of the liquid inside the tube followed by flow focusing due to the concave interface. The jet generation process can be divided into two parts that occur in different time scales, i.e., the impact interval [impact duration ≤O (10-4) s ] and the focusing interval [focusing duration ≫O (10-4) s ]. During the impact interval, the liquid accelerates suddenly due to the impact. During the focusing interval, the microjet emerges due to flow focusing. In order to explain the sudden acceleration inside the tube during the impact interval, we develop a physical model based on a pressure impulse approach. Numerical simulations confirm the proposed model, indicating that the basic mechanism of the acceleration of the liquid due to the impulsive force is elucidated. Remarkably, the viscous effect is negligible during the impact interval. In contrast, during the focusing interval, the viscosity plays an important role in the microjet generation. We experimentally and numerically investigate the velocity of microjets with various viscosities. We find that higher viscosities lead to reduction of the jet velocity, which can be described by using the Reynolds number (the ratio between the inertia force and the viscous force). This device may be a starting point for next-generation technologies, such as high-viscosity inkjet printers including bioprinters and needle-free injection devices for minimally invasive medical treatments.

  4. Three-dimensional attached viscous flow basic principles and theoretical foundations

    CERN Document Server

    Hirschel, Ernst Heinrich; Kordulla, Wilhelm

    2014-01-01

    Viscous flow is usually treated in the frame of boundary-layer theory and as a two-dimensional flow. At best, books on boundary layers provide the describing equations for three-dimensional boundary layers, and solutions only for certain special cases.   This book presents the basic principles and theoretical foundations of three-dimensional attached viscous flows as they apply to aircraft of all kinds. Though the primary flight speed range is that of civil air transport vehicles, flows past other flying vehicles up to hypersonic speeds are also considered. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers, as this wider scope is necessary in view of the theoretical and practical problems that have to be overcome in practice.   The specific topics covered include weak, strong, and global interaction; the locality principle; properties of three-dimensional viscous flows; thermal surface effects; characteristic properties; wall compatibility con...

  5. Class of nonsingular exact solutions for Laplacian pattern formation

    International Nuclear Information System (INIS)

    Mineev-Weinstein, M.B.; Dawson, S.P.

    1994-01-01

    We present a class of exact solutions for the so-called Laplacian growth equation describing the zero-surface-tension limit of a variety of two-dimensional pattern formation problems. These solutions are free of finite-time singularities (cusps) for quite general initial conditions. They reproduce various features of viscous fingering observed in experiments and numerical simulations with surface tension, such as existence of stagnation points, screening, tip splitting, and coarsening. In certain cases the asymptotic interface consists of N separated moving Saffman-Taylor fingers

  6. Viscous cosmology in new holographic dark energy model and the cosmic acceleration

    International Nuclear Information System (INIS)

    Singh, C.P.; Srivastava, Milan

    2018-01-01

    In this work, we study a flat Friedmann-Robertson-Walker universe filled with dark matter and viscous new holographic dark energy. We present four possible solutions of the model depending on the choice of the viscous term. We obtain the evolution of the cosmological quantities such as scale factor, deceleration parameter and transition redshift to observe the effect of viscosity in the evolution. We also emphasis upon the two independent geometrical diagnostics for our model, namely the statefinder and the Om diagnostics. In the first case we study new holographic dark energy model without viscous and obtain power-law expansion of the universe which gives constant deceleration parameter and statefinder parameters. In the limit of the parameter, the model approaches to ΛCDM model. In new holographic dark energy model with viscous, the bulk viscous coefficient is assumed as ζ = ζ 0 + ζ 1 H, where ζ 0 and ζ 1 are constants, and H is the Hubble parameter. In this model, we obtain all possible solutions with viscous term and analyze the expansion history of the universe. We draw the evolution graphs of the scale factor and deceleration parameter. It is observed that the universe transits from deceleration to acceleration for small values of ζ in late time. However, it accelerates very fast from the beginning for large values of ζ. By illustrating the evolutionary trajectories in r - s and r - q planes, we find that our model behaves as an quintessence like for small values of viscous coefficient and a Chaplygin gas like for large values of bulk viscous coefficient at early stage. However, model has close resemblance to that of the ΛCDM cosmology in late time. The Om has positive and negative curvatures for phantom and quintessence models, respectively depending on ζ. Our study shows that the bulk viscosity plays very important role in the expansion history of the universe. (orig.)

  7. Viscous cosmology in new holographic dark energy model and the cosmic acceleration

    Science.gov (United States)

    Singh, C. P.; Srivastava, Milan

    2018-03-01

    In this work, we study a flat Friedmann-Robertson-Walker universe filled with dark matter and viscous new holographic dark energy. We present four possible solutions of the model depending on the choice of the viscous term. We obtain the evolution of the cosmological quantities such as scale factor, deceleration parameter and transition redshift to observe the effect of viscosity in the evolution. We also emphasis upon the two independent geometrical diagnostics for our model, namely the statefinder and the Om diagnostics. In the first case we study new holographic dark energy model without viscous and obtain power-law expansion of the universe which gives constant deceleration parameter and statefinder parameters. In the limit of the parameter, the model approaches to Λ CDM model. In new holographic dark energy model with viscous, the bulk viscous coefficient is assumed as ζ =ζ 0+ζ 1H, where ζ 0 and ζ 1 are constants, and H is the Hubble parameter. In this model, we obtain all possible solutions with viscous term and analyze the expansion history of the universe. We draw the evolution graphs of the scale factor and deceleration parameter. It is observed that the universe transits from deceleration to acceleration for small values of ζ in late time. However, it accelerates very fast from the beginning for large values of ζ . By illustrating the evolutionary trajectories in r-s and r-q planes, we find that our model behaves as an quintessence like for small values of viscous coefficient and a Chaplygin gas like for large values of bulk viscous coefficient at early stage. However, model has close resemblance to that of the Λ CDM cosmology in late time. The Om has positive and negative curvatures for phantom and quintessence models, respectively depending on ζ . Our study shows that the bulk viscosity plays very important role in the expansion history of the universe.

  8. Unsteady Viscous Flow Past an Impulsively Started Porous Vertical ...

    African Journals Online (AJOL)

    This paper presents a new numerical approach for solving unsteady two dimensional boundary layer flow past an infinite vertical porous surface with the flow generated by Newtonian heating and impulsive motion in the presence of viscous dissipation and temperature dependent viscosity. The viscosity of the fluid under ...

  9. Second law analysis of a reacting temperature dependent viscous ...

    African Journals Online (AJOL)

    In this paper, entropy generation during the flow of a reacting viscous fluid through an inclined Channel with isothermal walls are investigated. The coupled energy and momentum equations were solved numerically. Previous results in literature (Adesanya et al 2006 [[17]) showed both velocity and temperature have two ...

  10. Viscous slip coefficients for binary gas mixtures measured from mass flow rates through a single microtube

    Science.gov (United States)

    Yamaguchi, H.; Takamori, K.; Perrier, P.; Graur, I.; Matsuda, Y.; Niimi, T.

    2016-09-01

    The viscous slip coefficient for helium-argon binary gas mixture is extracted from the experimental values of the mass flow rate through a microtube. The mass flow rate is measured by the constant-volume method. The viscous slip coefficient was obtained by identifying the measured mass flow rate through a microtube with the corresponding analytical expression, which is a function of the Knudsen number. The measurements were carried out in the slip flow regime where the first-order slip boundary condition can be applied. The measured viscous slip coefficients of binary gas mixtures exhibit a concave function of the molar ratio of the mixture, showing a similar profile with numerical results. However, from the detailed comparison between the measured and numerical values with the complete and incomplete accommodation at a surface, it is inappropriate to estimate the viscous slip coefficient for the mixture numerically by employing separately measured tangential momentum accommodation coefficient for each component. The time variation of the molar ratio in the downstream chamber was measured by sampling the gas from the chamber using the quadrupole mass spectrometer. In our measurements, it is indicated that the volume flow rate of argon is larger than that of helium because of the difference in the tangential momentum accommodation coefficient.

  11. Numerical solution of problems concerning the thermal convection of a variable-viscosity liquid

    Science.gov (United States)

    Zherebiatev, I. F.; Lukianov, A. T.; Podkopaev, Iu. L.

    A stabilizing-correction scheme is constructed for integrating the fourth-order equation describing the dynamics of a viscous incompressible liquid. As an example, a solution is obtained to the problem of the solidification of a liquid in a rectangular region with allowance for convective energy transfer in the liquid phase as well as temperature-dependent changes of viscosity. It is noted that the proposed method can be used to study steady-state problems of thermal convection in ingots obtained through continuous casting.

  12. Interacting viscous ghost tachyon, K-essence and dilaton scalar field models of dark energy

    International Nuclear Information System (INIS)

    Karami, K; Fahimi, K

    2013-01-01

    We study the correspondence between the interacting viscous ghost dark energy model with the tachyon, K-essence and dilaton scalar field models in the framework of Einstein gravity. We consider a spatially non-flat FRW universe filled with interacting viscous ghost dark energy and dark matter. We reconstruct both the dynamics and potential of these scalar field models according to the evolutionary behavior of the interacting viscous ghost dark energy model, which can describe the accelerated expansion of the universe. Our numerical results show that the interaction and viscosity have opposite effects on the evolutionary properties of the ghost scalar field models. (paper)

  13. The partially filled viscous ring damper.

    Science.gov (United States)

    Alfriend, K. T.

    1973-01-01

    The problem of a spinning satellite with a partially filled viscous ring damper is investigated. It is shown that there are two distinct modes of motion, the nutation-synchronous mode and spin-synchronous mode. From an approximate solution of the equations of motion a time constant is obtained for each mode. From a consideration of the fluid dynamics several methods are developed for determining the damping constant.

  14. Hydrodynamic response of viscous fluids under seismic excitation

    International Nuclear Information System (INIS)

    Ma, D.C.

    1993-01-01

    Hydrodynamic response of liquid-tank systems, such as reactor vessels, spent-fuel pools and liquid storage tanks have been studied extensively in the last decade (Chang et al. 1988; Ma et al. 1991). However, most of the studies are conducted with the assumption of an inviscid fluid. In recent years, the hydrodynamic response of viscous fluids has received increasing attention in high level waste storage tanks containing viscous waste material. This paper presents a numerical study on the hydrodynamic response of viscous fluids in a large 2-D fluid-tank system under seismic excitation. Hydrodynamic responses (i.e. sloshing wave height, fluid pressures, shear stress, etc.) are calculated for a fluid with various viscosities. Four fluid viscosities are considered. They are 1 cp, 120 cp, 1,000 cp and 12,000 cp (1 cp = 1.45 x 10 -7 lb-sec/in 2 ). Note that the liquid sodium of the Liquid-Metal Reactor (LMR) reactor has a viscosity of 1.38 x 10 -5 lb-sec/in 2 (about 95 cp) at an operational temperature of 900 degree F. Section 2 describes the pertinent features of the mathematical model. In Section 3, the fundamental sloshing phenomena of viscous fluid are examined. Sloshing wave height and shear stress for fluid with different viscosities are compared. The conclusions are given in Section 4

  15. Explicit appropriate basis function method for numerical solution of stiff systems

    International Nuclear Information System (INIS)

    Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling

    2015-01-01

    Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations

  16. Automatic validation of numerical solutions

    DEFF Research Database (Denmark)

    Stauning, Ole

    1997-01-01

    This thesis is concerned with ``Automatic Validation of Numerical Solutions''. The basic theory of interval analysis and self-validating methods is introduced. The mean value enclosure is applied to discrete mappings for obtaining narrow enclosures of the iterates when applying these mappings...... differential equations, but in this thesis, we describe how to use the methods for enclosing iterates of discrete mappings, and then later use them for discretizing solutions of ordinary differential equations. The theory of automatic differentiation is introduced, and three methods for obtaining derivatives...... are described: The forward, the backward, and the Taylor expansion methods. The three methods have been implemented in the C++ program packages FADBAD/TADIFF. Some examples showing how to use the three metho ds are presented. A feature of FADBAD/TADIFF not present in other automatic differentiation packages...

  17. Linear stability analysis and nonlinear simulation of the channeling effect on viscous fingering instability in miscible displacement

    Science.gov (United States)

    Shahnazari, M. R.; Maleka Ashtiani, I.; Saberi, A.

    2018-03-01

    In this paper, the effect of channeling on viscous fingering instability of miscible displacement in porous media is studied. In fact, channeling is introduced as a solution to stabilize the viscous fingering instability. In this solution, narrow channels were placed next to the walls, and by considering an exponential function to model the channeling effect, a heterogeneous media is assumed. In linear stability analysis, the governing equations are transferred to Fourier space, and by introducing a novel numerical method, the transferred equations are analyzed. The growth rate based on the wave number diagram has been drawn up in three sections of the medium. It is found that the flow becomes more stable at the center and unstable along the walls when the permeability ratio is increased. Also when the permeability ratio is approximately equal to one, the channeling has no significant effect. In nonlinear simulations, by using stream function and vortices, new equations have been rewritten and it is shown that channeling has a profound effect on the growth of the fingers and mechanisms. In addition to the superposition of velocity vectors and concentration contours, the development of instability is investigated using the mixing length and sweep efficiency diagram. The results show that although channeling reduces instability, it increases the displacement process time.

  18. Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

    Science.gov (United States)

    Abdulwahhab, Muhammad Alim

    2016-10-01

    Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

  19. Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdi Rashidi

    2008-01-01

    Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

  20. Numerical simulations of flying and swimming of biological systems with the viscous vortex particle method

    Science.gov (United States)

    Eldredge, Jeff

    2005-11-01

    Many biological mechanisms of locomotion involve the interaction of a fluid with a deformable surface undergoing large unsteady motion. Analysis of such problems poses a significant challenge to conventional grid-based computational approaches. Particularly in the moderate Reynolds number regime where many insects and fish function, viscous and inertial processes are both important, and vorticity serves a crucial role. In this work, the viscous vortex particle method is shown to provide an efficient, intuitive simulation approach for investigation of these biological systems. In contrast with a grid-based approach, the method solves the Navier--Stokes equations by tracking computational particles that carry smooth blobs of vorticity and exchange strength with one another to account for viscous diffusion. Thus, computational resources are focused on the physically relevant features of the flow, and there is no need for artificial boundary conditions. Building from previously-developed techniques for the creation of vorticity to enforce no-throughflow and no-slip conditions, the present method is extended to problems of coupled fluid--body dynamics by enforcement of global conservation of momenta. The application to several two-dimensional model problems is demonstrated, including single and multiple flapping wings and free swimming of a three-linkage fish.

  1. Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere

    OpenAIRE

    You, Bo; Li, Fang

    2016-01-01

    This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive equations of large-scale moist atmosphere by asymptotic a priori estimate and construct an exponential attractor by using the smoothing property of the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere...

  2. Optimal contant time injection policy for enhanced oil recovery and characterization of optimal viscous profiles

    Science.gov (United States)

    Daripa, Prabir

    2011-11-01

    We numerically investigate the optimal viscous profile in constant time injection policy of enhanced oil recovery. In particular, we investigate the effect of a combination of interfacial and layer instabilities in three-layer porous media flow on the overall growth of instabilities and thereby characterize the optimal viscous profile. Results based on monotonic and non-monotonic viscous profiles will be presented. Time permitting. we will also present results on multi-layer porous media flows for Newtonian and non-Newtonian fluids and compare the results. The support of Qatar National Fund under a QNRF Grant is acknowledged.

  3. Spurious solutions in few-body equations. II. Numerical investigations

    International Nuclear Information System (INIS)

    Adhikari, S.K.

    1979-01-01

    A recent analytic study of spurious solutions in few-body equations by Adhikari and Gloeckle is here complemented by numerical investigations. As proposed by Adhikari and Gloeckle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence, if proven convenient, the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations

  4. Numerical solution of electrostatic problems of the accelerator project VICKSI

    International Nuclear Information System (INIS)

    Janetzki, U.

    1975-03-01

    In this work, the numerical solution to a few of the electrostatic problems is dealt with which have occured within the framework of the heavy ion accelerator project VICKSI. By means of these selected examples, the versatile applicability of the numerical method is to be demonstrated, and simultaneously assistance is given for the solution of similar problems. The numerical process for solving ion-optics problems consists generally of two steps. In the first step, the potential distribution for a given boundary value problem is iteratively calculated for the Laplace equation, and then the image characteristics of the electostatic lense are investigated using the Raytrace method. (orig./LH) [de

  5. One-Dimensional Problem of a Conducting Viscous Fluid with One Relaxation Time

    Directory of Open Access Journals (Sweden)

    Angail A. Samaan

    2011-01-01

    Full Text Available We introduce a magnetohydrodynamic model of boundary-layer equations for conducting viscous fluids. This model is applied to study the effects of free convection currents with thermal relaxation time on the flow of a viscous conducting fluid. The method of the matrix exponential formulation for these equations is introduced. The resulting formulation together with the Laplace transform technique is applied to a variety problems. The effects of a plane distribution of heat sources on the whole and semispace are studied. Numerical results are given and illustrated graphically for the problem.

  6. Efficient numerical solution to vacuum decay with many fields

    Energy Technology Data Exchange (ETDEWEB)

    Masoumi, Ali; Olum, Ken D.; Shlaer, Benjamin, E-mail: ali@cosmos.phy.tufts.edu, E-mail: kdo@cosmos.phy.tufts.edu, E-mail: shlaer@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

    2017-01-01

    Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.

  7. Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

    International Nuclear Information System (INIS)

    Kaya, Dogan; El-Sayed, Salah M.

    2003-01-01

    In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

  8. Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

    International Nuclear Information System (INIS)

    Pappas, George

    2009-01-01

    We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R ISCO ), the rotation frequency and the epicyclic frequencies Ω ρ , Ω z . Finally we present some results of the comparison.

  9. Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

    Energy Technology Data Exchange (ETDEWEB)

    Pappas, George, E-mail: gpappas@phys.uoa.g [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)

    2009-10-01

    We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R{sub ISCO}), the rotation frequency and the epicyclic frequencies {Omega}{sub {rho}}, {Omega}{sub z}. Finally we present some results of the comparison.

  10. Transport coefficients in second-order non-conformal viscous hydrodynamics

    International Nuclear Information System (INIS)

    Ryblewski, Radoslaw

    2015-01-01

    Based on the exact solution of Boltzmann kinetic equation in the relaxation-time approximation, the precision of the two most recent formulations of relativistic second-order non-conformal viscous hydrodynamics (14-moment approximation and causal Chapman-Enskog method), standard Israel-Stewart theory, and anisotropic hydrodynamics framework, in the simple case of one-dimensional Bjorken expansion, is tested. It is demonstrated that the failure of Israel-Stewart theory in reproducing exact solutions of the Boltzmann kinetic equation occurs due to neglecting and/or choosing wrong forms of some of the second-order transport coefficients. In particular, the importance of shear-bulk couplings in the evolution equations for dissipative quantities is shown. One finds that, in the case of the bulk viscous pressure correction, such coupling terms are as important as the corresponding first-order Navier-Stokes term and must be included in order to obtain, at least qualitative, overall agreement with the kinetic theory. (paper)

  11. Numerical solution of distributed order fractional differential equations

    Science.gov (United States)

    Katsikadelis, John T.

    2014-02-01

    In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

  12. Numerical solution of ordinary differential equations. For classical, relativistic and nano systems

    International Nuclear Information System (INIS)

    Greenspan, D.

    2006-01-01

    An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)

  13. Numerical solutions of the Vlasov equation

    International Nuclear Information System (INIS)

    Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

    1985-01-01

    A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)

  14. Design method for fluid viscous dampers

    Energy Technology Data Exchange (ETDEWEB)

    Jia, Jiuhong; Hua, Hongxing [Shanghai Jiaotong University, State Key Laboratory of Mechanical System and Vibration, Shanghai (China); Du, Jianye; Wang, Yu [Naval Arming Academy, Institute of Naval Vessels, Beijing (China)

    2008-09-15

    A basic design method of doubly acting fluid viscous dampers with double guide bars is presented. The flow of the viscoelastic fluid between two parallel plates, one of which is started suddenly and the other of which is still, is analyzed. According to this solution, the velocity and the shear stress of the fluid at the fringe of the piston are solved approximately. A mathematical model of viscous dampers is derived, and the shock test is carried out. From experimental results, the parameters of the mathematical model are determined. Consequently, a semi-empirical design equation is obtained. Applying this equation to a certain practical damper, the damping material is chosen and the physical dimensions of the damper are determined. Shock tests using this damper are performed. Theoretical results are in good agreement with experimental results, which validates the reliability of the calculated physical dimensions of the specimen damper and the validity of the basic design equation. (orig.)

  15. SIMULATIONS OF VISCOUS ACCRETION FLOW AROUND BLACK HOLES IN A TWO-DIMENSIONAL CYLINDRICAL GEOMETRY

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seong-Jae; Hyung, Siek [School of Science Education (Astronomy), Chungbuk National University, Chungbuk 28644 (Korea, Republic of); Chattopadhyay, Indranil; Kumar, Rajiv [ARIES, Manora Peak, Nainital-263002, Uttarakhand (India); Ryu, Dongsu, E-mail: seong@chungbuk.ac.kr [Department of Physics, School of Natural Sciences UNIST, Ulsan 44919 (Korea, Republic of)

    2016-11-01

    We simulate shock-free and shocked viscous accretion flows onto a black hole in a two-dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian total variation diminishing plus remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. The inviscid shock-free accretion disk solution produced a thick disk structure, while the viscous shock-free solution attained a Bondi-like structure, but in either case, no jet activity nor any quasi-periodic oscillation (QPO)-like activity developed. The steady-state shocked solution in the inviscid as well as in the viscous regime matched theoretical predictions well. However, increasing viscosity renders the accretion shock unstable. Large-amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. This oscillation of the inner part of the disk is interpreted as the source of QPO in hard X-rays observed in micro-quasars. Strong shock oscillation induces strong episodic jet emission. The jets also show the existence of shocks, which are produced as one shell hits the preceding one. The periodicities of the jets and shock oscillation are similar; the jets for the higher viscosity parameter appear to be stronger and faster.

  16. A Gas-kinetic Discontinuous Galerkin Method for Viscous Flow Equations

    International Nuclear Information System (INIS)

    Liu, Hongwei; Xu, Kun

    2007-01-01

    This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for viscous flow computation. The construction of the RKDG method is based on a gas-kinetic formulation, which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at the cell interface through a simple hybrid gas distribution function. Due to the intrinsic connection between the gaskinetic BGK model and the Navier-Stokes equations, the Navier-Stokes flux is automatically obtained by the present method. Numerical examples for both one dimensional (10) and two dimensional(20) compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current RKDG method

  17. A comparison of viscous-plastic sea ice solvers with and without replacement pressure

    Science.gov (United States)

    Kimmritz, Madlen; Losch, Martin; Danilov, Sergey

    2017-07-01

    Recent developments of the explicit elastic-viscous-plastic (EVP) solvers call for a new comparison with implicit solvers for the equations of viscous-plastic sea ice dynamics. In Arctic sea ice simulations, the modified and the adaptive EVP solvers, and the implicit Jacobian-free Newton-Krylov (JFNK) solver are compared against each other. The adaptive EVP method shows convergence rates that are generally similar or even better than those of the modified EVP method, but the convergence of the EVP methods is found to depend dramatically on the use of the replacement pressure (RP). Apparently, using the RP can affect the pseudo-elastic waves in the EVP methods by introducing extra non-physical oscillations so that, in the extreme case, convergence to the VP solution can be lost altogether. The JFNK solver also suffers from higher failure rates with RP implying that with RP the momentum equations are stiffer and more difficult to solve. For practical purposes, both EVP methods can be used efficiently with an unexpectedly low number of sub-cycling steps without compromising the solutions. The differences between the RP solutions and the NoRP solutions (when the RP is not being used) can be reduced with lower thresholds of viscous regularization at the cost of increasing stiffness of the equations, and hence the computational costs of solving them.

  18. Three-dimensional viscous-inviscid coupling method for wind turbine computations

    DEFF Research Database (Denmark)

    Ramos García, Néstor; Sørensen, Jens Nørkær; Shen, Wen Zhong

    2016-01-01

    In this paper, a computational model for predicting the aerodynamic behavior of wind turbine wakes and blades subjected to unsteady motions and viscous effects is presented. The model is based on a three-dimensional panel method using a surface distribution of quadrilateral sources and doublets......, which is coupled to a viscous boundary layer solver. Unlike Navier-Stokes codes that need to solve the entire flow domain, the panel method solves the flow around a complex geometry by distributing singularity elements on the body surface, obtaining a faster solution and making this type of codes...... suitable for the design of wind turbines. A free-wake model has been employed to simulate the wake behind a wind turbine by using vortex filaments that carry the vorticity shed by the trailing edge of the blades. Viscous and rotational effects inside the boundary layer are taken into account via...

  19. Modelling the normal bouncing dynamics of spheres in a viscous fluid

    Directory of Open Access Journals (Sweden)

    Izard Edouard

    2017-01-01

    Full Text Available Bouncing motions of spheres in a viscous fluid are numerically investigated by an immersed boundary method to resolve the fluid flow around solids which is combined to a discrete element method for the particles motion and contact resolution. Two well-known configurations of bouncing are considered: the normal bouncing of a sphere on a wall in a viscous fluid and a normal particle-particle bouncing in a fluid. Previous experiments have shown the effective restitution coefficient to be a function of a single parameter, namely the Stokes number which compares the inertia of the solid particle with the fluid viscous dissipation. The present simulations show a good agreement with experimental observations for the whole range of investigated parameters. However, a new definition of the coefficient of restitution presented here shows a dependence on the Stokes number as in previous works but, in addition, on the fluid to particle density ratio. It allows to identify the viscous, inertial and dry regimes as found in experiments of immersed granular avalanches of Courrech du Pont et al. Phys. Rev. Lett. 90, 044301 (2003, e.g. in a multi-particle configuration.

  20. Exact and numerical solutions of generalized Drinfeld-Sokolov equations

    International Nuclear Information System (INIS)

    Ugurlu, Yavuz; Kaya, Dogan

    2008-01-01

    In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

  1. Numerical study of water entry supercavitating flow around a vertical circular cylinder influenced by turbulent drag-reducing additives

    International Nuclear Information System (INIS)

    Jiang, C X; Cheng, J P; Li, F C

    2015-01-01

    This paper attempts to introduce a numerical simulation procedure to simulate water-entry problems influenced by turbulent drag-reducing additives in a viscous incompressible medium. Firstly we performed a numerical investigation on water-entry supercavities in water and turbulent drag-reducing solution at the impact velocity of 28.4 m/s to confirm the accuracy of the numerical method. Based on the verification, projectile entering water and turbulent drag-reducing solution at relatively high velocity of 142.7 m/s (phase transition is considered) is simulated. The cross viscosity equation was adopted to represent the shear-thinning characteristic of aqueous solution of drag-reducing additives. The configuration and dynamic characteristics of water entry supercavity, flow resistance were discussed respectively. It was obtained that the numerical simulation results are in consistence with experimental data. Numerical results show that the supercavity length in drag-reducing solution is larger than one in water and the velocity attenuates faster at high velocity than at low velocity; the influence of drag-reducing solution is more obvious at high impact velocity. Turbulent drag-reducing additives have the great potential for enhancement of supercavity

  2. High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

    Energy Technology Data Exchange (ETDEWEB)

    Dumbser, Michael, E-mail: michael.dumbser@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy); Peshkov, Ilya, E-mail: peshkov@math.nsc.ru [Open and Experimental Center for Heavy Oil, Université de Pau et des Pays de l' Adour, Avenue de l' Université, 64012 Pau (France); Romenski, Evgeniy, E-mail: evrom@math.nsc.ru [Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, 2 Pirogova Str., 630090 Novosibirsk (Russian Federation); Zanotti, Olindo, E-mail: olindo.zanotti@unitn.it [Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, 38123 Trento (Italy)

    2016-06-01

    Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier

  3. High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

    International Nuclear Information System (INIS)

    Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy; Zanotti, Olindo

    2016-01-01

    Highlights: • High order schemes for a unified first order hyperbolic formulation of continuum mechanics. • The mathematical model applies simultaneously to fluid mechanics and solid mechanics. • Viscous fluids are treated in the frame of hyper-elasticity as generalized visco-plastic solids. • Formal asymptotic analysis reveals the connection with the Navier–Stokes equations. • The distortion tensor A in the model appears to be well-suited for flow visualization. - Abstract: This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov and Romenski [110], further denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables in the proposed first order system. A very important key feature of the HPR model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well as the behavior of elastic and visco-plastic solids. Actually, the model treats viscous and inviscid fluids as generalized visco-plastic solids. This is achieved via a stiff source term that accounts for strain relaxation in the evolution equations of A. Also heat conduction is included via a first order hyperbolic system for the thermal impulse, from which the heat flux is computed. The governing PDE system is hyperbolic and fully consistent with the first and the second principle of thermodynamics. It is also fundamentally different from first order Maxwell–Cattaneo-type relaxation models based on extended irreversible thermodynamics. The HPR model represents therefore a novel and unified description of continuum mechanics, which applies at the same time to fluid mechanics and solid mechanics. In this paper, the direct connection between the HPR model and the classical hyperbolic–parabolic Navier

  4. Simulation of swimming strings immersed in a viscous fluid flow

    Science.gov (United States)

    Huang, Wei-Xi; Sung, Hyung Jin

    2006-11-01

    In nature, many phenomena involve interactions between flexible bodies and their surrounding viscous fluid, such as a swimming fish or a flapping flag. The intrinsic dynamics is complicate and not well understood. A flexible string can be regarded as a one-dimensional flag model. Many similarities can be found between the flapping string and swimming fish, although different wake speed results in a drag force for the flapping string and a propulsion force for the swimming fish. In the present study, we propose a mathematical formulation for swimming strings immersed in a viscous fluid flow. Fluid motion is governed by the Navier-Stokes equations and a momentum forcing is added in order to bring the fluid to move at the same velocity with the immersed surface. A flexible inextensible string model is described by another set of equations with an additional momentum forcing which is a result of the fluid viscosity and the pressure difference across the string. The momentum forcing is calculated by a feedback loop. Simulations of several numerical examples are carried out, including a hanging string which starts moving under gravity without ambient fluid, a swinging string immersed in a quiescent viscous fluid, a string swimming within a uniform surrounding flow, and flow over two side-by-side strings. The numerical results agree well with the theoretical analysis and previous experimental observations. Further simulation of a swimming fish is under consideration.

  5. Exact and numerical solutions of generalized Drinfeld-Sokolov equations

    Energy Technology Data Exchange (ETDEWEB)

    Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com

    2008-04-14

    In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

  6. Viscous wing theory development. Volume 2: GRUMWING computer program user's manual

    Science.gov (United States)

    Chow, R. R.; Ogilvie, P. L.

    1986-01-01

    This report is a user's manual which describes the operation of the computer program, GRUMWING. The program computes the viscous transonic flow over three-dimensional wings using a boundary layer type viscid-inviscid interaction approach. The inviscid solution is obtained by an approximate factorization (AFZ)method for the full potential equation. The boundary layer solution is based on integral entrainment methods.

  7. Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

    Energy Technology Data Exchange (ETDEWEB)

    Woods, Mark Christopher [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Holmes, Mark [Rensselaer Polytechnic Inst., Troy, NY (United States); Sailor, William C [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2017-07-01

    A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

  8. Solution of Milne problem by Laplace transformation with numerical inversion

    International Nuclear Information System (INIS)

    Campos Velho, H.F. de.

    1987-12-01

    The Milne problem for monoenergetic neutrons, by Laplace Transform of the neutron transport integral equation with numerical inversion of the transformed solution by gaussian quadrature, using the fatorization of the dispersion function. The resulted is solved compared its analitical solution. (author) [pt

  9. Viscous Dissipation and Heat Conduction in Binary Neutron-Star Mergers.

    Science.gov (United States)

    Alford, Mark G; Bovard, Luke; Hanauske, Matthias; Rezzolla, Luciano; Schwenzer, Kai

    2018-01-26

    Inferring the properties of dense matter is one of the most exciting prospects from the measurement of gravitational waves from neutron star mergers. However, it requires reliable numerical simulations that incorporate viscous dissipation and energy transport as these can play a significant role in the survival time of the post-merger object. We calculate time scales for typical forms of dissipation and find that thermal transport and shear viscosity will not be important unless neutrino trapping occurs, which requires temperatures above 10 MeV and gradients over length scales of 0.1 km or less. On the other hand, if direct-Urca processes remain suppressed, leaving modified-Urca processes to establish flavor equilibrium, then bulk viscous dissipation could provide significant damping to density oscillations right after merger. When comparing with data from state-of-the-art merger simulations, we find that the bulk viscosity takes values close to its resonant maximum in a typical merger, motivating a more careful assessment of the role of bulk viscous dissipation in the gravitational-wave signal from merging neutron stars.

  10. Viscous Dissipation and Heat Conduction in Binary Neutron-Star Mergers

    Science.gov (United States)

    Alford, Mark G.; Bovard, Luke; Hanauske, Matthias; Rezzolla, Luciano; Schwenzer, Kai

    2018-01-01

    Inferring the properties of dense matter is one of the most exciting prospects from the measurement of gravitational waves from neutron star mergers. However, it requires reliable numerical simulations that incorporate viscous dissipation and energy transport as these can play a significant role in the survival time of the post-merger object. We calculate time scales for typical forms of dissipation and find that thermal transport and shear viscosity will not be important unless neutrino trapping occurs, which requires temperatures above 10 MeV and gradients over length scales of 0.1 km or less. On the other hand, if direct-Urca processes remain suppressed, leaving modified-Urca processes to establish flavor equilibrium, then bulk viscous dissipation could provide significant damping to density oscillations right after merger. When comparing with data from state-of-the-art merger simulations, we find that the bulk viscosity takes values close to its resonant maximum in a typical merger, motivating a more careful assessment of the role of bulk viscous dissipation in the gravitational-wave signal from merging neutron stars.

  11. Heat transfer analysis for magnetohydrodynamics axisymmetric flow between stretching disks in the presence of viscous dissipation and Joule heating

    Directory of Open Access Journals (Sweden)

    N. Khan

    2015-05-01

    Full Text Available The investigation of heat transfer analysis on steady MHD axi-symmetric flow between two infinite stretching disks in the presence of viscous dissipation and Joule heating is basic objective of this paper. Attention has been focused to acquire the similarity solutions of the equations governing the flow and thermal fields. The transformed boundary value problem is solved analytically using homotopy analysis method. The series solutions are developed and the convergence of these solutions is explicitly discussed. The analytical expressions for fluid velocity, pressure and temperature are constructed and analyzed for various set of parameter values. The numerical values for skin friction coefficient and the Nusselt number are presented in tabular form. Particular attention is given to the variations of Prandtl and Eckert numbers. We examined that the dimensionless temperature field is enhanced when we increase the values of Eckert number and Prandtl number.

  12. Numerical Study of the Magnetic Field Effects on the Heat Transfer and Entropy Generation Aspects of a Power Law Fluid over an Axisymmetric Stretching Plate Structure

    Directory of Open Access Journals (Sweden)

    Payam Hooshmand

    2017-03-01

    Full Text Available Numerical investigation of the effects of magnetic field strength, thermal radiation, Joule heating, and viscous heating on a forced convective flow of a non-Newtonian, incompressible power law fluid in an axisymmetric stretching sheet with variable temperature wall is accomplished. The power law shear thinning viscosity-shear rate model for the anisotropic solutions and the Rosseland approximation for the thermal radiation through a highly absorbing medium are considered. The temperature dependent heat sources, Joule heating, and viscous heating are considered as the source terms in the energy balance. The non-dimensional boundary layer equations are solved numerically in terms of similarity variable. A parameter study on the Nusselt number, viscous components of entropy generation, and thermal components of entropy generation in fluid is performed as a function of thermal radiation parameter (0 to 2, Brinkman number (0 to 10, Prandtl number (0 to 10, Hartmann number (0 to 1, power law index (0 to 1, and heat source coefficient (0 to 0.1.

  13. Turbulence modeling of the Von Karman flow: Viscous and inertial stirrings

    International Nuclear Information System (INIS)

    Poncet, Sebastien; Schiestel, Roland; Monchaux, Romain

    2008-01-01

    The present work considers the turbulent Von Karman flow generated by two counter-rotating smooth flat (viscous stirring) or bladed (inertial stirring) disks. Numerical predictions based on one-point statistical modeling using a low-Reynolds number second-order full stress transport closure (RSM model) are compared to velocity measurements performed at CEA (Commissariat a l'Energie Atomique, France). The main and significant novelty of this paper is the use of a drag force in the momentum equations to reproduce the effects of inertial stirring instead of modeling the blades themselves. The influences of the rotational Reynolds number, the aspect ratio of the cavity, the rotating disk speed ratio and of the presence or not of impellers are investigated to get a precise knowledge of both the dynamics and the turbulence properties in the Von Karman configuration. In particular, we highlighted the transition between the merged and separated boundary layer regimes and the one between the Batchelor [Batchelor, G.K., 1951. Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Quat. J. Mech. Appl. Math. 4 (1), 29-41] and the Stewartson [Stewartson, K., 1953. On the flow between two rotating coaxial disks. Proc. Camb. Philos. Soc. 49, 333-341] flow structures in the smooth disk case. We determined also the transition between the one cell and the two cell regimes for both viscous and inertial stirrings

  14. Implementation aspects of the Boundary Element Method including viscous and thermal losses

    DEFF Research Database (Denmark)

    Cutanda Henriquez, Vicente; Juhl, Peter Møller

    2014-01-01

    The implementation of viscous and thermal losses using the Boundary Element Method (BEM) is based on the Kirchhoff’s dispersion relation and has been tested in previous work using analytical test cases and comparison with measurements. Numerical methods that can simulate sound fields in fluids...

  15. Calculations of stationary solutions for the non linear viscous resistive MHD equations in slab geometry

    International Nuclear Information System (INIS)

    Edery, D.

    1983-11-01

    The reduced system of the non linear resistive MHD equations is used in the 2-D one helicity approximation in the numerical computations of stationary tearing modes. The critical magnetic Raynolds number S (S=tausub(r)/tausub(H) where tausub(R) and tausub(H) are respectively the characteristic resistive and hydro magnetic times) and the corresponding linear solution are computed as a starting approximation for the full non linear equations. These equations are then treated numerically by an iterative procedure which is shown to be rapidly convergent. A numerical application is given in the last part of this paper

  16. Optimisation of ultrafiltration of a highly viscous protein solution using spiral-wound modules

    DEFF Research Database (Denmark)

    Lipnizki, Jens; Casani, S.; Jonsson, Gunnar Eigil

    2005-01-01

    The ultrafiltration process of highly viscous protein process water with spiral-wound modules was optimised by analysing the fouling and developing a strategy to reduce it. It was shown that the flux reduction during filtration is mainly caused by the adsorption of proteins on the membrane and no...

  17. Viscous self interacting dark matter and cosmic acceleration

    Science.gov (United States)

    Atreya, Abhishek; Bhatt, Jitesh R.; Mishra, Arvind

    2018-02-01

    Self interacting dark matter (SIDM) provides us with a consistent solution to certain astrophysical observations in conflict with collision-less cold DM paradigm. In this work we estimate the shear viscosity (η) and bulk viscosity (ζ) of SIDM, within kinetic theory formalism, for galactic and cluster size SIDM halos. To that extent we make use of the recent constraints on SIDM cross-section for the dwarf galaxies, LSB galaxies and clusters. We also estimate the change in solution of Einstein's equation due to these viscous effects and find that σ/m constraints on SIDM from astrophysical data provide us with sufficient viscosity to account for the observed cosmic acceleration at present epoch, without the need of any additional dark energy component. Using the estimates of dark matter density for galactic and cluster size halo we find that the mean free path of dark matter ~ few Mpc. Thus the smallest scale at which the viscous effect start playing the role is cluster scale. Astrophysical data for dwarf, LSB galaxies and clusters also seems to suggest the same. The entire analysis is independent of any specific particle physics motivated model for SIDM.

  18. Numerical solution of large sparse linear systems

    International Nuclear Information System (INIS)

    Meurant, Gerard; Golub, Gene.

    1982-02-01

    This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

  19. On mesh refinement and accuracy of numerical solutions

    NARCIS (Netherlands)

    Zhou, Hong; Peters, Maria; van Oosterom, Adriaan

    1993-01-01

    This paper investigates mesh refinement and its relation with the accuracy of the boundary element method (BEM) and the finite element method (FEM). TO this end an isotropic homogeneous spherical volume conductor, for which the analytical solution is available, wag used. The numerical results

  20. The numerical solution of boundary value problems over an infinite domain

    International Nuclear Information System (INIS)

    Shepherd, M.; Skinner, R.

    1976-01-01

    A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail

  1. Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil

    Science.gov (United States)

    Kryštůfek, P.; Kozel, K.

    2015-05-01

    The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Euler equations in 2D compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil. The results are compared with the solution using the software Ansys Fluent 15.0.7.

  2. Numerical solution of second-order stochastic differential equations with Gaussian random parameters

    Directory of Open Access Journals (Sweden)

    Rahman Farnoosh

    2014-07-01

    Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.

  3. Chemical stability of diphenhydramine hydrochloride from an elixir and lidocaine hydrochloride from a viscous solution when mixed together.

    Science.gov (United States)

    Gupta, Vishnu D

    2006-01-01

    The stability of diphenhydramine hydrochloride (from an elixir) and lidocaine hydrochloride (from a viscous solution) in a mixture (1:1) was studied using a stability-indicating high-peformance liquid chromatographic assay method. The concentrations of the drugs were related directly to peak heights and the percent relative standard deviations based on five injections were 1.4 for diphenhydramine and 1.3 for lidocaine. The products of hydrolysis from the both the drugs and a number of excipients present in the dosage forms did not interfere with the developed assay procedure. The mixture was stable for at least 21 days when stored in amber-colored bottles at room temperature. The pH value of the mixture remained constant, and the physical appearance did not change during the study period.

  4. New numerical method for solving the solute transport equation

    International Nuclear Information System (INIS)

    Ross, B.; Koplik, C.M.

    1978-01-01

    The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

  5. Numerical solution of the resistive magnetohydrodynamic boundary-layer equations

    International Nuclear Information System (INIS)

    Glasser, A.H.; Jardin, S.C.; Tesauro, G.

    1983-10-01

    Three different techniques are presented for numerical solution of the equations governing the boundary layer of resistive magnetohydrodynamic tearing and interchange instabilities in toroidal geometry. Excellent agreement among these methods and with analytical results provides confidence in the correctness of the results. Solutions obtained in regimes where analytical medthods fail indicate a new scaling for the tearing mode as well as the existence of a new regime of stability

  6. Numerical solution of the radionuclide transport equation

    International Nuclear Information System (INIS)

    Hadermann, J.; Roesel, F.

    1983-11-01

    A numerical solution of the one-dimensional geospheric radionuclide chain transport equation based on the pseudospectral method is developed. The advantages of this approach are flexibility in incorporating space and time dependent migration parameters, arbitrary boundary conditions and solute rock interactions as well as efficiency and reliability. As an application the authors investigate the impact of non-linear sorption isotherms on migration in crystalline rock. It is shown that non-linear sorption, in the present case a Freundlich isotherm, may reduce concentration at the geosphere outlet by orders of magnitude provided the migration time is comparable or larger than the half-life of the nuclide in question. The importance of fixing dispersivity within the continuum approach is stressed. (Auth.)

  7. Numerical study of traveling-wave solutions for the Camassa-Holm equation

    International Nuclear Information System (INIS)

    Kalisch, Henrik; Lenells, Jonatan

    2005-01-01

    We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied

  8. Numerical solutions of a three-point boundary value problem with an ...

    African Journals Online (AJOL)

    Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.

  9. Numerical solution of the polymer system

    Energy Technology Data Exchange (ETDEWEB)

    Haugse, V.; Karlsen, K.H.; Lie, K.-A.; Natvig, J.R.

    1999-05-01

    The paper describes the application of front tracking to the polymer system, an example of a nonstrictly hyperbolic system. Front tracking computes piecewise constant approximations based on approximate Remain solutions and exact tracking of waves. It is well known that the front tracking method may introduce a blow-up of the initial total variation for initial data along the curve where the two eigenvalues of the hyperbolic system are identical. It is demonstrated by numerical examples that the method converges to the correct solution after a finite time that decreases with the discretization parameter. For multidimensional problems, front tracking is combined with dimensional splitting and numerical experiments indicate that large splitting steps can be used without loss of accuracy. Typical CFL numbers are in the range of 10 to 20 and comparisons with the Riemann free, high-resolution method confirm the high efficiency of front tracking. The polymer system, coupled with an elliptic pressure equation, models two-phase, tree-component polymer flooding in an oil reservoir. Two examples are presented where this model is solved by a sequential time stepping procedure. Because of the approximate Riemann solver, the method is non-conservative and CFL members must be chosen only moderately larger than unity to avoid substantial material balance errors generated in near-well regions after water breakthrough. Moreover, it is demonstrated that dimensional splitting may introduce severe grid orientation effects for unstable displacements that are accentuated for decreasing discretization parameters. 9 figs., 2 tabs., 26 refs.

  10. On the numerical evaluation of algebro-geometric solutions to integrable equations

    International Nuclear Information System (INIS)

    Kalla, C; Klein, C

    2012-01-01

    Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations

  11. Viscous Fingering in Deformable Systems

    Science.gov (United States)

    Guan, Jian Hui; MacMinn, Chris

    2017-11-01

    Viscous fingering is a classical hydrodynamic instability that occurs when an invading fluid is injected into a porous medium or a Hele-Shaw cell that contains a more viscous defending fluid. Recent work has shown that viscous fingering in a Hele-Shaw cell is supressed when the flow cell is deformable. However, the mechanism of suppression relies on a net volumetric expansion of the flow area. Here, we study flow in a novel Hele-Shaw cell consisting of a rigid bottom plate and a flexible top plate that deforms in a way that is volume-conserving. In other words, fluid injection into the flow cell leads to a local expansion of the flow area (outward displacement of the flexible surface) that must be coupled to non-local contraction (inward displacement of the flexible surface). We explore the impact of this volumetric confinement on steady viscous flow and on viscous fingering. We would like to thank EPSRC for the funding for this work.

  12. Numerical Solution of Differential Algebraic Equations and Applications

    DEFF Research Database (Denmark)

    Thomsen, Per Grove

    2005-01-01

    These lecture notes have been written as part of a special course on the numerical solution of Differential Algebraic Equations and applications . The course was held at IMM in the spring of 2005. The authors of the different chapters have all taken part in the course and the chapters are written...

  13. Numerical solution of field theories using random walks

    International Nuclear Information System (INIS)

    Barnes, T.; Daniell, G.J.

    1985-01-01

    We show how random walks in function space can be employed to evaluate field theoretic vacuum expectation values numerically. Specific applications which we study are the two-point function, mass gap, magnetization and classical solutions. This technique offers the promise of faster calculations using less computer memory than current methods. (orig.)

  14. Mathematical theory of viscous fluids: retrospective and future perspectives

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2010-01-01

    Roč. 27, č. 2 (2010), s. 533-555 ISSN 1078-0947 R&D Projects: GA ČR GA201/08/0315 Institutional research plan: CEZ:AV0Z10190503 Keywords : viscous fluid * Navier-Stokes-Fourier system * global-intime solutions Subject RIV: BA - General Mathematics Impact factor: 0.986, year: 2010 http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4942

  15. Circulation shedding in viscous starting flow past a flat plate

    International Nuclear Information System (INIS)

    Nitsche, Monika; Xu, Ling

    2014-01-01

    Numerical simulations of viscous flow past a flat plate moving in the direction normal to itself reveal details of the vortical structure of the flow. At early times, most of the vorticity is attached to the plate. This paper introduces a definition of the shed circulation at all times and shows that it indeed represents vorticity that separates and remains separated from the plate. During a large initial time period, the shed circulation satisfies the scaling laws predicted for self-similar inviscid separation. Various contributions to the circulation shedding rate are presented. The results show that during this initial time period, viscous diffusion of vorticity out of the vortex is significant but appears to be independent of the value of the Reynolds number. At later times, the departure of the shed circulation from its large Reynolds number behaviour is significantly affected by diffusive loss of vorticity through the symmetry axis. A timescale is proposed that describes when the viscous loss through the axis becomes relevant. The simulations provide benchmark results to evaluate simpler separation models such as point vortex and vortex sheet models. A comparison with vortex sheet results is included. (paper)

  16. Nonlinear viscous vortex motion in two-dimensional Josephson-junction arrays

    International Nuclear Information System (INIS)

    Hagenaars, T.J.; Tiesinga, P.H.E.; van Himbergen, J.E.; Jose, J.V.

    1994-01-01

    When a vortex in a two-dimensional Josephson-junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a nonlinear viscous force of the form F D =η(y)y=[A/(1+By]y, where y is the vortex velocity, η(y) is the velocity-dependent viscosity, and A and B are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies

  17. Numerical double layer solutions with ionization

    International Nuclear Information System (INIS)

    Andersson, D.; Soerensen, J.

    1982-08-01

    Maxwell's equation div D = ro in one dimension is solved numerically, taking ionization into account. Time independent anode sheath and double layer solutions are obtained. By varying voltage, neutral gas pressure, temperature of the trapped ions on the cathode side and density and temperature of the trapped electrones on the anode side, diagrams are constructed that show permissible combinations of these parameters. Results from a recent experiment form a subset. Distribution functions, the Langmuir condition, some scaling laws and a possible application to the lower ionosphere are discussed. (Authors)

  18. Numerical solution of dynamic equilibrium models under Poisson uncertainty

    DEFF Research Database (Denmark)

    Posch, Olaf; Trimborn, Timo

    2013-01-01

    We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retar...... solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households....

  19. Case studies in the numerical solution of oscillatory integrals

    International Nuclear Information System (INIS)

    Adam, G.

    1992-06-01

    A numerical solution of a number of 53,249 test integrals belonging to nine parametric classes was attempted by two computer codes: EAQWOM (Adam and Nobile, IMA Journ. Numer. Anal. (1991) 11, 271-296) and DO1ANF (Mark 13, 1988) from the NAG library software. For the considered test integrals, EAQWOM was found to be superior to DO1ANF as it concerns robustness, reliability, and friendly user information in case of failure. (author). 9 refs, 3 tabs

  20. Viscous shear in the Kerr metric

    International Nuclear Information System (INIS)

    Anderson, M.R.; Lemos, J.P.S.

    1988-01-01

    Models of viscous flows on to black holes commonly assume a zero-torque boundary condition at the radius of the last stable Keplerian orbit. It is here shown that this condition is wrong. The viscous torque is generally non-zero at both the last stable orbit and the horizon itself. The existence of a non-zero viscous torque at the horizon does not require the transfer of energy or angular momentum across any spacelike distance, and so does not violate causality. Further, in comparison with the viscous torque in the distant, Newtonian regime, the viscous torque on the horizon is often reversed, so that angular momentum is viscously advected inwards rather than outwards. This phenomenon is first suggested by an analysis of the quasi-stationary case, and then demonstrated explicitly for a series of cold, dynamical flows which fall freely from the last stable orbit in the Schwarzschild and Kerr metrics. In the steady flows constructed here, the net torque on the hole is always directed in the usual sense; any reversal in the viscous torque is offset by an increase in the convected flux of angular momentum. (author)

  1. Solutions manual to accompany An introduction to numerical methods and analysis

    CERN Document Server

    Epperson, James F

    2014-01-01

    A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp

  2. The effectiveness of domain balancing strategies on workstation clusters demonstrated by viscous flow problems

    NARCIS (Netherlands)

    Streng, Martin; Streng, M.; ten Cate, Eric; ten Cate, Eric (H.H.); Geurts, Bernardus J.; Kuerten, Johannes G.M.

    1998-01-01

    We consider several aspects of efficient numerical simulation of viscous compressible flow on both homogeneous and heterogeneous workstation-clusters. We consider dedicated systems, as well as clusters operating in a multi-user environment. For dedicated homogeneous clusters, we show that with

  3. Electric field stabilization of viscous liquid layers coating the underside of a surface

    Science.gov (United States)

    Anderson, Thomas G.; Cimpeanu, Radu; Papageorgiou, Demetrios T.; Petropoulos, Peter G.

    2017-05-01

    We investigate the electrostatic stabilization of a viscous thin film wetting the underside of a horizontal surface in the presence of an electric field applied parallel to the surface. The model includes the effect of bounding solid dielectric regions above and below the liquid-air system that are typically found in experiments. The competition between gravitational forces, surface tension, and the nonlocal effect of the applied electric field is captured analytically in the form of a nonlinear evolution equation. A semispectral solution strategy is employed to resolve the dynamics of the resulting partial differential equation. Furthermore, we conduct direct numerical simulations (DNS) of the Navier-Stokes equations using the volume-of-fluid methodology and assess the accuracy of the obtained solutions in the long-wave (thin-film) regime when varying the electric field strength from zero up to the point when complete stabilization occurs. We employ DNS to examine the limitations of the asymptotically derived behavior as the liquid layer thickness increases and find excellent agreement even beyond the regime of strict applicability of the asymptotic solution. Finally, the asymptotic and computational approaches are utilized to identify robust and efficient active control mechanisms allowing the manipulation of the fluid interface in light of engineering applications at small scales, such as mixing.

  4. Viscous Regularization of the Euler Equations and Entropy Principles

    KAUST Repository

    Guermond, Jean-Luc

    2014-03-11

    This paper investigates a general class of viscous regularizations of the compressible Euler equations. A unique regularization is identified that is compatible with all the generalized entropies, à la [Harten et al., SIAM J. Numer. Anal., 35 (1998), pp. 2117-2127], and satisfies the minimum entropy principle. A connection with a recently proposed phenomenological model by [H. Brenner, Phys. A, 370 (2006), pp. 190-224] is made. © 2014 Society for Industrial and Applied Mathematics.

  5. Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

    Directory of Open Access Journals (Sweden)

    Ravi Kanth A.S.V.

    2016-01-01

    Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

  6. A numerical study for off-centered stagnation flow towards a rotating disc

    Directory of Open Access Journals (Sweden)

    M. Heydari

    2015-09-01

    Full Text Available In this investigation, a semi-numerical method based on Bernstein polynomials for solving off-centered stagnation flow towards a rotating disc is introduced. This method expands the desired solutions in terms of a set of Bernstein polynomials over a closed interval and then makes use of the tau method to determine the expansion coefficients to construct approximate solutions. This method can satisfy boundary conditions at infinity. The properties of Bernstein polynomials are presented and are utilized to reduce the solution of governing nonlinear equations and their associated boundary conditions to the solution of algebraic equations. Graphical results are presented to investigate the influence of the rotation ratio α on the radial velocity, azimuthal velocity and the induced velocities. A comparative study with the previous results of viscous fluid flow in the literature is made.

  7. Numerical solution of a reaction-diffusion equation

    International Nuclear Information System (INIS)

    Moyano, Edgardo A.; Scarpettini, Alberto F.

    2000-01-01

    The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)

  8. Deformation and transport of micro-fibers and helices in viscous flows

    Science.gov (United States)

    Lindner, Anke

    Fluid-structure interactions between flexible objects and viscous flows are, to a large extent, governed by the shape of the flexible object. Using microfabrication methods, we obtain complex ``particles'' in fiber and helix form with perfect control not only over the material properties, but also the particle geometry. We then perform an experimental study on the deformation and transport of these particles in microfluidic flows. Fibers are shown to drift laterally in confined flows due to the transport anisotropy of the elongated object. When these fibers interact with lateral walls, complex dynamics are observed, such as fiber oscillation. Fiber flexibility modifies these dynamics. Flexible microhelices are easily stretched by a viscous flow and we characterize the overall shape as a function of the frictional properties. The deformation of these helices is well-described by non-linear finite extensibility. Due to the non-uniform distribution of the pitch of a helix subject to viscous drag, linear and nonlinear behavior is identified along the contour length of a single helix. When a polymer solution is used for the viscous flow, an interesting multiscale problem arises and the typical polymer size needs to be compared not only to the global size of the helix, but also to the dimensions of the ribbon.

  9. Relic gravitons and viscous cosmologies

    International Nuclear Information System (INIS)

    Cataldo, Mauricio; Mella, Patricio

    2006-01-01

    Previously it was shown that there exists a class of viscous cosmological models which violate the dominant energy condition for a limited amount of time after which they are smoothly connected to the ordinary radiation era (which preserves the dominant energy conditions). This violation of the dominant energy condition at an early cosmological epoch may influence the slopes of energy spectra of relic gravitons that might be of experimental relevance. However, the bulk viscosity coefficient of these cosmologies became negative during the ordinary radiation era, and then the entropy of the sources driving the geometry decreases with time. We show that in the presence of viscous sources with a linear barotropic equation of state p=γρ we get viscous cosmological models with positive bulk viscous stress during all their evolution, and hence the matter entropy increases with the expansion time. In other words, in the framework of viscous cosmologies, there exist isotropic models compatible with the standard second law of thermodynamics which also may influence the slopes of energy spectra of relic gravitons

  10. Friedmann model with viscous cosmology in modified f(R,T) gravity theory

    Energy Technology Data Exchange (ETDEWEB)

    Singh, C.P.; Kumar, Pankaj [Delhi Technological University, Department of Applied Mathematics, Delhi (India)

    2014-10-15

    In this paper, we introduce the bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function f(R,T), where R and T denote the curvature scalar and the trace of the energy.momentum tensor, respectively, within the framework of a flat Friedmann-Robertson-Walker model. As an equation of state for a prefect fluid, we take p = (γ - 1)ρ, where 0 ≤ γ ≤ 2 and a viscous term as a bulk viscosity due to the isotropic model, of the form ξ = ξ{sub 0} + ξ{sub 1}H, where ξ{sub 0} and ξ{sub 1} are constants, and H is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non-viscous and viscous fluids, respectively, by assuming a simplest particular model of the form of f(R,T) = R + 2f(T), where f(T) = αT (α is a constant). A big-rip singularity is also observed for γ < 0 at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of α to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits a transition from a decelerated phase to an accelerated phase under certain constraints of ξ{sub 0} and ξ{sub 1}. We compare the viscous models with the non-viscous one through the graph plotted between the scale factor and cosmic time and find that the bulk viscosity plays a major role in the expansion of the universe. A similar graph is plotted for the deceleration parameter with non-viscous and viscous fluids and we find a transition from decelerated to accelerated phase with some form of bulk viscosity. (orig.)

  11. On the General Analytical Solution of the Kinematic Cosserat Equations

    KAUST Repository

    Michels, Dominik L.

    2016-09-01

    Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

  12. On the General Analytical Solution of the Kinematic Cosserat Equations

    KAUST Repository

    Michels, Dominik L.; Lyakhov, Dmitry; Gerdt, Vladimir P.; Hossain, Zahid; Riedel-Kruse, Ingmar H.; Weber, Andreas G.

    2016-01-01

    Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

  13. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  14. 2nd International Workshop on the Numerical Solution of Markov Chains

    CERN Document Server

    1995-01-01

    Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.

  15. The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet

    International Nuclear Information System (INIS)

    Sajid, M.; Hayat, T.

    2009-01-01

    This work is concerned with the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet. The cases of two dimensional and axisymmetric shrinking have been discussed. Exact series solution is obtained using the homotopy analysis method (HAM). The convergence of the obtained series solution is discussed explicitly. The obtained HAM solution is valid for all values of the suction parameter and Hartman number.

  16. Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

    Science.gov (United States)

    Kryštůfek, P.; Kozel, K.

    2014-03-01

    The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.

  17. Numerical Solution of Compressible Steady Flows around the NACA 0012 Airfoil

    Directory of Open Access Journals (Sweden)

    Kozel K

    2013-04-01

    Full Text Available The article presents results of a numerical solution of subsonic and transonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the NACA 0012 airfoil. Authors used Runge-Kutta method to numerically solve the flows around the NACA 0012 airfoil.

  18. Numerical solutions of diffusive logistic equation

    International Nuclear Information System (INIS)

    Afrouzi, G.A.; Khademloo, S.

    2007-01-01

    In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

  19. Numerical analysis of hydrodynamic forces acting on vertical lift gates; Analise dos esforcos hidrodinamicas em comportas hidraulicas

    Energy Technology Data Exchange (ETDEWEB)

    Andrade, Jell Lima de [Mecanica Pesada S.A., Taubate, SP (Brazil); Amorim, Jose Carlos Cesar [Instituto Militar de Engenharia (IME), Rio de Janeiro, RJ (Brazil)]. E-mail: jcamorim@ime.eb.br

    1997-07-01

    A numerical analysis has been developed for calculating viscous flows controlled by a vertical lift gate and hydrodynamic forces acting on it. The numerical solution is obtained from the incompressible Navier-Stoles equations. The numerical techniques is based on a finite element method. A Poisson equation is derived from the pressure-weighted substitution of the full momentum equations into the continuity equation. Turbulence effects are simulated by a K-{epsilon} turbulence model. The procedure developed here is applied for a vertical lift gate operating in a CESP installation, and the results are compared with available experimental data at various opening positions. Good agreement is obtained for the velocity and pressure distributions. (author)

  20. A Thermodynamically Consistent Approach to Phase-Separating Viscous Fluids

    Science.gov (United States)

    Anders, Denis; Weinberg, Kerstin

    2018-04-01

    The de-mixing properties of heterogeneous viscous fluids are determined by an interplay of diffusion, surface tension and a superposed velocity field. In this contribution a variational model of the decomposition, based on the Navier-Stokes equations for incompressible laminar flow and the extended Korteweg-Cahn-Hilliard equations, is formulated. An exemplary numerical simulation using C1-continuous finite elements demonstrates the capability of this model to compute phase decomposition and coarsening of the moving fluid.

  1. Energy change of a heavy quark in a viscous quark–gluon plasma with fluctuations

    International Nuclear Information System (INIS)

    Jiang, Bing-feng; Hou, De-fu; Li, Jia-rong

    2016-01-01

    When a heavy quark travels through the quark–gluon plasma, the polarization and fluctuating chromoelectric fields will be produced simultaneously in the plasma. The drag force due to those fields exerting in return on the moving heavy quark will cause energy change to it. Based on the dielectric functions derived from the viscous chromohydrodynamics, we have studied the collisional energy change of a heavy quark traversing the viscous quark–gluon plasma including fluctuations of chromoelectric field. Numerical results indicate that the chromoelectric field fluctuations lead to an energy gain of the moving heavy quark. Shear viscosity suppresses the fluctuation-induced energy gain and the viscous suppression effect for the charm quark is much more remarkable than that for the bottom quark. While, the fluctuation energy gain is much smaller than the polarization energy loss in magnitude and the net energy change for the heavy quark is at loss.

  2. Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

    Directory of Open Access Journals (Sweden)

    Kryštůfek P.

    2014-03-01

    Full Text Available The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.

  3. A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

    KAUST Repository

    Pathmanathan, Pras

    2010-06-01

    Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

  4. A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

    KAUST Repository

    Pathmanathan, Pras; Bernabeu, Miguel O.; Bordas, Rafel; Cooper, Jonathan; Garny, Alan; Pitt-Francis, Joe M.; Whiteley, Jonathan P.; Gavaghan, David J.

    2010-01-01

    Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

  5. LED-based Photometric Stereo: Modeling, Calibration and Numerical Solutions

    DEFF Research Database (Denmark)

    Quéau, Yvain; Durix, Bastien; Wu, Tao

    2018-01-01

    We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in pr...

  6. 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.

  7. Dynamic behaviour of a planar micro-beam loaded by a fluid-gap: Analytical and numerical approach in a high frequency range, benchmark solutions

    Science.gov (United States)

    Novak, A.; Honzik, P.; Bruneau, M.

    2017-08-01

    Miniaturized vibrating MEMS devices, active (receivers or emitters) or passive devices, and their use for either new applications (hearing, meta-materials, consumer devices,…) or metrological purposes under non-standard conditions, are involved today in several acoustic domains. More in-depth characterisation than the classical ones available until now are needed. In this context, the paper presents analytical and numerical approaches for describing the behaviour of three kinds of planar micro-beams of rectangular shape (suspended rigid or clamped elastic planar beam) loaded by a backing cavity or a fluid-gap, surrounded by very thin slits, and excited by an incident acoustic field. The analytical approach accounts for the coupling between the vibrating structure and the acoustic field in the backing cavity, the thermal and viscous diffusion processes in the boundary layers in the slits and the cavity, the modal behaviour for the vibrating structure, and the non-uniformity of the acoustic field in the backing cavity which is modelled in using an integral formulation with a suitable Green's function. Benchmark solutions are proposed in terms of beam motion (from which the sensitivity, input impedance, and pressure transfer function can be calculated). A numerical implementation (FEM) is handled against which the analytical results are tested.

  8. Numerical modelling of nearshore wave transformation

    Digital Repository Service at National Institute of Oceanography (India)

    Chandramohan, P.; Nayak, B.U.; SanilKumar, V.

    A software has been developed for numerical refraction study based on finite amplitude wave theories. Wave attenuation due to shoaling, bottom friction, bottom percolation and viscous dissipation has also been incorporated. The software...

  9. The simulation of solute transport: An approach free of numerical dispersion

    International Nuclear Information System (INIS)

    Carrera, J.; Melloni, G.

    1987-01-01

    The applicability of most algorithms for simulation of solute transport is limited either by instability or by numerical dispersion, as seen by a review of existing methods. A new approach is proposed that is free of these two problems. The method is based on the mixed Eulerian-Lagrangian formulation of the mass-transport problem, thus ensuring stability. Advection is simulated by a variation of reverse-particle tracking that avoids the accumulation of interpolation errors, thus preventing numerical dispersion. The algorithm has been implemented in a one-dimensional code. Excellent results are obtained, in comparison with an analytical solution. 36 refs., 14 figs., 1 tab

  10. Urease plays an important role in the chemotactic motility of Helicobacter pylori in a viscous environment.

    Science.gov (United States)

    Nakamura, H; Yoshiyama, H; Takeuchi, H; Mizote, T; Okita, K; Nakazawa, T

    1998-10-01

    Helicobacter pylori exhibits chemotactic responses to urea, flurofamide, acetohydroxamic acid, and sodium bicarbonate. In buffer, the chemotactic activities of a urease-positive strain were higher than those of the isogenic urease-negative strain. Moreover, the chemotactic activities of the urease-positive strain were increased in a viscous solution containing 3% polyvinylpyrrolidone, whereas those of the urease-negative mutant were not. These results are in accordance with the fact that the mutant strain did not show swarming in motility agar regardless of having flagella. Incubation of the wild-type strain with flurofamide resulted in partial inhibition of the chemotactic activities in the viscous solution. In addition, incubation with acetohydroxamic acid, a low-molecular-weight, diffusible urease inhibitor, resulted in complete loss of chemotactic activity in the viscous solution. The inhibition of the chemotactic activity by urease inhibitors paralleled the inhibition of urease. The chemotactic activity of H. pylori was also inhibited by the proton carrier carbonyl cyanide m-chlorophenylhydrazone, showing that H. pylori utilizes proton motive force for motility. These results indicate that cytoplasmic urease plays an important role in the chemotactic motility of H. pylori under a condition that mimics the ecological niche of the bacterium, the gastric mucous layer.

  11. Preparation and use of viscous-elastic clay-polymer mixtures in drilling

    Energy Technology Data Exchange (ETDEWEB)

    Davydov, V K; Tyurin, I P

    1979-01-01

    A highly viscous-elastic mixture (VUS) has been widely used as a buffer liquid. It consists of a weakly concentrated aqueous polyacrylamide solute with additives of small quantities of an aqueous hexaresorcin tar and formalin solution. Laboratory tests have shown that when this mixture is prepared, a bentonite suspension is required with a pH 7, containing minimum 10% solid phase and an aqueous polyacrylamide solution with concentration of no less than 1%. Tests have shown that the effect of this formula varies according to proportions in the mixture. Temperature and selection of the formula must be made on an individual basis.

  12. Performance analysis of numeric solutions applied to biokinetics of radionuclides

    International Nuclear Information System (INIS)

    Mingatos, Danielle dos Santos; Bevilacqua, Joyce da Silva

    2013-01-01

    Biokinetics models for radionuclides applied to dosimetry problems are constantly reviewed by ICRP. The radionuclide trajectory could be represented by compartmental models, assuming constant transfer rates between compartments. A better understanding of physiological or biochemical phenomena, improve the comprehension of radionuclide behavior in the human body and, in general, more complex compartmental models are proposed, increasing the difficulty of obtaining the analytical solution for the system of first order differential equations. Even with constant transfer rates numerical solutions must be carefully implemented because of almost singular characteristic of the matrix of coefficients. In this work we compare numerical methods with different strategies for ICRP-78 models for Thorium-228 and Uranium-234. The impact of uncertainty in the parameters of the equations is also estimated for local and global truncation errors. (author)

  13. Evidence of nonuniqueness and oscillatory solutions in computational fluid mechanics

    International Nuclear Information System (INIS)

    Nunziato, J.W.; Gartling, D.K.; Kipp, M.E.

    1985-01-01

    We will review some of our recent experiences in computing solutions for nonlinear fluids in relatively simple, two-dimensional geometries. The purpose of this discussion will be to display by example some of the interesting but difficult questions that arise when ill-behaved solutions are obtained numerically. We will consider two examples. As the first example, we will consider a nonlinear elastic (compressible) fluid with chemical reactions and discuss solutions for detonation and detonation failure in a two-dimensional cylinder. In this case, the numerical algorithm utilizes a finite-difference method with artificial viscosity (von Neumann-Richtmyer method) and leads to two, distinctly different, stable solutions depending on the time step criterion used. The second example to be considered involves the convection of a viscous fluid in a rectangular container as a result of an exothermic polymerization reaction. A solidification front develops near the top of the container and propagates down through the fluid, changing the aspect ratio of the region ahead of the front. Using a Galerkin-based finite element method, a numerical solution of the partial differential equations is obtained which tracks the front and correctly predicts the fluid temperatures near the walls. However, the solution also exhibits oscillatory behavior with regard to the number of cells in the fluid ahead of the front and in the strength of the cells. More definitive experiments and analysis are required to determine whether this oscillatory phenomena is a numerical artifact or a physical reality. 20 refs., 14 figs

  14. Experimental investigation of the brittle-viscous transition in mafic rocks - Interplay between fracturing, reaction, and viscous deformation

    Science.gov (United States)

    Marti, Sina; Stünitz, Holger; Heilbronner, Renée; Plümper, Oliver; Drury, Martyn

    2017-12-01

    Rock deformation experiments are performed on fault gouge fabricated from 'Maryland Diabase' rock powder to investigate the transition from dominant brittle to dominant viscous behaviour. At the imposed strain rates of γ˙ = 3 ·10-5 - 3 ·10-6 s-1, the transition is observed in the temperature range of (600 °C < T < 800 °C) at confining pressures of (0.5 GPa ≤ Pc ≤ 1.5 GPa). The transition thereby takes place by a switch from brittle fracturing and cataclastic flow to viscous dissolution-precipitation creep and grain boundary sliding. Mineral reactions and resulting grain size refinement by nucleation are observed to be critical processes for the switch to viscous deformation, i.e., grain size sensitive creep. In the transitional regime, the mechanical response of the sample is a mixed-mode between brittle and viscous rheology and microstructures associated with both brittle and viscous deformation are observed. As grain size reduction by reaction and nucleation is a time dependent process, the brittle-viscous transition is not only a function of T but to a large extent also of microstructural evolution.

  15. Features of free and forced vibrations in systems with dry and viscous friction

    International Nuclear Information System (INIS)

    Kislyi, A.A.; Borovik, O.V.

    1995-01-01

    Curve-fitting methods are usually used to obtain the exact solution to vibration problems in which allowance is made for dry (Coulomb) friction, but these methods permit determination of the laws of motion only in individual cases. The fact that the initial differential equations contain a piecewise-linear function characterizing dry friction makes it difficult to establish-and, thus to analyze-the general law governing vibratory motion for this case. As a result, dry friction is replaced by an equivalent viscous friction, and the corresponding areas of the hysteresis loops are equated. However, such a substitution cannot be justified in many cases, since dry and viscous friction differ in physical nature and differently affect the main characteristics of both free and forced vibrations. Moreover, the area of the hysteresis loop is proportional to the square of the amplitude in viscous friction but is proportional to the first power of the latter in dry friction. If the method of signum-function delay is used, then it becomes possible to determine the continuous laws of motion of such systems and establish the features of dry friction compared to viscous friction

  16. Numerical solution of a model for a superconductor field problem

    International Nuclear Information System (INIS)

    Alsop, L.E.; Goodman, A.S.; Gustavson, F.G.; Miranker, W.L.

    1979-01-01

    A model of a magnetic field problem occurring in connection with Josephson junction devices is derived, and numerical solutions are obtained. The model is of mathematical interest, because the magnetic vector potential satisfies inhomogeneous Helmholtz equations in part of the region, i.e., the superconductors, and the Laplace equation elsewhere. Moreover, the inhomogeneities are the guage constants for the potential, which are different for each superconductor, and their magnitudes are proportional to the currents flowing in the superconductors. These constants are directly related to the self and mutual inductances of the superconducting elements in the device. The numerical solution is obtained by the iterative use of a fast Poisson solver. Chebyshev acceleration is used to reduce the number of iterations required to obtain a solution. A typical problem involves solving 100,000 simultaneous equations, which the algorithm used with this model does in 20 iterations, requiring three minutes of CPU time on an IBM VM/370/168. Excellent agreement is obtained between calculated and observed values for the inductances

  17. Numerical Transducer Modeling

    DEFF Research Database (Denmark)

    Henriquez, Vicente Cutanda

    This thesis describes the development of a numerical model of the propagation of sound waves in fluids with viscous and thermal losses, with application to the simulation of acoustic transducers, in particular condenser microphones for measurement. The theoretical basis is presented, numerical...... manipulations are developed to satisfy the more complicated boundary conditions, and a model of a condenser microphone with a coupled membrane is developed. The model is tested against measurements of ¼ inch condenser microphones and analytical calculations. A detailed discussion of the results is given....

  18. On the numerical solution of fault trees

    International Nuclear Information System (INIS)

    Demichela, M.; Piccinini, N.; Ciarambino, I.; Contini, S.

    2003-01-01

    In this paper an account will be given of the numerical solution of the logic trees directly extracted from the Recursive Operability Analysis. Particular attention will be devoted to the use of the NOT and INH logic gates for correct logical representation of Fault Trees prior to their quantitative resolution. The NOT gate is needed for correct logical representation of events when both non-intervention and correct intervention of a protective system may lead to a Top Event. The INH gate must be used to correctly represent the time link between two events that are both necessary, but must occur in sequence. Some numerical examples will be employed to show both the correct identification of the events entering the INH gates and how use of the AND gate instead of the INH gate leads to overestimation of the probability of occurrence of a Top Event

  19. Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

    Science.gov (United States)

    Gómez-Aguilar, J. F.

    2018-03-01

    In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

  20. Numerical solutions of ordinary and partial differential equations in the frequency domain

    International Nuclear Information System (INIS)

    Hazi, G.; Por, G.

    1997-01-01

    Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)

  1. The Numerical Solution of an Abelian Ordinary Differential Equation ...

    African Journals Online (AJOL)

    In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...

  2. Viscous-Fluid-Spring Damper Retrofit of a Steel Moment Frame Structure

    International Nuclear Information System (INIS)

    Hussain, Saif; Van Benschoten, Paul; Al Satari, Mohamed; Lin, Silian

    2008-01-01

    The subject building is a peculiar pre-Northridge steel moment resisting frame building. Upon investigating the existing lateral resisting system, numerous significant deficiencies were identified; inherent lack of redundancy, poor geometry and inadequate stiffness of the lateral resisting system. All of which resulted in an extremely soft 5-story structure with a primary torsional mode of vibration at T 1 = 5.46 s. Significant structural modifications were deemed necessary to meet the ''life-safety'' performance objective as outlined in rehabilitation standards such as ASCE 41. Both increased stiffness and damping were required to adequately retrofit the building. Furthermore, adjacent building separation as well as deformation compatibility issues needed to be addressed and resolved. A three-dimensional computer model of the building was created using ETABS mathematically simulating the building's dynamic characteristics in its current condition. Multiple seismic retrofit systems were investigated such as Buckling Restrained Braced Frames (BRBF's). However, based on the performance effectiveness and constructability of the retrofit schemes studied, the Viscous-Fluid-Spring Damper (VFSD) system was proposed as the ''optimum'' solution for the building. The VFSD, was chosen because it combines the relatively compact size and minimally invasive constructability with the required properties (an elastomeric spring in parallel with a nonlinear velocity dependent viscous damper). A site-specific response spectrum was developed for the Design Basis Earthquake (DBE, 475 year return period) event, and three pairs of representative earthquake horizontal ground motion time-histories were scaled to match this DBE. The proposed scheme reduced the building maximum inter-story drift ratio from 5.4% to about 1%. Similarly, the maximum roof displacement was reduced by about 70% (23'' to 7'')

  3. Analysis on the Viscous Pumping in a Magnetic Fluid Seal Under a Rotating Load and the Seal Design

    OpenAIRE

    長屋, 幸助; 大沼, 浩身; 佐藤, 淳

    1990-01-01

    This paper discusses effects of viscous pumping in a magnetic fluid seal under a rotating load. The Reynolds equation was presented for the seal based on magnetic fluid mechanics, and the expressions for obtaining pressures in the seal, eccentricities of the rotating shaft due to the viscous pumping and seal pressures were given. Numerical Calculations were carried out for some sample problems, and the effect of magnetic flux densities on the pressure in the seal and the seal pressures were c...

  4. Long-wave analysis and control of the viscous Rayleigh-Taylor instability with electric fields

    Science.gov (United States)

    Cimpeanu, Radu; Anderson, Thomas; Petropoulos, Peter; Papageorgiou, Demetrios

    2016-11-01

    We investigate the electrostatic stabilization of a viscous thin film wetting the underside of a solid surface in the presence of a horizontally acting electric field. The competition between gravity, surface tension and the nonlocal effect of the applied electric field is captured analytically in the form of a nonlinear evolution equation. A semi-spectral solution strategy is employed to resolve the dynamics of the resulting partial differential equation. Furthermore, we conduct direct numerical simulations (DNS) of the Navier-Stokes equations and assess the accuracy of the obtained solutions when varying the electric field strength from zero up to the point when complete stabilization at the target finite wavelengths occurs. We employ DNS to examine the limitations of the asymptotically derived behavior in the context of increasing liquid film heights, with agreement found to be excellent even beyond the target lengthscales. Regimes in which the thin film assumption is no longer valid and droplet pinch-off occurs are then analyzed. Finally, the asymptotic and computational approaches are used in conjunction to identify efficient active control mechanisms allowing the manipulation of the fluid interface in light of engineering applications at small scales, such as mixing.

  5. Scrutinization of thermal radiation, viscous dissipation and Joule heating effects on Marangoni convective two-phase flow of Casson fluid with fluid-particle suspension

    Science.gov (United States)

    Mahanthesh, B.; Gireesha, B. J.

    2018-03-01

    The impact of Marangoni convection on dusty Casson fluid boundary layer flow with Joule heating and viscous dissipation aspects is addressed. The surface tension is assumed to vary linearly with temperature. Physical aspects of magnetohydrodynamics and thermal radiation are also accounted. The governing problem is modelled under boundary layer approximations for fluid phase and dust particle phase and then Runge-Kutta-Fehlberg method based numeric solutions are established. The momentum and heat transport mechanisms are focused on the result of distinct governing parameters. The Nusselt number is also calculated. It is established that the rate of heat transfer can be enhanced by suspending dust particles in the base fluid. The temperature field of fluid phase and temperature of dust phase are quite reverse for thermal dust parameter. The radiative heat, viscous dissipation and Joule heating aspects are constructive for thermal fields of fluid and dust phases. The velocity of dusty Casson fluid dominates the velocity of dusty fluid while this trend is opposite in the case of temperature. Moreover qualitative behaviour of fluid phase and dust phase temperature/velocity are similar.

  6. Sensitivity of the solution of the Elder problem to density, velocity and numerical perturbations

    Science.gov (United States)

    Park, Chan-Hee; Aral, Mustafa M.

    2007-06-01

    In this paper the Elder problem is studied with the purpose of evaluating the inherent instabilities associated with the numerical solution of this problem. Our focus is first on the question of the existence of a unique numerical solution for this problem, and second on the grid density and fluid density requirements necessary for a unique numerical solution. In particular we have investigated the instability issues associated with the numerical solution of the Elder problem from the following perspectives: (i) physical instability issues associated with density differences; (ii) sensitivity of the numerical solution to idealization irregularities; and, (iii) the importance of a precise velocity field calculation and the association of this process with the grid density levels that is necessary to solve the Elder problem accurately. In the study discussed here we have used a finite element Galerkin model we have developed for solving density-dependent flow and transport problems, which will be identified as TechFlow. In our study, the numerical results of Frolkovič and de Schepper [Frolkovič, P. and H. de Schepper, 2001. Numerical modeling of convection dominated transport coupled with density-driven flow in porous media, Adv. Water Resour., 24, 63-72.] were replicated using the grid density employed in their work. We were also successful in duplicating the same result with a less dense grid but with more computational effort based on a global velocity estimation process we have adopted. Our results indicate that the global velocity estimation approach recommended by Yeh [Yeh, G.-T., 1981. On the computation of Darcian velocity and mass balance in finite element modelling of groundwater flow, Water Resour. Res., 17(5), 1529-1534.] allows the use of less dense grids while obtaining the same accuracy that can be achieved with denser grids. We have also observed that the regularity of the elements in the discretization of the solution domain does make a difference

  7. Fast numerical solution of KKR-CPA equations: Testing new algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Bruno, E.; Florio, G.M.; Ginatempo, B.; Giuliano, E.S. (Universita di Messina (Italy))

    1994-04-01

    Some numerical methods for the solution of KKR-CPA equations are discussed and tested. New, efficient, computational algorithms are proposed, allowing a remarkable reduction of computing time and a good reliability in evaluating spectral quantities. 16 refs., 7 figs.

  8. Viscous dissipation and radiation effects on MHD natural convection in a square enclosure filled with a porous medium

    Energy Technology Data Exchange (ETDEWEB)

    Ahmed, Sameh E., E-mail: sameh_sci_math@yahoo.com [Department of Mathematics, Faculty of Sciences, South Valley University, Qena (Egypt); Hussein, Ahmed Kadhim, E-mail: ahmedkadhim7474@gmail.com [College of Engineering, Mechanical Engineering Department, Babylon University, Babylon City—Hilla (Iraq); Mohammed, H.A. [Department of Thermofluids, Faculty of Mechanical Engineering, University Teknologi Malaysia (UTM), 81310 UTM Skudai, Johor Bahru (Malaysia); Adegun, I.K. [Department of Mechanical Engineering, University of Ilorin, Ilorin (Nigeria); Zhang, Xiaohui [School of Physics Science and Technology, School of Energy—Soochow University, Suzhou 215006, Jiangsu (China); Kolsi, Lioua [Unite de Metrologie en Mecanique des Fluides et Thermique, Ecole Nationale d’Ingenieurs, Monastir (Tunisia); Hasanpour, Arman [Department of Mechanical Engineering, Babol University of Technology, PO Box 484, Babol (Iran, Islamic Republic of); Sivasankaran, S. [Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603 (Malaysia)

    2014-01-15

    Highlights: • Ha decelerates the flow field. • Ha enhances conduction. • Magnetic field orientation is important. • Radiation parameter important. • Nu decreases as Ha increases. -- Abstract: Numerical two-dimensional analysis using finite difference approach with “line method” is performed on the laminar magneto-hydrodynamic natural convection in a square enclosure filled with a porous medium to investigate the effects of viscous dissipation and radiation. The enclosure heated from left vertical sidewall and cooled from an opposing right vertical sidewall. The top and bottom walls of the enclosure are considered adiabatic. The flow in the square enclosure is subjected to a uniform magnetic field at various orientation angles (φ = 0°, 30°, 45°, 60° and 90°). Numerical computations occur at wide ranges of Rayleigh number, viscous dissipation parameter, magnetic field orientation angles, Hartmann number and radiation parameter. Numerical results are presented with the aid of tables and graphical illustrations. The results of the present work explain that the local and average Nusselt numbers at the hot and cold sidewalls increase with increasing the radiation parameter. From the other side, the role of viscous dissipation parameter is to reduce the local and average Nusselt numbers at the hot left wall, while it improves them at the cold right wall. The results are compared with another published results and it found to be in a good agreement.

  9. Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

    International Nuclear Information System (INIS)

    Bhattacharyya Krishnendu; Hayat Tasawar; Alsaedi Ahmed

    2014-01-01

    An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations (PDEs) are converted into a nonlinear self-similar ordinary differential equation (ODE). For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  10. A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

    International Nuclear Information System (INIS)

    Trogdon, Thomas; Deconinck, Bernard

    2014-01-01

    In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg–de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t. (paper)

  11. Dynamics of the east India coastal current. 2. Numerical solutions

    Digital Repository Service at National Institute of Oceanography (India)

    McCreary, J.P.; Han, W.; Shankar, D.; Shetye, S.R.

    A linear, continuously stratified model is used to investigate the dynamics of the East India Coastal Current (EICC). Solutions are found numerically in a basin that resembles the Indian Ocean basin north of 29 degrees S, and they are forced...

  12. Effects of viscous dissipation and slip velocity on two-dimensional and axisymmetric squeezing flow of Cu-water and Cu-kerosene nanofluids

    Directory of Open Access Journals (Sweden)

    Umar Khan

    2015-03-01

    Full Text Available Squeezing flow of nanofluids has been taken into account under the effects of viscous dissipation and velocity slip. Two types of base fluids are used to study the behavior of Copper nanoparticles between parallel plates. Nonlinear ordinary differential equations governing the flow are obtained by imposing similarity transformations on conservation laws. Resulting equations are solved by using an efficient analytical technique the variation of parameters method (VPM. Influences of nanoparticle concentration and different emerging parameters on flow profiles are presented graphically coupled with comprehensive discussions. A numerical solution is also sought for the sake of comparison. Effect of different parameters on skin friction coefficient and Nusselt number is also discussed.

  13. CSR Fields: Direct Numerical Solution of the Maxwell's Equation

    International Nuclear Information System (INIS)

    Novokhatski, Alexander

    2011-01-01

    We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in (1). Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in (2). We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields (3).

  14. Impact of ultra-viscous drops: air-film gliding and extreme wetting

    KAUST Repository

    Langley, Kenneth

    2017-01-23

    A drop impacting on a solid surface must push away the intervening gas layer before making contact. This entails a large lubricating air pressure which can deform the bottom of the drop, thus entrapping a bubble under its centre. For a millimetric water drop, the viscous-dominated flow in the thin air layer counteracts the inertia of the drop liquid. For highly viscous drops the viscous stresses within the liquid also affect the interplay between the drop and the gas. Here the drop also forms a central dimple, but its outer edge is surrounded by an extended thin air film, without contacting the solid. This is in sharp contrast with impacts of lower-viscosity drops where a kink in the drop surface forms at the edge of the central disc and makes a circular contact with the solid. Larger drop viscosities make the central air dimple thinner. The thin outer air film subsequently ruptures at numerous random locations around the periphery, when it reaches below 150 nm thickness. This thickness we measure using high-speed two-colour interferometry. The wetted circular contacts expand rapidly, at orders of magnitude larger velocities than would be predicted by a capillary-viscous balance. The spreading velocity of the wetting spots is independent of the liquid viscosity. This may suggest enhanced slip of the contact line, assisted by rarefied-gas effects, or van der Waals forces in what we call extreme wetting. Myriads of micro-bubbles are captured between the local wetting spots.

  15. The Chimera Method of Simulation for Unsteady Three-Dimensional Viscous Flow

    Science.gov (United States)

    Meakin, Robert L.

    1996-01-01

    The Chimera overset grid method is reviewed and discussed in the context of a method of solution and analysis of unsteady three-dimensional viscous flows. The state of maturity of the various pieces of support software required to use the approach is discussed. A variety of recent applications of the method is presented. Current limitations of the approach are defined.

  16. Numerical solution of High-kappa model of superconductivity

    Energy Technology Data Exchange (ETDEWEB)

    Karamikhova, R. [Univ. of Texas, Arlington, TX (United States)

    1996-12-31

    We present formulation and finite element approximations of High-kappa model of superconductivity which is valid in the high {kappa}, high magnetic field setting and accounts for applied magnetic field and current. Major part of this work deals with steady-state and dynamic computational experiments which illustrate our theoretical results numerically. In our experiments we use Galerkin discretization in space along with Backward-Euler and Crank-Nicolson schemes in time. We show that for moderate values of {kappa}, steady states of the model system, computed using the High-kappa model, are virtually identical with results computed using the full Ginzburg-Landau (G-L) equations. We illustrate numerically optimal rates of convergence in space and time for the L{sup 2} and H{sup 1} norms of the error in the High-kappa solution. Finally, our numerical approximations demonstrate some well-known experimentally observed properties of high-temperature superconductors, such as appearance of vortices, effects of increasing the applied magnetic field and the sample size, and the effect of applied constant current.

  17. Comparing numerical methods for the solutions of the Chen system

    International Nuclear Information System (INIS)

    Noorani, M.S.M.; Hashim, I.; Ahmad, R.; Bakar, S.A.; Ismail, E.S.; Zakaria, A.M.

    2007-01-01

    In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given

  18. Effect of constant heat flux at outer cylinder on stability of viscous ...

    African Journals Online (AJOL)

    In this paper, the stability of the Couette flow of a viscous incompressible fluid between two concentric rotating cylinders is studied in the presence of a radial temperature gradient, when the outer cylinder is maintained at a constant heat flux. The analytical solution of the eigen-value problem is obtained by using the ...

  19. Vectorization on the star computer of several numerical methods for a fluid flow problem

    Science.gov (United States)

    Lambiotte, J. J., Jr.; Howser, L. M.

    1974-01-01

    A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

  20. Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

    Directory of Open Access Journals (Sweden)

    Bolandtalat A.

    2016-01-01

    Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

  1. NUMERICAL AND ANALYTICAL SOLUTIONS OF NEUTRINO-DOMINATED ACCRETION FLOWS WITH A NON-ZERO TORQUE BOUNDARY CONDITION AND ITS APPLICATIONS IN GAMMA-RAY BURSTS

    Energy Technology Data Exchange (ETDEWEB)

    Xie, Wei; Lei, Wei-Hua; Wang, Ding-Xiong, E-mail: leiwh@hust.edu.cn [School of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China)

    2016-12-20

    A stellar-mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of a “no torque” boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses and reexamine their properties. We find that an NDAF with such a boundary torque can be powerful enough to account for those bright short GRBs, energetic long GRBs, and ultra-long GRBs. The disk becomes viscously unstable, which makes it possible to interpret the variability of GRB prompt emission and the steep decay phase in the early X-ray afterglow. Finally, we study the gravitational waves radiated from a processing BH-NDAF. We find that the effects of the boundary torque on the strength of the gravitational waves can be ignored.

  2. A numerical solution of the coupled proton-H atom transport equations for the proton aurora

    International Nuclear Information System (INIS)

    Basu, B.; Jasperse, J.R.; Grossbard, N.J.

    1990-01-01

    A numerical code has been developed to solve the coupled proton-H atom linear transport equations for the proton aurora. The transport equations have been simplified by using plane-parallel geometry and the forward-scattering approximations only. Otherwise, the equations and their numerical solutions are exact. Results are presented for the particle fluxes and the energy deposition rates, and they are compared with the previous analytical results that were obtained by using additional simplifying approximations. It is found that although the analytical solutions for the particle fluxes differ somewhat from the numerical solutions, the energy deposition rates calculated by the two methods agree to within a few percent. The accurate particle fluxes given by the numerical code are useful for accurate calculation of the characteristic quantities of the proton aurora, such as the ionization rates and the emission rates

  3. Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

    Science.gov (United States)

    Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

    2017-12-01

    Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

  4. Air-driven viscous film flow coating the interior of a vertical tube

    Science.gov (United States)

    Ogrosky, H. Reed; Camassa, Roberto; Olander, Jeffrey

    2017-11-01

    We discuss a model for the flow of a viscous liquid film coating the interior of a vertical tube when the film is driven upwards against gravity by airflow through the center of the tube. The model consists of two components: (i) a nonlinear model, exploiting the slowly-varying liquid-air interface, for the interfacial stresses created by the airflow, and (ii) a long-wave asymptotic model for the air-liquid interface. The stability of small interfacial disturbances is studied analytically, and it is shown that the modeled free surface stresses contribute to both an increased upwards disturbance velocity and a more rapid instability growth than those of a previously developed model. Numerical solutions to the long-wave model exhibit saturated waves whose profiles and velocities show improvement, with respect to the previous model, in matching experiments. The model results are then compared with additional experiments for a slightly modified version of the problem. We gratefully acknowledge funding from NSF DMS-0509423, DMS-0908423, DMS-1009750, DMS-1517879, RTG DMS-0943851, CMG ARC-1025523 and NIEHS 534197-3411.

  5. Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption

    Directory of Open Access Journals (Sweden)

    Khilap Singh

    2016-01-01

    Full Text Available A numerical model is developed to examine the effects of thermal radiation on unsteady mixed convection flow of a viscous dissipating incompressible micropolar fluid adjacent to a heated vertical stretching surface in the presence of the buoyancy force and heat generation/absorption. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. The dimensionless governing equations for this investigation are solved by Runge-Kutta-Fehlberg fourth fifth-order method with shooting technique. Numerical solutions are then obtained and investigated in detail for different interesting parameters such as the local skin-friction coefficient, wall couple stress, and Nusselt number as well as other parametric values such as the velocity, angular velocity, and temperature.

  6. Analysis of numerical solutions for Bateman equations; Analise de solucoes numericas para as equacoes de Bateman

    Energy Technology Data Exchange (ETDEWEB)

    Loch, Guilherme G.; Bevilacqua, Joyce S., E-mail: guiloch@ime.usp.br, E-mail: joyce@ime.usp.br [Universidade de Sao Paulo (IME/USP), Sao Paulo, SP (Brazil). Departamento de Matematica Aplicada. Instituto de Matematica e Estatistica; Hiromoto, Goro; Rodrigues Junior, Orlando, E-mail: rodrijr@ipen.br, E-mail: hiromoto@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN-CNEN/SP), Sao Paulo, SP (Brazil)

    2013-07-01

    The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)

  7. Numerical solution of the full potential equation using a chimera grid approach

    Science.gov (United States)

    Holst, Terry L.

    1995-01-01

    A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

  8. Numerical solution of the ekpyrotic scenario in the moduli space approximation

    International Nuclear Information System (INIS)

    Soerensen, Torquil MacDonald

    2005-01-01

    A numerical solution to the equations of motion for the ekpyrotic bulk brane scenario in the moduli space approximation is presented. The visible universe brane has positive tension, and we use a potential that goes to zero exponentially at large distance, and also goes to zero at small distance. In the case considered, no bulk brane, visible brane collision occurs in the solution. This property and the general behavior of the solution is qualitatively the same when the visible brane tension is negative, and for many different parameter choices

  9. A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

    International Nuclear Information System (INIS)

    Adam, G.

    1979-01-01

    A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

  10. special algorithm for the numerical solution of system of initial value ...

    African Journals Online (AJOL)

    Nwokem et al.

    Science World Journal Vol 12(No 4) 2017 ... Over the years, several researchers have considered the collocation method as a way of generating numerical solutions to ... study problems in mathematics, engineering, computer science and.

  11. MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink

    Directory of Open Access Journals (Sweden)

    Hunegnaw Dessie

    2014-09-01

    Full Text Available In this analysis, MHD boundary layer flow and heat transfer of a fluid with variable viscosity through a porous medium towards a stretching sheet by taking in to the effects of viscous dissipation in presence of heat source/sink is considered. The symmetry groups admitted by the corresponding boundary value problem are obtained by using Lie’s scaling group of transformations. These transformations are used to convert the partial differential equations of the governing equations into self-similar non-linear ordinary differential equations. Numerical solutions of these equations are obtained by Runge-Kutta fourth order with shooting method. Numerical results obtained for different parameters such as viscosity variation parameter A, permeability parameter k1, heat source/sink parameter λ, magnetic field parameter M, Prandtl number Pr, and Eckert number Ec are drawn graphically and effects of different flow parameters on velocity and temperature profiles are discussed. The skin-friction coefficient -f″(0 and heat transfer coefficient −θ′(0 are presented in tables.

  12. Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes

    Science.gov (United States)

    Capuano, M.; Bogey, C.; Spelt, P. D. M.

    2018-05-01

    A computational method for the simulation of viscous and compressible gas-gas flows is presented. It consists in solving the Navier-Stokes equations associated with a convection equation governing the motion of the interface between two gases using high-order finite-difference schemes. A discontinuity-capturing methodology based on sensors and a spatial filter enables capturing shock waves and deformable interfaces. One-dimensional test cases are performed as validation and to justify choices in the numerical method. The results compare well with analytical solutions. Shock waves and interfaces are accurately propagated, and remain sharp. Subsequently, two-dimensional flows are considered including viscosity and thermal conductivity. In Richtmyer-Meshkov instability, generated on an air-SF6 interface, the influence of the mesh refinement on the instability shape is studied, and the temporal variations of the instability amplitude is compared with experimental data. Finally, for a plane shock wave propagating in air and impacting a cylindrical bubble filled with helium or R22, numerical Schlieren pictures obtained using different grid refinements are found to compare well with experimental shadow-photographs. The mass conservation is verified from the temporal variations of the mass of the bubble. The mean velocities of pressure waves and bubble interface are similar to those obtained experimentally.

  13. Damping characteristics and flow behaviors of an ER fluid with a piston sine vibration in a viscous damper

    International Nuclear Information System (INIS)

    Yamaguchi, Hiroshi; Zhang, Xin-Rong; Niu, Xiao-Dong

    2010-01-01

    The damping characteristics and flow behaviors of ER fluids inside a piston–cylinder viscous damper subjected to external electric fields are studied based on experiment, theoretical analysis and numerical simulation. The viscous damper is a closed system with an inner piston and an outer cylinder, which is designed and constructed in our laboratory. In the experiment, the test ER fluid is enclosed in the gap of a piston–cylinder system. To examine the damping characteristics of the test ER fluid, a piston sine vibration experiment is performed with accompanying theoretical analyses. In addition, in order to investigate the ER flow behaviors inside the damper, a numerical simulation is carried out. The present study discloses the damping characteristics and the fluid mechanism of the ER fluid in the piston–cylinder damper with an applied external electric field

  14. Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

    Directory of Open Access Journals (Sweden)

    Aydin Secer

    2013-01-01

    Full Text Available An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

  15. An implicit multigrid algorithm for computing hypersonic, chemically reacting viscous flows

    International Nuclear Information System (INIS)

    Edwards, J.R.

    1996-01-01

    An implicit algorithm for computing viscous flows in chemical nonequilibrium is presented. Emphasis is placed on the numerical efficiency of the time integration scheme, both in terms of periteration workload and overall convergence rate. In this context, several techniques are introduced, including a stable, O(m 2 ) approximate factorization of the chemical source Jacobian and implementations of V-cycle and filtered multigrid acceleration methods. A five species-seventeen reaction air model is used to calculate hypersonic viscous flow over a cylinder at conditions corresponding to flight at 5 km/s, 60 km altitude and at 11.36 km/s, 76.42 km altitude. Inviscid calculations using an eleven-species reaction mechanism including ionization are presented for a case involving 11.37 km/s flow at an altitude of 84.6 km. Comparisons among various options for the implicit treatment of the chemical source terms and among different multilevel approaches for convergence acceleration are presented for all simulations

  16. Numerical solution of modified differential equations based on symmetry preservation.

    Science.gov (United States)

    Ozbenli, Ersin; Vedula, Prakash

    2017-12-01

    In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

  17. Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

    Science.gov (United States)

    Polyanin, A. D.; Sorokin, V. G.

    2017-12-01

    The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

  18. Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions

    Directory of Open Access Journals (Sweden)

    Marina Popolizio

    2018-01-01

    Full Text Available Multiterm fractional differential equations (MTFDEs nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag–Leffler (ML functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.

  19. Ten themes of viscous liquid dynamics

    DEFF Research Database (Denmark)

    Dyre, J. C.

    2007-01-01

    Ten ‘themes' of viscous liquid physics are discussed with a focus on how they point to a general description of equilibrium viscous liquid dynamics (i.e., fluctuations) at a given temperature. This description is based on standard time-dependent Ginzburg-Landau equations for the density fields...

  20. Theory of a new elastic-plastic-viscous model and its application to the nuclear fuel mechanical analysis

    International Nuclear Information System (INIS)

    Moreno, A.

    1977-01-01

    A new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (author)

  1. Numerical solution of compressible flow equations inside an ejector

    International Nuclear Information System (INIS)

    Omid khah, M. R.; Navid Famili, M. H.; Jalili Keshtiban, E.

    2002-01-01

    Ejector is important equipment in the chemical industry. It is mainly used for vaccuming and mixing of flows. In the present work a computer modeling of the flow inside an ejector is used to give a better understanding of the principle of the operation of an ejector. Since the fluid inside an ejector passes through subsonic, sonic and supersonic regimens, the pressure field is used as the controlling variable and the density is found through the constitutive equations. The control volume method with a co-location grid, attached to the boundary is used to discretize the domain. The overall solution is obtained by the SIMPLEC method and to dissociate the pressure and the velocity grid Rhie-Chow interpolation method is employed. A central difference approximation method is used to approximate the density on the elements borders and the upwind approximation is used to correct the density correction factors. Both upwind, quick and minimum gradient methods were used to approximate the momentum variables on the control volumes. The resultant matrices are solved with the tri-diagonal method. The accuracy of the model is checked by simulating a flow regiment in a converging-diverging nozzle, and comparing the results with the available experimental data. The results show that for an inviscid the first order approximation produce as an accurate results as the higher order approximations while it has a better stability. However, for the viscous fluid the second order approximation produces a better understanding of the physics of the problem. The solution also showes that the flow field inside an ejector is a complex one and the shock wave has a great influence on the pressure field especially close to the walls. The upper convective quick method did not converge well in the shock calculations while the slowest descent method had a very stable behavior in the analysis of the shock behavior

  2. Numerical solutions of stochastic Lotka-Volterra equations via operational matrices

    Directory of Open Access Journals (Sweden)

    F. Hosseini Shekarabi

    2016-03-01

    Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.

  3. Numerical solution for heave of expansive soils

    International Nuclear Information System (INIS)

    Sadrnezhad, S. A.

    1999-01-01

    A numerical solution for heave prediction is developed within the context theories for both saturated and unsaturated soil behaviors. Basically, lowering the potential level of compressing on a saturated layer will cause heaving due to water absorption. This water absorption is in an opposite way, similar to water dissipation as what happens during unloading in consolidation process. However, in unsaturated layers any change of the stability of potential energy level will cause the tendency of change in particle interconnection forces. So, any change by either distressing or the variation of moisture ratio will lead to soil heave. In this paper a finite element solution is employed for predicting the heave in saturated soil similar to unloading in consolidation. Also, in the case of unsaturated soil, equivalent soil suction as negative pore water pressures in applied to soil elements as equivalent nodal forces. To show the potential of this method, test results were com pated with those obtained from computations. These comparisons show that the presented method is capable of predicting the heave phenomenon quite well

  4. The numerical solution of ICRF fields in axisymmetric mirrors

    International Nuclear Information System (INIS)

    Phillips, M.W.; Todd, A.M.M.

    1986-01-01

    The numerics of a numerical code called GARFIELD (Grumman Aerospace RF fIELD code) designed to calculate the three-dimensional structure of ICRF fields in axisymmetric mirrors is presented. The code solves the electromagnetic wave equation for the electric field using a cold plasma dispersion relation with a small collision term to simulate absorption. The full wave solution including E.B is computed. The fields are Fourier analyzed in the poloidal direction and solved on a grid in the axial and radial directions. A two-dimensional equilibrium can be used as the source of equilibrium data. This allows us to extend previous studies of ICRF wave propagation and absorption in mirrors to include the effect of axial variation of the magnetic field and density. (orig.)

  5. Viscous fingering and channeling in chemical enhanced oil recovery

    Science.gov (United States)

    Daripa, Prabir; Dutta, Sourav

    2017-11-01

    We have developed a hybrid numerical method based on discontinuous finite element method and modified method of characteristics to compute the multiphase multicomponent fluid flow in porous media in the context of chemical enhanced oil recovery. We use this method to study the effect of various chemical components on the viscous fingering and channeling in rectilinear and radial flow configurations. We will also discuss about the efficiency of various flooding schemes based on these understandings. Time permitting, we will discuss about the effect of variable injection rates in these practical setting. U.S. National Science Foundation Grant DMS-1522782.

  6. Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

    Science.gov (United States)

    Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

    2014-01-01

    Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

  7. Numerical solution of modified fokker-planck equation with poissonian input

    Czech Academy of Sciences Publication Activity Database

    Náprstek, Jiří; Král, Radomil

    2010-01-01

    Roč. 17, 3/4 (2010), s. 251-268 ISSN 1802-1484 R&D Projects: GA AV ČR(CZ) IAA200710805; GA ČR(CZ) GA103/09/0094 Institutional research plan: CEZ:AV0Z20710524 Keywords : Fokker-Planck equation * poisson ian exciation * numerical solution * transition effects Subject RIV: JN - Civil Engineering

  8. Numerical tools for musical instruments acoustics: analysing nonlinear physical models using continuation of periodic solutions

    OpenAIRE

    Karkar , Sami; Vergez , Christophe; Cochelin , Bruno

    2012-01-01

    International audience; We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self- sustained oscillation. Numerical continuation consists in following how a given solution of a set of equations is modified when one (or several) parameter of these equations are allowed to vary. Several physical models (clarinet, saxophone, and violin) are formulated as nonlinear dynamical systems, whose periodic solution...

  9. Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

    Directory of Open Access Journals (Sweden)

    Elmira Ashpazzadeh

    2018-04-01

    Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

  10. Numerical benchmarking of SPEEDUP trademark against point kinetics solutions

    International Nuclear Information System (INIS)

    Gregory, M.V.

    1993-02-01

    SPEEDUP trademark is a state-of-the-art, dynamic, chemical process modeling package offered by Aspen Technology. In anticipation of new customers' needs for new analytical tools to support the site's waste management activities, SRTC has secured a multiple-user license to SPEEDUP trademark. In order to verify both the installation and mathematical correctness of the algorithms in SPEEDUP trademark, we have performed several numerical benchmarking calculations. These calculations are the first steps in establishing an on-site quality assurance pedigree for SPEEDUP trademark. The benchmark calculations consisted of SPEEDUP trademark Version 5.3L representations of five neutron kinetics benchmarks (each a mathematically stiff system of seven coupled ordinary differential equations), whose exact solutions are documented in the open literature. In all cases, SPEEDUP trademark solutions to be in excellent agreement with the reference solutions. A minor peculiarity in dealing with a non-existent discontinuity in the OPERATION section of the model made itself evident

  11. A note on numerical solution of a parabolic-Schrödinger equation

    Science.gov (United States)

    Ozdemir, Yildirim; Alp, Mustafa

    2016-08-01

    In the present study, a nonlocal boundary value problem for a parabolic-Schrödinger equation is considered. The stability estimates for the solution of the given problem is established. The first and second order of difference schemes are presented for approximately solving a specific nonlocal boundary problem. The theoretical statements for the solution of these difference schemes are supported by the result of numerical examples.

  12. A numerical solution for a class of time fractional diffusion equations with delay

    Directory of Open Access Journals (Sweden)

    Pimenov Vladimir G.

    2017-09-01

    Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

  13. Random ordinary differential equations and their numerical solution

    CERN Document Server

    Han, Xiaoying

    2017-01-01

    This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs).   RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems.  They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor ...

  14. Six-dimensional localized black holes: Numerical solutions

    International Nuclear Information System (INIS)

    Kudoh, Hideaki

    2004-01-01

    To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six-dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature T≅1/2πl, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes

  15. Direct numerical simulation of circular-cap bubbles in low viscous liquids using counter diffusion lattice Boltzmann method

    Energy Technology Data Exchange (ETDEWEB)

    Ryu, Seungyeob, E-mail: syryu@kaeri.re.kr [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Kim, Youngin; Yoon, Juhyeon [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Ko, Sungho, E-mail: sunghoko@cnu.ac.kr [Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-dong, Yuseong-gu, Daejeon 305-764 (Korea, Republic of)

    2014-01-15

    Highlights: • We directly simulate circular-cap bubbles in low viscous liquids. • The counter diffusion multiphase lattice Boltzmann method is proposed. • The present method is validated through benchmark tests and experimental results. • The high-Reynolds-number bubbles can be simulated without any turbulence models. • The present method is feasible for the direct simulation of bubbly flows. -- Abstract: The counter diffusion lattice Boltzmann method (LBM) is used to directly simulate rising circular-cap bubbles in low viscous liquids. A counter diffusion model for single phase flows has been extended to multiphase flows, and the implicit formulation is converted into an explicit one for easy calculation. Bubbles at high Reynolds numbers ranging from O(10{sup 2}) to O(10{sup 4}) are simulated successfully without any turbulence models, which cannot be done for the existing LBM versions. The characteristics of the circular-cap bubbles are studied for a wide range of Morton numbers and compared with the previous literature. Calculated results agree with the theoretical and experimental data. Consequently, the wake phenomena of circular-cap bubbles and bubble induced turbulence are presented.

  16. Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

    International Nuclear Information System (INIS)

    Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

    2015-01-01

    Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM

  17. The thinning of viscous liquid threads.

    Science.gov (United States)

    Castrejon-Pita, J. Rafael; Castrejon-Pita, Alfonso A.; Hutchings, Ian M.

    2012-11-01

    The thinning neck of dripping droplets is studied experimentally for viscous Newtonian fluids. High speed imaging is used to measure the minimum neck diameter in terms of the time τ to breakup. Mixtures of water and glycerol with viscosities ranging from 20 to 363 mPa s are used to model the Newtonian behavior. The results show the transition from potential to inertial-viscous regimes occurs at the predicted values of ~Oh2. Before this transition the neck contraction rate follows the inviscid scaling law ~τ 2 / 3 . After the transition, the neck thinning tends towards the linear viscous scaling law ~ τ . Project supported by the EPSRC-UK (EP/G029458/1) and Cambridge-KACST.

  18. Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method

    Directory of Open Access Journals (Sweden)

    De-Gang Wang

    2012-01-01

    Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

  19. Gravitational collision efficiency of nonspherical aerosols II: motion of an oblate spheroid in a viscous fluid

    Energy Technology Data Exchange (ETDEWEB)

    Tuttle, R.F.; Loyalka, S.K.

    1985-06-01

    The collisional dynamics of nonspherical aerosols is modeled by the introduction of a shape factor, US . Mechanistic calculation of US requires knowledge of the flow fields around the aerosols. Since actual aerosols can be complicated in shape and since the computation of flow fields can be quite difficult, insights into the nature of US are gained by using the superposition technique and studying aerosols that have tractable flow fields. The motion of an oblate spheroid in a viscous fluid is considered. The Navier-Stokes equations and associated boundary conditions are represented in oblate spheroidal coordinates. A combination of finite differences and spline-interpolation techniques is used to transform these equations to a form suitable for numerical computations. Converged results for the flow fields are obtained for a 0 to 5 range of Reynolds numbers. In the limit of zero Reynolds number, the results are found to be in agreement with the analytical solutions of Oberbeck.

  20. Computations of ideal and real gas high altitude plume flows

    Science.gov (United States)

    Feiereisen, William J.; Venkatapathy, Ethiraj

    1988-01-01

    In the present work, complete flow fields around generic space vehicles in supersonic and hypersonic flight regimes are studied numerically. Numerical simulation is performed with a flux-split, time asymptotic viscous flow solver that incorporates a generalized equilibrium chemistry model. Solutions to generic problems at various altitude and flight conditions show the complexity of the flow, the equilibrium chemical dissociation and its effect on the overall flow field. Viscous ideal gas solutions are compared against equilibrium gas solutions to illustrate the effect of equilibrium chemistry. Improved solution accuracy is achieved through adaptive grid refinement.

  1. Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

    Science.gov (United States)

    Jiang, Fei

    2018-04-01

    We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

  2. Droplet breakup driven by shear thinning solutions in a microfluidic T-junction

    Science.gov (United States)

    Chiarello, Enrico; Gupta, Anupam; Mistura, Giampaolo; Sbragaglia, Mauro; Pierno, Matteo

    2017-12-01

    Droplet-based microfluidics turned out to be an efficient and adjustable platform for digital analysis, encapsulation of cells, drug formulation, and polymerase chain reaction. Typically, for most biomedical applications, the handling of complex, non-Newtonian fluids is involved, e.g., synovial and salivary fluids, collagen, and gel scaffolds. In this study, we investigate the problem of droplet formation occurring in a microfluidic T-shaped junction, when the continuous phase is made of shear thinning liquids. At first, we review in detail the breakup process, providing extensive, side-by-side comparisons between Newtonian and non-Newtonian liquids over unexplored ranges of flow conditions and viscous responses. The non-Newtonian liquid carrying the droplets is made of Xanthan solutions, a stiff, rodlike polysaccharide displaying a marked shear thinning rheology. By defining an effective Capillary number, a simple yet effective methodology is used to account for the shear-dependent viscous response occurring at the breakup. The droplet size can be predicted over a wide range of flow conditions simply by knowing the rheology of the bulk continuous phase. Experimental results are complemented with numerical simulations of purely shear thinning fluids using lattice Boltzmann models. The good agreement between the experimental and numerical data confirm the validity of the proposed rescaling with the effective Capillary number.

  3. The Numerical Solution of the Equilibrium Problem for a Stretchable Elastic Beam

    Science.gov (United States)

    Mehdiyeva, G. Y.; Aliyev, A. Y.

    2017-08-01

    The boundary value problem under consideration describes the equilibrium of an elastic beam that is stretched or contracted by specified forces. The left end of the beam is free of load, and the right end is rigidly lapped. To solve the problem numerically, an appropriate difference problem is constructed. Solving the difference problem, we obtain an approximate solution of the problem. We estimate the approximate solution of the stated problem.

  4. Criteria for the reliability of numerical approximations to the solution of fluid flow problems

    International Nuclear Information System (INIS)

    Foias, C.

    1986-01-01

    The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number N of elements (Galerkin modes, finite-difference cells, finite-elements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the Navier-Stokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations. 56 refs

  5. Numerical modeling of foam flows

    International Nuclear Information System (INIS)

    Cheddadi, Ibrahim

    2010-01-01

    Liquid foam flows are involved in numerous applications, e.g. food and cosmetics industries, oil extraction, nuclear decontamination. Moreover, their study leads to fundamental knowledge: as it is easier to manipulate and analyse, foam is used as a model material to understand the flow of emulsions, polymers, pastes, or cell aggregates, all of which display both solid and liquid behaviour. Systematic experiments performed by Francois Graner et al. provide precise data that emphasize the non Newtonian properties of the foam. Meanwhile, Pierre Saramito proposed a visco-elasto-plastic continuous tensorial model, akin to predict the behaviour of the foam. The goal of this thesis is to understand this complex behaviour, using these two elements. We have built and validated a resolution algorithm based on a bidimensional finite elements methods. The numerical solutions are in excellent agreement with the spatial distribution of all measured quantities, and confirm the predictive capabilities of the model. The dominant parameters have been identified and we evidenced the fact that the viscous, elastic, and plastic contributions to the flow have to be treated simultaneously in a tensorial formalism. We provide a substantial contribution to the understanding of foams and open the path to realistic simulations of complex VEP flows for industrial applications. (author)

  6. Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model

    Directory of Open Access Journals (Sweden)

    Nikola V. Georgiev

    2003-01-01

    Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.

  7. A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation

    Directory of Open Access Journals (Sweden)

    Hakon A. Hoel

    2007-07-01

    Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.

  8. Numerical Simulations of Saturn's B Ring: Granular Friction as a Mediator between Self-gravity Wakes and Viscous Overstability

    Energy Technology Data Exchange (ETDEWEB)

    Ballouz, Ronald-Louis; Richardson, Derek C. [Department of Astronomy, University of Maryland, College Park, MD 20742-2421 (United States); Morishima, Ryuji [University of California, Los Angeles, Institute of Geophysics and Planetary Physics, Los Angeles, CA (United States)

    2017-04-01

    We study the B ring’s complex optical depth structure. The source of this structure may be the complex dynamics of the Keplerian shear and the self-gravity of the ring particles. The outcome of these dynamic effects depends sensitively on the collisional and physical properties of the particles. Two mechanisms can emerge that dominate the macroscopic physical structure of the ring: self-gravity wakes and viscous overstability. Here we study the interplay between these two mechanisms by using our recently developed particle collision method that allows us to better model the inter-particle contact physics. We find that for a constant ring surface density and particle internal density, particles with rough surfaces tend to produce axisymmetric ring features associated with the viscous overstability, while particles with smoother surfaces produce self-gravity wakes.

  9. Theory of a new elastic-plastic-viscous model and its application to the nuclear fuel mechanical analysis

    International Nuclear Information System (INIS)

    Moreno, A.

    1977-01-01

    In this work a new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (Author) 91 refs

  10. Development of numerical solution techniques in the KIKO3D code

    International Nuclear Information System (INIS)

    Panka, Istvan; Kereszturi, Andras; Hegedus, Csaba

    2005-01-01

    The paper describes the numerical methods applied in KIKO3D three-dimensional reactor dynamics code and present a new, more effective method (Bi-CGSTAB) for accelerating the large sparse matrix equation solution. The convergence characteristics were investigated in a given macro time step of a Control Rod Ejection transient. The results obtained by the old GMRES and new Bi-CGSTAB methods are compared. It is concluded that the real relative errors of the solutions obtained by GMRES or Bi - CGSTAB algorithms are in fact closer together than the estimated relative errors. The KIKO3D-Bi-CGSTAB method converges safely and it is 7-12 % faster than the old KIKO3D-GMRES solution (Authors)

  11. Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed hybrid finite element solution

    NARCIS (Netherlands)

    Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.R.J.

    2007-01-01

    The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci. 35 (1997) 793-802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues.

  12. Computational cardiology: the bidomain based modified Hill model incorporating viscous effects for cardiac defibrillation

    Science.gov (United States)

    Cansız, Barış; Dal, Hüsnü; Kaliske, Michael

    2017-10-01

    Working mechanisms of the cardiac defibrillation are still in debate due to the limited experimental facilities and one-third of patients even do not respond to cardiac resynchronization therapy. With an aim to develop a milestone towards reaching the unrevealed mechanisms of the defibrillation phenomenon, we propose a bidomain based finite element formulation of cardiac electromechanics by taking into account the viscous effects that are disregarded by many researchers. To do so, the material is deemed as an electro-visco-active material and described by the modified Hill model (Cansız et al. in Comput Methods Appl Mech Eng 315:434-466, 2017). On the numerical side, we utilize a staggered solution method, where the elliptic and parabolic part of the bidomain equations and the mechanical field are solved sequentially. The comparative simulations designate that the viscoelastic and elastic formulations lead to remarkably different outcomes upon an externally applied electric field to the myocardial tissue. Besides, the achieved framework requires significantly less computational time and memory compared to monolithic schemes without loss of stability for the presented examples.

  13. Numerical solution for identification of feedback coefficients in nuclear reactors

    International Nuclear Information System (INIS)

    Ebizuka, Yoshie; Sakai, Hideo

    1975-01-01

    Quasilinearization technique was studied to determine the Kinetic parameters of nuclear reactors. The method of solution was generalized to the determination of the parameters contained in a nonlinear system with nonlinear boundary conditions. A computer program, SNR-3, was developed to solve the resulting nonlinear two-point boundary value equations with generalized boundary conditions. In this paper, the problem formulation and the method of solution are explained for a general type of time dependent problem. A flow chart shows the procedure of numerical solution. The method was then applied to the determination of the critical factor and the reactivity feedback coefficients of reactors to investigate the accuracy and the applicability of the present method. The results showed that the present method was considerably successful, but that the random observation error effected the results of the identification. (Aoki, K.)

  14. Microencapsulation of Bioactive Principles with an Airless Spray-Gun Suitable for Processing High Viscous Solutions

    Directory of Open Access Journals (Sweden)

    Moreno Cocchietto

    2013-11-01

    Full Text Available Purpose: to design, assemble and test a prototype of a novel production plant, suitable for producing microparticles (MPs by processing highly viscous feed solutions (FSs. Methods: the prototype has been built using a commercial air compressor, a piston pump, an airless spray-gun, a customized air-treatment section, a timer, a rotating base, and a filtration section. Preliminary prototype parameter setting was carried out to individuate the best performing nozzle’s dimension, the nebulization timing, and the CaCl2 concentration in the gelation fluid. In addition, prototype throughput (1 L to 5 L and the range of practicable feed solution (FS viscosities were assayed. A set of four batches was prepared in order to characterize the MPs, in terms of mean particle size and distribution, flow properties, swelling, encapsulation efficiency and release. Results: according to a qualitative scoring, the large nozzle was suitable to nebulize FSs at a higher alginate concentration. Conversely, the small nozzle performed better in the processing of FSs with an alginate concentration up to 2% w/v. Only at the highest degree of viscosity, corresponding to 5% w/v of alginate, the FS processing was not technically possible. Among the CaCl2 concentrations considered, 15% w/v was recognized as the most versatile. The prototype appears to be convenient and suitable to grant a high yield starting from 2 L of FS. The flow behavior of the FSs assayed can be satisfactorily described with the Carreau-Yasuda equation and the throughput begins to slightly decrease for FSs at alginate concentrations exceeding 3% w/v. MP morphology was irregular with crumpled shape. The angle of repose indicates a good flowability and the release studies showed gastro-resistance and potential prolonged release applications. Conclusions: the novel prototype of production plant is suitable to process large amounts (2 L or more of FSs, characterized by a high viscosity, to produce MPs

  15. Microencapsulation of bioactive principles with an airless spray-gun suitable for processing high viscous solutions.

    Science.gov (United States)

    Cocchietto, Moreno; Blasi, Paolo; Lapasin, Romano; Moro, Chiara; Gallo, Davide; Sava, Gianni

    2013-11-19

    to design, assemble and test a prototype of a novel production plant, suitable for producing microparticles (MPs) by processing highly viscous feed solutions (FSs). the prototype has been built using a commercial air compressor, a piston pump, an airless spray-gun, a customized air-treatment section, a timer, a rotating base, and a filtration section. Preliminary prototype parameter setting was carried out to individuate the best performing nozzle's dimension, the nebulization timing, and the CaCl2 concentration in the gelation fluid. In addition, prototype throughput (1 L to 5 L) and the range of practicable feed solution (FS) viscosities were assayed. A set of four batches was prepared in order to characterize the MPs, in terms of mean particle size and distribution, flow properties, swelling, encapsulation efficiency and release. according to a qualitative scoring, the large nozzle was suitable to nebulize FSs at a higher alginate concentration. Conversely, the small nozzle performed better in the processing of FSs with an alginate concentration up to 2% w/v. Only at the highest degree of viscosity, corresponding to 5% w/v of alginate, the FS processing was not technically possible. Among the CaCl2 concentrations considered, 15% w/v was recognized as the most versatile. The prototype appears to be convenient and suitable to grant a high yield starting from 2 L of FS. The flow behavior of the FSs assayed can be satisfactorily described with the Carreau-Yasuda equation and the throughput begins to slightly decrease for FSs at alginate concentrations exceeding 3% w/v. MP morphology was irregular with crumpled shape. The angle of repose indicates a good flowability and the release studies showed gastro-resistance and potential prolonged release applications. the novel prototype of production plant is suitable to process large amounts (2 L or more) of FSs, characterized by a high viscosity, to produce MPs suitable for bioactive principle delivery.

  16. Numerical investigation on compressible flow characteristics in axial compressors using a multi block finite-volume scheme

    International Nuclear Information System (INIS)

    Farhanieh, B.; Amanifard, N.; Ghorbanian, K.

    2002-01-01

    An unsteady two-dimensional numerical investigation was performed on the viscous flow passing through a multi-blade cascade. A Cartesian finite-volume approach was linked to Van-Leer's and Roe's flux splitting schemes to evaluate inviscid flux terms. To prevent the oscillatory behavior of numerical results and to increase the accuracy, Mon tonic Upstream Scheme for Conservation Laws was added to flux splitting schemes. The Baldwin-Lo max (B L) turbulence model was implemented to solve the turbulent case studies. Implicit solution was also provided using Lower and Upper (L U) decomposition technique to compare with explicit solutions. To validate the numerical procedure, two test cases are prepared and flow over a Na Ca 0012 airfoil was investigated and the pressure coefficients were compared to the reference data. The numerical solver was implemented to study the flow passing over a compressor cascade. The results of various combinations of splitting schemes and the Mon tonic Upstream Scheme for Conventional Laws limiter were compared with each other to find the suitable methods in cascade problems. Finally the convergence histories of implemented schemes were compared to each other to show the behavior of the solver in using various methods before implementation of them in flow instability studies

  17. PROTOTYPING NON-EQUILIBRIUM VISCOUS-TIMESCALE ACCRETION THEORY USING LMC X-3

    Energy Technology Data Exchange (ETDEWEB)

    Cambier, Hal J.; Smith, David M. [Physics Department, University of California, Santa Cruz, CA 95064 (United States)

    2013-04-10

    Explaining variability observed in the accretion flows of black hole X-ray binary systems remains challenging, especially concerning timescales less than, or comparable to, the viscous timescale but much larger than the inner orbital period despite decades of research identifying numerous relevant physical mechanisms. We take a simplified but broad approach to study several mechanisms likely relevant to patterns of variability observed in the persistently high-soft Roche-lobe overflow system LMC X-3. Based on simple estimates and upper bounds, we find that physics beyond varying disk/corona bifurcation at the disk edge, Compton-heated winds, modulation of total supply rate via irradiation of the companion, and the likely extent of the partial hydrogen ionization instability is needed to explain the degree, and especially the pattern, of variability in LMC X-3 largely due to viscous dampening. We then show how evaporation-condensation may resolve or compound the problem given the uncertainties associated with this complex mechanism and our current implementation. We briefly mention our plans to resolve the question, refine and extend our model, and alternatives we have not yet explored.

  18. The Effects of Variable Viscosity, Viscous Dissipation and Chemical Reaction on Heat and Mass Transfer Flow of MHD Micropolar Fluid along a Permeable Stretching Sheet in a Non-Darcian Porous Medium

    Directory of Open Access Journals (Sweden)

    A. M. Salem

    2013-01-01

    Full Text Available A numerical model is developed to study the effects of temperature-dependent viscosity on heat and mass transfer flow of magnetohydrodynamic(MHD micropolar fluids with medium molecular weight along a permeable stretching surface embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction. The governing boundary equations for momentum, angular momentum (microrotation, and energy and mass transfer are transformed to a set of nonlinear ordinary differential equations by using similarity solutions which are then solved numerically by shooting technique. A comparison between the analytical and the numerical solutions has been included. The effects of the various physical parameters entering into the problem on velocity, microrotation, temperature and concentration profiles are presented graphically. Finally, the effects of pertinent parameters on local skin-friction coefficient, local Nusselt number and local Sherwood number are also presented graphically. One important observation is that for some kinds of mixtures (e.g., H2, air with light and medium molecular weight, the magnetic field and temperature-dependent viscosity effects play a significant role and should be taken into consideration as well.

  19. Viscous forces and bulk viscoelasticity near jamming

    NARCIS (Netherlands)

    Baumgarten, K.; Tighe, B.P.

    2017-01-01

    When weakly jammed packings of soft, viscous, non-Brownian spheres are probed mechanically, they respond with a complex admixture of elastic and viscous effects. While many of these effects are understood for specific, approximate models of the particles' interactions, there are a number of proposed

  20. A numerical solution to the radial equation of the tidal wave propagation

    International Nuclear Information System (INIS)

    Makarious, S.H.

    1981-08-01

    The tidal wave function y(x) is a solution to an inhomogeneous, linear, second-order differential equation with variable coefficient. Numerical values for the height-dependence terms, in the observed tides, have been utilized in finding y(x) as a solution to an initial-value problem. Complex Fast Fourier Transform technique is also used to obtain the solution in a complex form. Based on a realistic temperature structure, the atmosphere - below 110 km - has been divided into layers with distinct characteristics, and thus the technique of propagation in stratified media has been applied. The reduced homogeneous equation assumes the form of Helmholtz equation and with initial conditions the general solution is obtained. (author)

  1. 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.

  2. Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes

    International Nuclear Information System (INIS)

    Wehner, M.F.

    1983-01-01

    A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs

  3. Thin sheet numerical modelling of continental collision

    NARCIS (Netherlands)

    Jimenez-Munt, I.; Garcia-Gastellanos, D.; Fernandez, M.

    2005-01-01

    We study the effects of incorporating surface mass transport and the gravitational potential energy of both crust and lithospheric mantle to the viscous thin sheet approach. Recent 2D (cross-section) numerical models show that surface erosion and sediment transport can play a major role in shaping

  4. A numerical method for finding sign-changing solutions of superlinear Dirichlet problems

    Energy Technology Data Exchange (ETDEWEB)

    Neuberger, J.M.

    1996-12-31

    In a recent result it was shown via a variational argument that a class of superlinear elliptic boundary value problems has at least three nontrivial solutions, a pair of one sign and one which sign changes exactly once. These three and all other nontrivial solutions are saddle points of an action functional, and are characterized as local minima of that functional restricted to a codimension one submanifold of the Hilbert space H-0-1-2, or an appropriate higher codimension subset of that manifold. In this paper, we present a numerical Sobolev steepest descent algorithm for finding these three solutions.

  5. A New Method to Solve Numeric Solution of Nonlinear Dynamic System

    Directory of Open Access Journals (Sweden)

    Min Hu

    2016-01-01

    Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

  6. Reusable Object-Oriented Solutions for Numerical Simulation of PDEs in a High Performance Environment

    Directory of Open Access Journals (Sweden)

    Andrea Lani

    2006-01-01

    Full Text Available Object-oriented platforms developed for the numerical solution of PDEs must combine flexibility and reusability, in order to ease the integration of new functionalities and algorithms. While designing similar frameworks, a built-in support for high performance should be provided and enforced transparently, especially in parallel simulations. The paper presents solutions developed to effectively tackle these and other more specific problems (data handling and storage, implementation of physical models and numerical methods that have arisen in the development of COOLFluiD, an environment for PDE solvers. Particular attention is devoted to describe a data storage facility, highly suitable for both serial and parallel computing, and to discuss the application of two design patterns, Perspective and Method-Command-Strategy, that support extensibility and run-time flexibility in the implementation of physical models and generic numerical algorithms respectively.

  7. Remarks on the global existence in the dynamics of a viscous, heat-conducting, one-dimensional gas

    International Nuclear Information System (INIS)

    Song Jiang

    1994-01-01

    We consider initial boundary value problems for the equations of the motion of a viscous, heat-conducting, one-dimensional gas which is confined to a fixed tube with impermeable ends and whose viscosity varies with density, and prove the global existence of smooth (large) solutions. (author). 17 refs

  8. A Mass Conservative Numerical Solution for Two-Phase Flow in Porous Media With Application to Unsaturated Flow

    DEFF Research Database (Denmark)

    Celia, Michael A.; Binning, Philip John

    1992-01-01

    that the algorithm produces solutions that are essentially mass conservative and oscillation free, even in the presence of steep infiltrating fronts. When the algorithm is applied to the case of air and water flow in unsaturated soils, numerical results confirm the conditions under which Richards's equation is valid....... Numerical results also demonstrate the potential importance of air phase advection when considering contaminant transport in unsaturated soils. Comparison to several other numerical algorithms shows that the modified Picard approach offers robust, mass conservative solutions to the general equations...

  9. Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

    Directory of Open Access Journals (Sweden)

    Henrique Silva Furtado

    2009-09-01

    Full Text Available Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid-liquid interface thickness (2λ of 8 nanometers reproduced the solute (Cu equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007] was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification, indicating the necessity for new and more acute experimental data.

  10. Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem

    Directory of Open Access Journals (Sweden)

    Won-Tak Hong

    2016-01-01

    Full Text Available We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1 as well as oscillating singularities (of type rαsin⁡(ϵlog⁡r. It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.

  11. Efficient Numerical Solution of Coupled Radial Differential Equations in Multichannel Scattering Problems

    International Nuclear Information System (INIS)

    Houfek, Karel

    2008-01-01

    Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.

  12. New numerical method for iterative or perturbative solution of quantum field theory

    International Nuclear Information System (INIS)

    Hahn, S.C.; Guralnik, G.S.

    1999-01-01

    A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)

  13. FOLDER: A numerical tool to simulate the development of structures in layered media

    Science.gov (United States)

    Adamuszek, Marta; Dabrowski, Marcin; Schmid, Daniel W.

    2015-04-01

    FOLDER is a numerical toolbox for modelling deformation in layered media during layer parallel shortening or extension in two dimensions. FOLDER builds on MILAMIN [1], a finite element method based mechanical solver, with a range of utilities included from the MUTILS package [2]. Numerical mesh is generated using the Triangle software [3]. The toolbox includes features that allow for: 1) designing complex structures such as multi-layer stacks, 2) accurately simulating large-strain deformation of linear and non-linear viscous materials, 3) post-processing of various physical fields such as velocity (total and perturbing), rate of deformation, finite strain, stress, deviatoric stress, pressure, apparent viscosity. FOLDER is designed to ensure maximum flexibility to configure model geometry, define material parameters, specify range of numerical parameters in simulations and choose the plotting options. FOLDER is an open source MATLAB application and comes with a user friendly graphical interface. The toolbox additionally comprises an educational application that illustrates various analytical solutions of growth rates calculated for the cases of folding and necking of a single layer with interfaces perturbed with a single sinusoidal waveform. We further derive two novel analytical expressions for the growth rate in the cases of folding and necking of a linear viscous layer embedded in a linear viscous medium of a finite thickness. We use FOLDER to test the accuracy of single-layer folding simulations using various 1) spatial and temporal resolutions, 2) time integration schemes, and 3) iterative algorithms for non-linear materials. The accuracy of the numerical results is quantified by: 1) comparing them to analytical solution, if available, or 2) running convergence tests. As a result, we provide a map of the most optimal choice of grid size, time step, and number of iterations to keep the results of the numerical simulations below a given error for a given time

  14. Supporting brace sizing in structures with added linear viscous fluid dampers: A filter design solution

    OpenAIRE

    Londono, J.M.; Wagg, D.; Neild, S.A.

    2014-01-01

    Viscous fluid dampers have proved to be effective in suppressing unwanted vibrations in a range of engineering structures. When dampers are fitted in a structure, a brace is typically used to attach them to the main structure. The stiffness of this brace can significantly alter the effectiveness of the damper, and in structures with multiple dampers, this can be a complex scenario to model. In this paper, we demonstrate that the effects of the brace compliance on the damper performance can be...

  15. Influences of viscous losses and end effects on liquid metal flow in electromagnetic pumps

    International Nuclear Information System (INIS)

    Kim, Hee Reyoung; Seo, Joon Ho; Hong, Sang Hee; Cho, Su won; Nam, Ho Yun; Cho, Man

    1996-01-01

    Analyses of the viscous and end effects on electromagnetic (EM) pumps of annular linear induction type for the sodium coolant circulation in Liquid Metal Fast Breeder Reactors have been carried out based on the MHD laminar flow analysis and the electromagnetic field theory. A one-dimensional MHD analysis for the liquid metal flowing through an annular channel has been performed on the basis of a simplified model of equivalent current sheets instead of three-phase currents in the discrete primary windings. The calculations show that the developed pressure difference resulted from electromagnetic and viscous forces in the liquid metal is expressed in terms of the slip, and that the viscous loss effects are negligible compared with electromagnetic driving forces except in the low-slip region where the pumps operate with very high flow velocities comparable with the synchronous velocity of the electromagnetic fields, which is not applicable to the practical EM pumps. A two-dimensional electromagnetic field analysis based on an equivalent current sheet model has found the vector potentials in closed form by means of the Fourier transform method. The resultant magnetic fields and driving forces exerted on the liquid metal reveal that the end effects due to finiteness of the pump length are formidable. In addition, a two-dimensional numerical analysis for vector potentials has been performed by the SOR iterative method on a realistic EM pump model with discretely-distributed currents in the primary windings. The numerical computations for the distributions of magnetic fields and developed pressure differences along the pump axial length also show considerable end effects at both inlet and outlet ends, especially at high flow velocities. Calculations of each magnetic force contribution indicate that the end effects are originated from the magnetic force caused by the induced current (υxB) generated by the liquid metal movement across the magnetic field rather than the one

  16. A well-posed numerical method to track isolated conformal map singularities in Hele-Shaw flow

    International Nuclear Information System (INIS)

    Baker, G.; Siegel, M.; Tanveer, S.

    1995-01-01

    We present a new numerical method for calculating an evolving 2D Hele-Shaw interface when surface tension effects are neglected. In the case where the flow is directed from the less viscous fluid into the more viscous fluid, the motion of the interface is ill-posed; small deviations in the initial condition will produce significant changes in the ensuing motion. The situation is disastrous for numerical computation, as small roundoff errors can quickly lead to large inaccuracies in the computed solution. Our method of computation is most easily formulated using a conformal map from the fluid domain into a unit disk. The method relies on analytically continuing the initial data and equations of motion into the region exterior to the disk, where the evolution problem becomes well-posed. The equations are then numerically solved in the extended domain. The presence of singularities in the conformal map outside of the disk introduces specific structures along the fluid interface. Our method can explicitly track the location of isolated pole and branch point singularities, allowing us to draw connections between the development of interfacial patterns and the motion of singularities as they approach the unit disk. In particular, we are able to relate physical features such as finger shape, side-branch formation, and competition between fingers to the nature and location of the singularities. The usefulness of this method in studying the formation of topological singularities (self-intersections of the interface) is also pointed out. 47 refs., 10 figs., 1 tab

  17. Volumetric studies and thermodynamics of viscous flow of hydroxamic acids in acetone + water solvent at temperatures 303.15 and 313.15 K

    International Nuclear Information System (INIS)

    Tiwari, Vaishali; Pande, Rama

    2006-01-01

    Densities ρ and viscosities η of two hydroxamic acids, N-phenyl-2-chlorobenzo- and N-o-tolyl-4-chlorobenzo-, have been determined as a function of their concentration in aqueous acetone solution at temperatures 303.15 and 313.15 K. Apparent molar volumes, standard-state partial molar volumes and relative viscosities have been calculated. The viscosity data have been analyzed using Jones-Dole equation. The activation thermodynamic parameters of viscous flow have been evaluated using Feakins equation. These were obtained to throw light on the mechanism of viscous flow. Thermodynamic interactions in solutions have been studied in terms of a number of excess functions calculated from the experimental data. The effect of hydroxamic acid concentration and temperature on these parameters has been discussed. The results were interpreted in the light of solute-solvent interactions in aquo-organic media

  18. Numerical analysis of compressible steady, unsteady, and inviscid, viscous flows in ca scads and effects of viscosity on the flows

    International Nuclear Information System (INIS)

    Shirani, E.; Zirak, S.

    2001-01-01

    Compressible flows for unsteady, inviscid and viscous cases have been studied. Important features of flows such as formation of shock waves across the flow in an unsteady flow as well as interaction of shock waves with boundary layers and their effects on the flow around the blades have been analyzed. Jameson control volume approach was used to spatially integrate the flow equations and the fourth order Runge-Kutta method was used for time integration. The obtained finite difference equations were used to simulate inviscid and viscous flows in V KI cascades and the effects of viscosity, angle of attack, bal de pitches and back pressure on the flow were obtained. It was shown that when the flow was assumed inviscid, the error on the distribution of pressure on the blades were about ten percent. Finally, unsteady flow were simulated and formation of shock waves and their motions were analyzed

  19. Stationary solution of the compressible magnetohydrodynamic equation and its stability with respect to initial disturbance

    Directory of Open Access Journals (Sweden)

    WU Renchao

    2016-06-01

    Full Text Available In this paper, we consider three dimensional compressible viscous magnetohydro dynamic equations(MHD with external potentialforce. We first derive the corresponding non-constantstationary solutions. Then we show global well-posedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that rescribed initial data is close to the stationary solution.

  20. Generation of highly-viscous microjets

    Science.gov (United States)

    Tagawa, Yoshiyuki; Onuki, Hajime; Oi, Yuto

    2015-11-01

    An ink-jet printing system (or a liquid-dispensing device) has ecological and cost advantages compared to other printing systems such as offset printing and gravure printing since it requires a small amount of liquids. However, most ink-jet printers are not able to eject high-viscous liquids more than 10 cSt. This limitation severely restricts applications of the ink-jet system. Here we present a novel jet-generation system, discharging jets of high-viscous liquids up to 1,000 cSt. The system employs an impulsive force and converges the force efficiently in order to accelerate the liquid-air interface strongly for generating viscous jets: It consists of a liquid container and a thin tube partially inserted in the liquid. The liquid-air interface inside the thin tube is set deeper than that outside of the tube. We then add an impulsive force on the bottom of the container, leading to the microjet generation inside the thin tube. The pressure field under the impulsive force is estimated using pressure-impulse approach, deriving the jet velocity. The jet velocity is experimentally measured with varying the impulsive force and liquid levels in the tube and the container. It is found that the measured velocities agree with the estimation. Owing to the simple structure of the generation system and an ability for ejecting viscous liquids, it could extend the limits of existing ink-jet printers and may be applicable for next-generation technologies such as 3D printing systems and needle-free injection devices. JSPS KAKENHI Grant Number 26709007.

  1. A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

    Science.gov (United States)

    Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)

    2002-01-01

    We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

  2. Quasi-brittle damage modeling based on incremental energy relaxation combined with a viscous-type regularization

    Science.gov (United States)

    Langenfeld, K.; Junker, P.; Mosler, J.

    2018-05-01

    This paper deals with a constitutive model suitable for the analysis of quasi-brittle damage in structures. The model is based on incremental energy relaxation combined with a viscous-type regularization. A similar approach—which also represents the inspiration for the improved model presented in this paper—was recently proposed in Junker et al. (Contin Mech Thermodyn 29(1):291-310, 2017). Within this work, the model introduced in Junker et al. (2017) is critically analyzed first. This analysis leads to an improved model which shows the same features as that in Junker et al. (2017), but which (i) eliminates unnecessary model parameters, (ii) can be better interpreted from a physics point of view, (iii) can capture a fully softened state (zero stresses), and (iv) is characterized by a very simple evolution equation. In contrast to the cited work, this evolution equation is (v) integrated fully implicitly and (vi) the resulting time-discrete evolution equation can be solved analytically providing a numerically efficient closed-form solution. It is shown that the final model is indeed well-posed (i.e., its tangent is positive definite). Explicit conditions guaranteeing this well-posedness are derived. Furthermore, by additively decomposing the stress rate into deformation- and purely time-dependent terms, the functionality of the model is explained. Illustrative numerical examples confirm the theoretical findings.

  3. Enhancement of oxygen mass transfer and gas holdup using palm oil in stirred tank bioreactors with xanthan solutions as simulated viscous fermentation broths.

    Science.gov (United States)

    Mohd Sauid, Suhaila; Krishnan, Jagannathan; Huey Ling, Tan; Veluri, Murthy V P S

    2013-01-01

    Volumetric mass transfer coefficient (kLa) is an important parameter in bioreactors handling viscous fermentations such as xanthan gum production, as it affects the reactor performance and productivity. Published literatures showed that adding an organic phase such as hydrocarbons or vegetable oil could increase the kLa. The present study opted for palm oil as the organic phase as it is plentiful in Malaysia. Experiments were carried out to study the effect of viscosity, gas holdup, and kLa on the xanthan solution with different palm oil fractions by varying the agitation rate and aeration rate in a 5 L bench-top bioreactor fitted with twin Rushton turbines. Results showed that 10% (v/v) of palm oil raised the kLa of xanthan solution by 1.5 to 3 folds with the highest kLa value of 84.44 h(-1). It was also found that palm oil increased the gas holdup and viscosity of the xanthan solution. The kLa values obtained as a function of power input, superficial gas velocity, and palm oil fraction were validated by two different empirical equations. Similarly, the gas holdup obtained as a function of power input and superficial gas velocity was validated by another empirical equation. All correlations were found to fit well with higher determination coefficients.

  4. Enhancement of Oxygen Mass Transfer and Gas Holdup Using Palm Oil in Stirred Tank Bioreactors with Xanthan Solutions as Simulated Viscous Fermentation Broths

    Directory of Open Access Journals (Sweden)

    Suhaila Mohd Sauid

    2013-01-01

    Full Text Available Volumetric mass transfer coefficient (kLa is an important parameter in bioreactors handling viscous fermentations such as xanthan gum production, as it affects the reactor performance and productivity. Published literatures showed that adding an organic phase such as hydrocarbons or vegetable oil could increase the kLa. The present study opted for palm oil as the organic phase as it is plentiful in Malaysia. Experiments were carried out to study the effect of viscosity, gas holdup, and kLa on the xanthan solution with different palm oil fractions by varying the agitation rate and aeration rate in a 5 L bench-top bioreactor fitted with twin Rushton turbines. Results showed that 10% (v/v of palm oil raised the kLa of xanthan solution by 1.5 to 3 folds with the highest kLa value of 84.44 h−1. It was also found that palm oil increased the gas holdup and viscosity of the xanthan solution. The kLa values obtained as a function of power input, superficial gas velocity, and palm oil fraction were validated by two different empirical equations. Similarly, the gas holdup obtained as a function of power input and superficial gas velocity was validated by another empirical equation. All correlations were found to fit well with higher determination coefficients.

  5. Computation of viscous transonic flow about a lifting airfoil

    Science.gov (United States)

    Walitt, L.; Liu, C. Y.

    1976-01-01

    The viscous transonic flow about a stationary body in free air was numerically investigated. The geometry chosen was a symmetric NACA 64A010 airfoil at a freestream Mach number of 0.8, a Reynolds number of 4 million based on chord, and angles of attack of 0 and 2 degrees. These conditions were such that, at 2 degrees incidence unsteady periodic motion was calculated along the aft portion of the airfoil and in its wake. Although no unsteady measurements were made for the NACA 64A010 airfoil at these flow conditions, interpolated steady measurements of lift, drag, and surface static pressures compared favorably with corresponding computed time-averaged lift, drag, and surface static pressures.

  6. Buckling and stretching of thin viscous sheets

    Science.gov (United States)

    O'Kiely, Doireann; Breward, Chris; Griffiths, Ian; Howell, Peter; Lange, Ulrich

    2016-11-01

    Thin glass sheets are used in smartphone, battery and semiconductor technology, and may be manufactured by producing a relatively thick glass slab and subsequently redrawing it to a required thickness. The resulting sheets commonly possess undesired centerline ripples and thick edges. We present a mathematical model in which a viscous sheet undergoes redraw in the direction of gravity, and show that, in a sufficiently strong gravitational field, buckling is driven by compression in a region near the bottom of the sheet, and limited by viscous resistance to stretching of the sheet. We use asymptotic analysis in the thin-sheet, low-Reynolds-number limit to determine the centerline profile and growth rate of such a viscous sheet.

  7. Numerical treatment of elliptic BVP with several solutions and of MHD equilibrium problems

    International Nuclear Information System (INIS)

    Meyer-Spasche, R.

    1975-12-01

    It is found out empirically that Newton iteration and difference methods are very suitable for the numerical treatment of elliptic boundary value problems (Lu)(x) = f(x,u(x)) in D c R 2 , u/deltaD = g having several solutions. Some convergence theorems for these methods are presented. Some notable numerical examples are given, including bifurcation diagrams, which are interesting in themselves and show also the applicability of the methods developed. (orig./WB) [de

  8. Numerical solutions of differential equations of an ionization chamber

    International Nuclear Information System (INIS)

    Novkovic, D.; Tomasevic, M.; Subotic, K.; Manic, S.

    1998-01-01

    A system of reduced differential equations generally valid for plane-parallel, cylindrical, and spherical ionization chambers filled with air, which is appropriate for numerical solution, has been derived. The system has been solved for all three geometries. The comparison of the calculated results of Armstrong and Tate, for plane-parallel ionization chambers, and Sprinkle and Tate, for spherical ionization chambers, with the present calculations has shown a good agreement. The calculated values for ionization chambers filled with CO 2 were also in good agreement with the experimental data of Moriuchi et al (author)

  9. MATHEMATICAL MODEL NON-ISOTHERMAL FLOW HIGHLY VISCOUS MEDIA CHANNELS MATRIX EXTRUDER

    Directory of Open Access Journals (Sweden)

    A. S. Sidorenko

    2015-01-01

    Full Text Available We consider a one-dimensional steady flow of highly viscous medium in a cylindrical channel with Dissipation and dependence of the viscosity on the temperature. It is assumed that a relatively small intervals of temperature variation of the dynamic viscosity with a sufficient degree of accuracy can be assumed to be linear. The model was based on the equations of hydrodynamics and the heat transfer fluid. In the task channel wall temperature is assumed constant. An approximate solution of the problem, according to which the distribution of velocity, pressure and temperature is sought in the form of an expansion in powers of the dimensionless transverse coordinates. A special case, when the ratio of the velocity distribution, pressure and temperature is allowed to restrict the number of terms in the expansion as follows: for speed - the first 3 to the pressure - the first two for the temperature - the first 5. The expressions to determine the temperature profile of the medium in the channel and characterization dissipative heating. To simulate the process of heat transfer highly viscous media developed a program for personal electronic computers. The calculation was performed using experimental research data melt flow grain mixture of buckwheat and soybeans for the load speed of 0.08 mm / s. The method of computer simulation carried out checks on the adequacy of the solutions to the real process of heat transfer. Analysis of the results indicates that for small values of the length of the channel influence dissipation function appears mainly at the wall. By increasing the reduced length of this phenomenon applies to all section of the channel. At high temperature profile along the channel length is determined entirely by dissipation. In the case of heat transfer due to frictional heat only, the form of curves of temperature distribution is a consequence of the interaction effects of heating due to viscous shear effects cooling by conduction. The

  10. Two-Phase Flow in Wire Coating with Heat Transfer Analysis of an Elastic-Viscous Fluid

    Directory of Open Access Journals (Sweden)

    Zeeshan Khan

    2016-01-01

    Full Text Available This work considers two-phase flow of an elastic-viscous fluid for double-layer coating of wire. The wet-on-wet (WOW coating process is used in this study. The analytical solution of the theoretical model is obtained by Optimal Homotopy Asymptotic Method (OHAM. The expression for the velocity field and temperature distribution for both layers is obtained. The convergence of the obtained series solution is established. The analytical results are verified by Adomian Decomposition Method (ADM. The obtained velocity field is compared with the existing exact solution of the same flow problem of second-grade fluid and with analytical solution of a third-grade fluid. Also, emerging parameters on the solutions are discussed and appropriate conclusions are drawn.

  11. Numerical study of fluid motion in bioreactor with two mixers

    Energy Technology Data Exchange (ETDEWEB)

    Zheleva, I., E-mail: izheleva@uni-ruse.bg [Department of Heat Technology, Hydraulics and Ecology, Angel Kanchev University of Rousse, 8 Studentska str., 7017 Rousse (Bulgaria); Lecheva, A., E-mail: alecheva@uni-ruse.bg [Department of Mathematics, Angel Kanchev University of Rousse, 8 Studentska str., 7017 Rousse (Bulgaria)

    2015-10-28

    Numerical study of hydrodynamic laminar behavior of a viscous fluid in bioreactor with multiple mixers is provided in the present paper. The reactor is equipped with two disk impellers. The fluid motion is studied in stream function-vorticity formulation. The calculations are made by a computer program, written in MATLAB. The fluid structure is described and numerical results are graphically presented and commented.

  12. Analytical and Numerical Studies of Several Fluid Mechanical Problems

    Science.gov (United States)

    Kong, D. L.

    2014-03-01

    In this thesis, three parts, each with several chapters, are respectively devoted to hydrostatic, viscous, and inertial fluids theories and applications. Involved topics include planetary, biological fluid systems, and high performance computing technology. In the hydrostatics part, the classical Maclaurin spheroids theory is generalized, for the first time, to a more realistic multi-layer model, establishing geometries of both the outer surface and the interfaces. For one of its astrophysical applications, the theory explicitly predicts physical shapes of surface and core-mantle-boundary for layered terrestrial planets, which enables the studies of some gravity problems, and the direct numerical simulations of dynamo flows in rotating planetary cores. As another application of the figure theory, the zonal flow in the deep atmosphere of Jupiter is investigated for a better understanding of the Jovian gravity field. An upper bound of gravity field distortions, especially in higher-order zonal gravitational coefficients, induced by deep zonal winds is estimated firstly. The oblate spheroidal shape of an undistorted Jupiter resulting from its fast solid body rotation is fully taken into account, which marks the most significant improvement from previous approximation based Jovian wind theories. High viscosity flows, for example Stokes flows, occur in a lot of processes involving low-speed motions in fluids. Microorganism swimming is such a typical case. A fully three dimensional analytic solution of incompressible Stokes equation is derived in the exterior domain of an arbitrarily translating and rotating prolate spheroid, which models a large family of microorganisms such as cocci bacteria. The solution is then applied to the magnetotactic bacteria swimming problem, and good consistency has been found between theoretical predictions and laboratory observations of the moving patterns of such bacteria under magnetic fields. In the analysis of dynamics of planetary

  13. Equivalent viscous damping procedure for multi-material systems

    International Nuclear Information System (INIS)

    Ahmed, H.; Ma, D.

    1979-01-01

    The inclusion of accurate viscous damping effects in the seismic analysis of nuclear power plants is discussed. A procedure to evaluate and use equivalent viscous damping coefficients in conjunction with the substructure method of finite element analysis is outlined in detail

  14. Numerical solution of plasma fluid equations using locally refined grids

    International Nuclear Information System (INIS)

    Colella, P.

    1997-01-01

    This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results

  15. Numerical study of unsteady viscous flow past oscillating airfoil

    Energy Technology Data Exchange (ETDEWEB)

    Jin Yan; Yuan Xin [Tsinghua Univ., Dept. of Thermal Engineering, Beijing (China)

    2001-07-01

    Accurate simulation of the dynamic stall of an oscillating airfoil is of major importance to wing and wind turbine blade design. However, dynamic stall is complicated and influenced by many factors, such as geometry shape of the airfoil, reduced frequency, etc. The difficulties of simulation are both mathematical (numerical method) and physical (turbulence model). The present paper has introduced a new numerical method (new LU-type scheme and fourth-order higher resolution MUSCL TVD scheme) and q-{omega} turbulence modelling to calculate the unsteady flowfields of an oscillating NACA0015 airfoil. The test targets include attached flow, light-stall and deep-stall of the airfoil. The calculated results for attached flow and light-stall are in good agreement with those of experiments. The calculated results for deep-stall also show improvement, especially during the downstroke of the oscillation. However, there is still a significant difference between the results of calculation and experiment in the hysteresis curves of the drag coefficient. One reason is that the q-{omega} turbulence model still has limitations. Another is that the drag coefficient is difficult to measure and the experiments are not reliable. (Author)

  16. Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

    Science.gov (United States)

    Felici, Helene M.; Drela, Mark

    1993-01-01

    A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

  17. A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

    Science.gov (United States)

    Yao, Lingxing; Mori, Yoichiro

    2017-12-01

    Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

  18. Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

    Science.gov (United States)

    Ceccobello, C.; Farinelli, R.; Titarchuk, L.

    2014-01-01

    We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the

  19. An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

    Science.gov (United States)

    Swidinsky, Andrei; Liu, Lifei

    2017-11-01

    We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

  20. New numerical solutions of three-dimensional compressible hydrodynamic convection. [in stars

    Science.gov (United States)

    Hossain, Murshed; Mullan, D. J.

    1990-01-01

    Numerical solutions of three-dimensional compressible hydrodynamics (including sound waves) in a stratified medium with open boundaries are presented. Convergent/divergent points play a controlling role in the flows, which are dominated by a single frequency related to the mean sound crossing time. Superposed on these rapid compressive flows, slower eddy-like flows eventually create convective transport. The solutions contain small structures stacked on top of larger ones, with vertical scales equal to the local pressure scale heights, H sub p. Although convective transport starts later in the evolution, vertical scales of H sub p are apparently selected at much earlier times by nonlinear compressive effects.

  1. The Navier-Stokes-Fourier system: From weak solutions to numerical analysis

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard

    2015-01-01

    Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml

  2. An Experimental and numerical Study for squeezing flow

    Science.gov (United States)

    Nathan, Rungun; Lang, Ji; Wu, Qianhong; Vucbmss Team

    2017-11-01

    We report an experimental and numerical study to examine the transient squeezing flow driven by sudden external impacts. The phenomenon is widely observed in industrial applications, e.g. squeeze dampers, or in biological systems, i.e. joints lubrication. However, there is a lack of investigation that captures the transient flow feature during the process. An experimental setup was developed that contains a piston instrumented with a laser displacement sensor and a pressure transducer. The heavy piston was released from rest, creating a fast compaction on the thin fluid gap underneath. The motion of the piston and the fluid pressure build-up was recorded. For this dynamic process, a CFD simulation was performed which shows excellent agreement with the experimental data. Both the numerical and experimental results show that, the squeezing flow starts with the inviscid limit when the viscous fluid effect has no time to appear, and thereafter becomes a developing flow, in which the inviscid core flow region decreases and the viscous wall region increases until the entire fluid gap is filled with viscous fluid flow. The study presented herein, filling the gap in the literature, will have broad impacts in industrial and biomedical applications. This research was supported by the National Science Foundation under Award 1511096, and supported by the Seed Grant from The Villanova Center for the Advancement of Sustainability in Engineering (VCASE).

  3. Investigation of heat and mass transfer of rotating MHD viscous flow between a stretching sheet and a porous surface

    DEFF Research Database (Denmark)

    Sheikholeslami, R; Ashorynejad, H.R; Barari, Amin

    2013-01-01

    the viscous dissipation is negligible. Originality/value – The equations of conservation of mass, momentum and energy are reduced to a non-linear ordinary differential equations system. Differential Transformation Method is utilized to approximate the solution for velocity and temperature profiles....

  4. Numerical Modeling for the Solute Uptake from Groundwater by Plants-Plant Uptake Package

    OpenAIRE

    El-Sayed, Amr A.

    2006-01-01

    A numerical model is presented to describe solute transport in groundwater coupled to sorption by plant roots, translocation into plant stems, and finally evapotranspiration. The conceptual model takes into account both Root Concentration Factor, RCF, and Transpiration Stream Concentration Factor, TSCF for chemicals which are a function of Kow. A similar technique used to simulate the solute transport in groundwater to simulate sorption and plant uptake is used. The mathematical equation is s...

  5. Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

    Directory of Open Access Journals (Sweden)

    Suheel Abdullah Malik

    2014-01-01

    Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

  6. Numerical Modeling Tools for the Prediction of Solution Migration Applicable to Mining Site

    International Nuclear Information System (INIS)

    Martell, M.; Vaughn, P.

    1999-01-01

    Mining has always had an important influence on cultures and traditions of communities around the globe and throughout history. Today, because mining legislation places heavy emphasis on environmental protection, there is great interest in having a comprehensive understanding of ancient mining and mining sites. Multi-disciplinary approaches (i.e., Pb isotopes as tracers) are being used to explore the distribution of metals in natural environments. Another successful approach is to model solution migration numerically. A proven method to simulate solution migration in natural rock salt has been applied to project through time for 10,000 years the system performance and solution concentrations surrounding a proposed nuclear waste repository. This capability is readily adaptable to simulate solution migration around mining

  7. A third-order KdV solution for internal solitary waves and its application in the numerical wave tank

    Directory of Open Access Journals (Sweden)

    Qicheng Meng

    2016-04-01

    Full Text Available A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system. The solution corrects an error by Mirie and Su (1984. A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam. Various analytical solutions, including the first-order to third-order KdV solutions, the eKdV solution and the MCC solution, have been used to initialise the flow fields in the CFD simulations of internal solitary waves. Two groups including 11 numerical cases have been carried out. In the same group, the initial wave amplitudes are the same but the implemented analytical solutions are different. The simulated wave profiles at different moments have been presented. The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively. It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases. The finding is significant for the further simulations involving internal solitary waves.

  8. Numerical study on the rotation of an elastic rod in a viscous fluid using an immersed boundary method

    International Nuclear Information System (INIS)

    Maniyeri, Ranjith; Kang, Sang Mo

    2012-01-01

    We present a three dimensional computational model based on an immersed boundary (IB) method to study the hydrodynamic features of a solid flexible cylindrical rod in a viscous fluid driven at one side by a tiny motor. The elastic rod is modelled by a number of circular cross-sections with twelve IB points on each cross-section. Three types of elastic links are created from each IB point to obtain an elastic network model of the rod and the first cross-section is modelled as the motor part. The elastic forces are computed based on an elastic energy approach and the motor forces are obtained from the applied angular frequency of rotation of the motor. The Stokes equations governing the fluid are solved on a staggered Cartesian grid system using the fractional-step based finite-volume method. Numerical simulations are performed to demonstrate the three dynamical stages of rod motion- twirling, whirling and overwhirling for different rotational frequency of the motor. It is revealed that for low rotational frequencies, the rod undergoes stable rigid body motion known as twirling. For high rotational frequencies of the motor, it is observed that the rod initially undergoes whirling motion and attains an unstable helical shape. Further, it is noticed that a discontinuous shape transition occurs for the rod and it folds back on itself. This unstable motion is referred to as overwhirling. It is also found that there exists a critical value of angular frequency of rotation of the motor below which the rod is subjected to twirling motion and above which it undergoes overwhirling motion

  9. Numerical modeling of solute transport in deformable unsaturated layered soil

    Directory of Open Access Journals (Sweden)

    Sheng Wu

    2017-07-01

    Full Text Available The effect of soil stratification was studied through numerical investigation based on the coupled model of solute transport in deformable unsaturated soil. The theoretical model implied two-way coupled excess pore pressure and soil deformation based on Biot's consolidation theory as well as a one-way coupled volatile pollutant concentration field developed from the advection-diffusion theory. Embedded in the model, the degree of saturation, fluid compressibility, self-weight of the soil matrix, porosity variance, longitudinal dispersion, and linear sorption were computed. Based on simulation results of a proposed three-layer landfill model using the finite element method, the multi-layer effects are discussed with regard to the hydraulic conductivity, shear modulus, degree of saturation, molecular diffusion coefficient, and thickness of each layer. Generally speaking, contaminants spread faster in a stratified field with a soft and highly permeable top layer; soil parameters of the top layer are more critical than the lower layers but controlling soil thicknesses will alter the results. This numerical investigation showed noticeable impacts of stratified soil properties on solute migration results, demonstrating the importance of correctly modeling layered soil instead of simply assuming the averaged properties across the soil profile.

  10. VISCOUS-LIKE INTERACTION OF THE SOLAR WIND WITH THE PLASMA TAIL OF COMET SWIFT-TUTTLE

    International Nuclear Information System (INIS)

    Reyes-Ruiz, Mauricio; Vazquez, Roberto; Perez-de-Tejada, Hector

    2010-01-01

    We compare the results of the numerical simulation of the viscous-like interaction of the solar wind with the plasma tail of a comet, with velocities of H 2 O+ ions in the tail of comet Swift-Tuttle determined by means of spectroscopic ground-based observations. Our aim is to constrain the value of the basic parameters in the viscous-like interaction model: the effective Reynolds number of the flow and the interspecies coupling timescale. We find that in our simulations the flow rapidly evolves from an arbitrary initial condition to a quasi-steady state for which there is a good agreement between the simulated tailward velocity of H 2 O+ ions and the kinematics derived from the observations. The fiducial case of our model, characterized by a low effective Reynolds number (Re eff ∼ 20) selected on the basis of a comparison to in situ measurements of the plasma flow at comet Halley, yields an excellent fit to the observed kinematics. Given the agreement between model and observations, with no ad hoc assumptions, we believe that this result suggests that viscous-like momentum transport may play an important role in the interaction of the solar wind and the cometary plasma environment.

  11. Robertson-Walker solutions for various types of energy-momentum tensor

    International Nuclear Information System (INIS)

    Lukacs, B.

    1976-01-01

    Robertson-Walker solutions are important in general relativity as universe solutions. This paper contains a number of Robertson-Walker-type solutions for certain cases, namely, for noncharged massless scalar meson fields, viscous fluids, Hookean elastic mediums, and Kelvin-Voigt viscoelastic systems. (author)

  12. Radiation and mass transfer effects on an unsteady MHD free convection flow past a heated vertical plate in a porous medium with viscous dissipation

    Directory of Open Access Journals (Sweden)

    Prasad Ramachandra V.

    2007-01-01

    Full Text Available An unsteady, two-dimensional, hydromagnetic, laminar free convective boundary-layer flow of an incompressible, Newtonian, electrically-conducting and radiating fluid past an infinite heated vertical porous plate with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and Sherwood number are presented and discussed. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer, whereas when thermal and solutal Grashof increases the velocity increases.

  13. Comparison study between the effects of different terms contributing to viscous dissipation in saturated porous media

    KAUST Repository

    Salama, Amgad

    2013-02-01

    Some sort of controversy is associated with the problem of viscous dissipation in saturated porous media for which we try to present a comparison study between the influences of the different terms contributing to this phenomenon. We consider viscous dissipation by studying the case of semi-infinite flat plate embedded in saturated porous medium and is kept at constant, higher temperature compared with the surrounding fluid. The fluid is induced to move upwards by natural convection during which viscous dissipation is considered. The boundary layer assumptions are considered to simplify the treatment and to highlight the influencing parameters. The behavior of temperature, and velocity fields in the neighborhood of the vertical flat plate were used to highlight the effects of these parameters. Three terms were considered to contribute to viscous dissipation, namely Darcy\\'s term, the Forchheimer term and Al-Hadharami\\'s term. Although there are no unanimous agreements between researchers to include the Forchhemier term in the dissipation function, some researchers argued it might have an indirect effect and hence for this sake and for completion purposes, we include it in this comparison study. Dimensional considerations reveal that Darcy\\'s term is influenced by Gebhart number, the Forchheimer term is controlled by the non-Darcy parameter and Al-Hadharami\\'s term is influenced by Darcy\\'s number. The governing, non-dimensional set of equations together with the imposed boundary conditions is numerically investigated by finite element method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e., viscous dissipation) is very much influenced by the relative magnitude of these dimensionless parameters. © 2012 Elsevier Masson SAS. All rights reserved.

  14. Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    Zhanhua Yu

    2011-01-01

    convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.

  15. Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions.

    Science.gov (United States)

    Lötstedt, Erik; Jentschura, Ulrich D

    2009-02-01

    In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

  16. Dynamics of viscous cosmologies in the full Israel-Stewart formalism

    Science.gov (United States)

    Lepe, Samuel; Otalora, Giovanni; Saavedra, Joel

    2017-07-01

    A detailed dynamical analysis for a bulk viscosity model in the full Israel-Stewart formalism for a spatially flat Friedmann-Robertson-Walker universe is performed. In our study we have considered the total cosmic fluid constituted by radiation, dark matter, and dark energy. The dark matter fluid is treated as an imperfect fluid which has a bulk viscosity that depends on its energy density in the usual form ξ (ρm)=ξ0ρm1 /2, whereas the other components are assumed to behave as perfect fluids with constant equation of state parameter. We show that the thermal history of the Universe is reproduced provided that the viscous coefficient satisfies the condition ξ0≪1 , either for a zero or a suitable nonzero coupling between dark energy and viscous dark matter. In this case, the final attractor is a dark-energy-dominated, accelerating universe, with an effective equation of state parameter in the quintessence-like, cosmological constant-like, or phantom-like regime, in agreement with observations. As our main result, we show that in order to obtain a viable cosmological evolution and at the same time alleviating the cosmological coincidence problem via the mechanism of scaling solution, an explicit interaction between dark energy and viscous dark matter seems inevitable. This result is consistent with the well-known fact that models where dark matter and dark energy interact with each other have been proposed to solve the coincidence problem. Furthermore, by insisting on above, we show that in the present context a phantom nature of this interacting dark energy fluid is also favored.

  17. Lattice Boltzmann method and gas-kinetic BGK scheme in the low-Mach number viscous flow simulations

    International Nuclear Information System (INIS)

    Xu Kun; He Xiaoyi

    2003-01-01

    Both lattice Boltzmann method (LBM) and the gas-kinetic BGK scheme are based on the numerical discretization of the Boltzmann equation with collisional models, such as, the Bhatnagar-Gross-Krook (BGK) model. LBM tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process. On the other hand, the gas-kinetic BGK scheme is a finite volume scheme, where the time-dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces. Currently, LBM is mainly used for low Mach number, nearly incompressible flow simulation. For the gas-kinetic scheme, the application is focusing on the high speed compressible flows. In this paper, we are going to compare both schemes in the isothermal low-Mach number flow simulations. The methodology for developing both schemes will be clarified through the introduction of operator splitting Boltzmann model and operator averaging Boltzmann model. From the operator splitting Boltzmann model, the error rooted in many kinetic schemes, which are based on the decoupling of particle transport and collision, can be easily understood. As to the test case, we choose to use the 2D cavity flow since it is one of the most extensively studied cases. Detailed simulation results with different Reynolds numbers, as well as the benchmark solutions, are presented

  18. Reynolds Number Effect on Spatial Development of Viscous Flow Induced by Wave Propagation Over Bed Ripples

    Science.gov (United States)

    Dimas, Athanassios A.; Kolokythas, Gerasimos A.

    Numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and appropriate bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme is used where central finite-differences, in the horizontal direction, and a pseudo-spectral approximation method with Chebyshev polynomials, in the vertical direction, are applied. A fractional time-step scheme is used for the temporal discretization. Over the rippled bed, the wave boundary layer thickness increases significantly, in comparison to the one over flat bed, due to flow separation at the ripple crests, which generates alternating circulation regions. The amplitude of the wall shear stress over the ripples increases with increasing ripple height or decreasing Reynolds number, while the corresponding friction force is insensitive to the ripple height change. The amplitude of the form drag forces due to dynamic and hydrostatic pressures increase with increasing ripple height but is insensitive to the Reynolds number change, therefore, the percentage of friction in the total drag force decreases with increasing ripple height or increasing Reynolds number.

  19. Physical hydrodynamic propulsion model study on creeping viscous

    Indian Academy of Sciences (India)

    The present investigation focusses on a mathematical study of creeping viscous flow induced by metachronal wave propagation in a horizontal ciliated tube containing porous media. Creeping flow limitations are imposed, i.e. inertial forces are small compared to viscous forces and therefore a very low Reynolds number (Re ...

  20. Nanoconfined ionic liquids: Disentangling electrostatic and viscous forces

    Science.gov (United States)

    Lhermerout, Romain; Perkin, Susan

    2018-01-01

    Recent reports of surface forces across nanoconfined ionic liquids have revealed the existence of an anomalously long-ranged interaction apparently of electrostatic origin. Ionic liquids are viscous, and therefore it is important to inspect rigorously whether the observed repulsive forces are indeed equilibrium forces or, rather, arise from the viscous force during drainage of the fluid between two confining surfaces. In this paper we present our direct measurements of surface forces between mica sheets approaching in the ionic liquid [C2C1Im ] [NTf2] , exploring three orders of magnitude in approach velocity. Trajectories are systematically fitted by solving the equation of motion, allowing us to disentangle the viscous and equilibrium contributions. First, we find that the drainage obeys classical hydrodynamics with a negative slip boundary condition in the range of the structural force, implying that a nanometer -thick portion of the liquid in the vicinity of the solid surface is composed of ordered molecules that do not contribute to the flow. Second, we show that a long-range static force must indeed be invoked, in addition to the viscous force, in order to describe the data quantitatively. This equilibrium interaction decays exponentially and with decay length in agreement with the screening length reported for the same system in previous studies. In those studies the decay was simply checked to be independent of velocity and measured at a low approach rate, rather than explicitly taking account of viscous effects: we explain why this gives indistinguishable outcomes for the screening length by noting that the viscous force is linear to very good approximation over a wide range of distances.

  1. An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications

    Directory of Open Access Journals (Sweden)

    Petráš Ivo

    2011-01-01

    Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.

  2. Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation

    International Nuclear Information System (INIS)

    Wei, T; Qin, H H; Shi, R

    2008-01-01

    In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a numerical algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimate and convergence analysis have also been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method

  3. Temperature prediction in a coal fired boiler with a fixed bed by fuzzy logic based on numerical solution

    International Nuclear Information System (INIS)

    Biyikoglu, A.; Akcayol, M.A.; Oezdemir, V.; Sivrioglu, M.

    2005-01-01

    In this study, steady state combustion in boilers with a fixed bed has been investigated. Temperature distributions in the combustion chamber of a coal fired boiler with a fixed bed are predicted using fuzzy logic based on data obtained from the numerical solution method for various coal and air feeding rates. The numerical solution method and the discretization of the governing equations of two dimensional turbulent flow in the combustion chamber and one dimensional coal combustion in the fixed bed are explained. Control Volume and Finite Difference Methods are used in the discretization of the equations in the combustion chamber and in the fixed bed, respectively. Results are presented as contours within the solution domain and compared with numerical ones. Comparison of the results shows that the difference between the numerical solution and fuzzy logic prediction throughout the computational domain is less than 1.5%. The statistical coefficient of multiple determinations for the investigated cases is about 0.9993 to 0.9998. This accuracy degree is acceptable in predicting the temperature values. So, it can be concluded that fuzzy logic provides a feasible method for defining the system properties

  4. A study to investigate viscous coupling effects on the hydraulic conductance of fluid layers in two-phase flow at the pore level.

    Science.gov (United States)

    Shams, Mosayeb; Raeini, Ali Q; Blunt, Martin J; Bijeljic, Branko

    2018-07-15

    This paper examines the role of momentum transfer across fluid-fluid interfaces in two-phase flow. A volume-of-fluid finite-volume numerical method is used to solve the Navier-Stokes equations for two-phase flow at the micro-scale. The model is applied to investigate viscous coupling effects as a function of the viscosity ratio, the wetting phase saturation and the wettability, for different fluid configurations in simple pore geometries. It is shown that viscous coupling effects can be significant for certain pore geometries such as oil layers sandwiched between water in the corner of mixed wettability capillaries. A simple parametric model is then presented to estimate general mobility terms as a function of geometric properties and viscosity ratio. Finally, the model is validated by comparison with the mobilities computed using direct numerical simulation. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

  5. Impact of ultra-viscous drops: air-film gliding and extreme wetting

    KAUST Repository

    Langley, Kenneth; Li, Erqiang; Thoroddsen, Sigurdur T

    2017-01-01

    water drop, the viscous-dominated flow in the thin air layer counteracts the inertia of the drop liquid. For highly viscous drops the viscous stresses within the liquid also affect the interplay between the drop and the gas. Here the drop also forms a

  6. Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

    DEFF Research Database (Denmark)

    Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

    2012-01-01

    In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

  7. Solved problems in classical mechanics analytical and numerical solutions with comments

    CERN Document Server

    de Lange, O L

    2010-01-01

    Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...

  8. Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

    KAUST Repository

    Frohne, Jö rg; Heister, Timo; Bangerth, Wolfgang

    2015-01-01

    © 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

  9. Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

    KAUST Repository

    Frohne, Jörg

    2015-08-06

    © 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

  10. Radiative heat transfer with hydromagnetic flow and viscous dissipation over a stretching surface in the presence of variable heat flux

    Directory of Open Access Journals (Sweden)

    Kumar Hitesh

    2009-01-01

    Full Text Available The boundary layer steady flow and heat transfer of a viscous incompressible fluid due to a stretching plate with viscous dissipation effect in the presence of a transverse magnetic field is studied. The equations of motion and heat transfer are reduced to non-linear ordinary differential equations and the exact solutions are obtained using properties of confluent hypergeometric function. It is assumed that the prescribed heat flux at the stretching porous wall varies as the square of the distance from origin. The effects of the various parameters entering into the problem on the velocity field and temperature distribution are discussed.

  11. Modeling the response of a standard accretion disc to stochastic viscous fluctuations

    Science.gov (United States)

    Ahmad, Naveel; Misra, Ranjeev; Iqbal, Naseer; Maqbool, Bari; Hamid, Mubashir

    2018-01-01

    The observed variability of X-ray binaries over a wide range of time-scales can be understood in the framework of a stochastic propagation model, where viscous fluctuations at different radii induce accretion rate variability that propagate inwards to the X-ray producing region. The scenario successfully explains the power spectra, the linear rms-flux relation as well as the time-lag between different energy photons. The predictions of this model have been obtained using approximate analytical solutions or empirically motivated models which take into account the effect of these propagating variability on the radiative process of complex accretion flows. Here, we study the variation of the accretion rate due to such viscous fluctuations using a hydro-dynamical code for the standard geometrically thin, gas pressure dominated α-disc with a zero torque boundary condition. Our results confirm earlier findings that the time-lag between a perturbation and the resultant inner accretion rate variation depends on the frequency (or time-period) of the perturbation. Here we have quantified that the time-lag tlag ∝f-0.54 , for time-periods less than the viscous time-scale of the perturbation radius and is nearly constant otherwise. This, coupled with radiative process would produce the observed frequency dependent time-lag between different energy bands. We also confirm that if there are random Gaussian fluctuations of the α-parameter at different radii, the resultant inner accretion rate has a power spectrum which is a power-law.

  12. On the viscous dissipation modeling of thermal fluid flow in a porous medium

    KAUST Repository

    Salama, Amgad

    2011-02-24

    The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e.; viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism. © 2011 Springer-Verlag.

  13. TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

    International Nuclear Information System (INIS)

    Walters, W.F.

    1983-01-01

    A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy

  14. Dilepton production in schematic causal viscous hydrodynamics

    International Nuclear Information System (INIS)

    Song, Taesoo; Han, Kyong Chol; Ko, Che Ming

    2011-01-01

    Assuming that in the hot dense matter produced in relativistic heavy-ion collisions, the energy density, entropy density, and pressure as well as the azimuthal and space-time rapidity components of the shear tensor are uniform in the direction transversal to the reaction plane, we derive a set of schematic equations from the Isreal-Stewart causal viscous hydrodynamics. These equations are then used to describe the evolution dynamics of relativistic heavy-ion collisions by taking the shear viscosity to entropy density ratio of 1/4π for the initial quark-gluon plasma (QGP) phase and of 10 times this value for the later hadron-gas (HG) phase. Using the production rate evaluated with particle distributions that take into account the viscous effect, we study dilepton production in central heavy-ion collisions. Compared with results from the ideal hydrodynamics, we find that although the dilepton invariant mass spectra from the two approaches are similar, the transverse momentum spectra are significantly enhanced at high transverse momenta by the viscous effect. We also study the transverse momentum dependence of dileptons produced from QGP for a fixed transverse mass, which is essentially absent in the ideal hydrodynamics, and find that this so-called transverse mass scaling is violated in the viscous hydrodynamics, particularly at high transverse momenta.

  15. Dynamics of two coaxial cylindrical shells containing viscous fluid

    International Nuclear Information System (INIS)

    Yeh, T.T.; Chen, S.S.

    1976-09-01

    This study was motivated by the need to design the thermal shield in reactor internals and other system components to avoid detrimental flow-induced vibrations. The system component is modeled as two coaxial shells separated by a viscous fluid. In the analysis, Flugge's shell equations of motion and linearized Navier-Stokes equation for viscous fluid are employed. First, a traveling-wave type solution is taken for shells and fluid. Then, from the interface conditions between the shells and fluid, the solution for the fluid medium is expressed in terms of shell displacements. Finally, using the shell equations of motion gives the frequency equation, from which the natural frequency, mode shape, and modal damping ratio of coupled modes can be calculated. The analytical results show a fairly good qualitative agreement with the published experimental data. Some important conclusions are as follows: (1) In computing the natural frequencies and mode shapes of uncoupled modes and coupled modes, the fluid may be considered inviscid and incompressible. (2) There exists out-of-phase and in-phase modes. The lowest natural frequency is always associated with the out-of-phase mode. (3) The lowest natural frequency of coupled modes is lower than the uncoupled modes. (4) The fluid viscosity contributes significantly to damping, in particular, the modal damping of the out-of-phase modes isrelatively large for small gaps. (5) If the fluid gap is small, or the fluid viscosity is relatively high, the simulation of the vibration Reynolds number should be included to ensure that modal damping of the model is properly accounted for. With the presented analysis and results, the frequency and damping characteristics can be analyzed and design parameters can be related to frequency and damping

  16. Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation

    OpenAIRE

    GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

    2016-01-01

    This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...

  17. On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

    Energy Technology Data Exchange (ETDEWEB)

    Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo; Aloy, Miguel-Ángel [Departamento de Astronomía y Astrofísica, Universidad de Valencia, C/Dr. Moliner 50, E-46100 Burjassot (Spain); Müller, Ewald, E-mail: tomasz.rembiasz@uv.es [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)

    2017-06-01

    We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.

  18. Thermal radiation influence on MHD flow of a rotating fluid with heat transfer through EFGM solutions

    Science.gov (United States)

    Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa

    2018-05-01

    The aim of this research work is to find the EFGM solutions of the unsteady magnetohydromagnetic natural convection heat transfer flow of a rotating, incompressible, viscous, Boussinesq fluid is presented in this study in the presence of radiative heat transfer. The Rosseland approximation for an optically thick fluid is invoked to describe the radiative flux. Numerical results obtained show that a decrease in the temperature boundary layer occurs when the Prandtl number and the radiation parameter are increased and the flow velocity approaches steady state as the time parameter t is increased. These findings are in quantitative agreement with earlier reported studies.

  19. Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

    Science.gov (United States)

    Markou, A. A.; Manolis, G. D.

    2018-03-01

    Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

  20. Violations of conservation laws in viscous liquid dynamics

    DEFF Research Database (Denmark)

    Dyre, Jeppe

    2007-01-01

    The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover,......, although particle number conservation applies strictly for any liquid, the solidity of viscous liquids implies that even this conservation law is apparently violated in coarse-grained descriptions of density fluctuations.......The laws expressing conservation of momentum and energy apply to any isolated system, but these laws are violated for highly viscous liquids under laboratory conditions because of the unavoidable interactions with the measuring equipment over the long times needed to study the dynamics. Moreover...

  1. A three-dimensional viscous topography mesoscale model

    Energy Technology Data Exchange (ETDEWEB)

    Eichhorn, J; Flender, M; Kandlbinder, T; Panhans, W G; Trautmann, T; Zdunkowski, W G [Mainz Univ. (Germany). Inst. fuer Physik der Atmosphaere; Cui, K; Ries, R; Siebert, J; Wedi, N

    1997-11-01

    This study describes the theoretical foundation and applications of a newly designed mesoscale model named CLIMM (climate model Mainz). In contrast to terrain following coordinates, a cartesian grid is used to keep the finite difference equations as simple as possible. The method of viscous topography is applied to the flow part of the model. Since the topography intersects the cartesian grid cells, the new concept of boundary weight factors is introduced for the solution of Poisson`s equation. A three-dimensional radiosity model was implemented to handle radiative transfer at the ground. The model is applied to study thermally induced circulations and gravity waves at an idealized mountain. Furthermore, CLIMM was used to simulate typical wind and temperature distributions for the city of Mainz and its rural surroundings. It was found that the model in all cases produced realistic results. (orig.) 38 refs.

  2. Formulating viscous hydrodynamics for large velocity gradients

    International Nuclear Information System (INIS)

    Pratt, Scott

    2008-01-01

    Viscous corrections to relativistic hydrodynamics, which are usually formulated for small velocity gradients, have recently been extended from Navier-Stokes formulations to a class of treatments based on Israel-Stewart equations. Israel-Stewart treatments, which treat the spatial components of the stress-energy tensor τ ij as dynamical objects, introduce new parameters, such as the relaxation times describing nonequilibrium behavior of the elements τ ij . By considering linear response theory and entropy constraints, we show how the additional parameters are related to fluctuations of τ ij . Furthermore, the Israel-Stewart parameters are analyzed for their ability to provide stable and physical solutions for sound waves. Finally, it is shown how these parameters, which are naturally described by correlation functions in real time, might be constrained by lattice calculations, which are based on path-integral formulations in imaginary time

  3. Modelling and numerical simulation of liquid-vapor phase transitions

    International Nuclear Information System (INIS)

    Caro, F.

    2004-11-01

    This work deals with the modelling and numerical simulation of liquid-vapor phase transition phenomena. The study is divided into two part: first we investigate phase transition phenomena with a Van Der Waals equation of state (non monotonic equation of state), then we adopt an alternative approach with two equations of state. In the first part, we study the classical viscous criteria for selecting weak solutions of the system used when the equation of state is non monotonic. Those criteria do not select physical solutions and therefore we focus a more recent criterion: the visco-capillary criterion. We use this criterion to exactly solve the Riemann problem (which imposes solving an algebraic scalar non linear equation). Unfortunately, this step is quite costly in term of CPU which prevent from using this method as a ground for building Godunov solvers. That is why we propose an alternative approach two equations of state. Using the least action principle, we propose a phase changing two-phase flow model which is based on the second thermodynamic principle. We shall then describe two equilibrium submodels issued from the relaxations processes when instantaneous equilibrium is assumed. Despite the weak hyperbolicity of the last sub-model, we propose stable numerical schemes based on a two-step strategy involving a convective step followed by a relaxation step. We show the ability of the system to simulate vapor bubbles nucleation. (author)

  4. assessment of concentration of air pollutants using analytical and numerical solution of the atmospheric diffusion equation

    International Nuclear Information System (INIS)

    Esmail, S.F.H.

    2011-01-01

    The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.

  5. Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

    Science.gov (United States)

    Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

    2013-08-01

    Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

  6. Solidity of viscous liquids

    DEFF Research Database (Denmark)

    Dyre, Jeppe

    1999-01-01

    Recent NMR experiments on supercooled toluene and glycerol by Hinze and Böhmer show that small rotation angles dominate with only a few large molecular rotations. These results are here interpreted by assuming that viscous liquids are solidlike on short length scales. A characteristic length...

  7. Application of a space-time CE/SE (Conversation Element/Solution Element) method to the numerical solution of chromatographic separation processes

    DEFF Research Database (Denmark)

    including convection-difmsion-reaction PDEs are numerically solved using the two methods on the same spatial grid. Even though the CE/SE method uses a simple stencil structure and is developed on a simple mathematical basis (i.e., Gauss' divergence theorem), accurate and computationally-efficient solutions...

  8. A note on numerical solution to the problem of criticality

    International Nuclear Information System (INIS)

    Kyncl, J.

    2002-01-01

    The contribution deals with numerical solution to the problem of criticality for neutron transport equation by the external source iteration method. Especially, the speed of convergence is examined. It is shown that if neutron absorption in the medium considered is high and if the space region occupied by the medium is large then a slow convergence of the iterations can be expected. This expectation is confirmed by results to CB4 benchmark obtained by MCNP code. Besides the results presented some questions concerning applications of them to criticality calculations are pointed out (Author)

  9. Nonlinear electrorheological instability of two Rivlin-Ericksen elastico-viscous fluids

    CERN Document Server

    El-Dib, Y O

    2003-01-01

    The behaviour of surface waves propagating between two Rivlin-Ericksen elastico-viscous fluids is examined. The investigation is made in the presence of a vertical electric field and a relative horizontal constant velocity. The influence of both surface tension and gravity force is taken into account. Due to the inclusion of streaming flow a mathematical simplification is considered. The viscoelastic contribution is demonstrated in the boundary conditions. From this point of view the approximation equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion under nonlinear boundary conditions lead to derivation of a nonlinear equation governing the interfacial displacement and having damping terms with complex coefficients. This equation is accomplished by utilizing the cubic nonlinearity. The use of the Gardner-Morikawa transformation yields a simplified linear dispersion relation so that the periodic solution for the linear form is utilized. The ...

  10. Use of Green's functions in the numerical solution of two-point boundary value problems

    Science.gov (United States)

    Gallaher, L. J.; Perlin, I. E.

    1974-01-01

    This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

  11. Initial value problem for Rayleigh--Taylor instability of viscous fluids

    International Nuclear Information System (INIS)

    Menikoff, R.; Mjolsness, R.C.; Sharp, D.H.; Zemach, C.; Doyle, B.J.

    1978-01-01

    The initial value problem associated with the development of small amplitude disturbances in Rayleigh--Taylor unstable, viscous, incompressible fluids is studied. Solutions to the linearized equations of motion which satisfy general initial conditions are obtained in terms of Fourier--Laplace transforms of the hydrodynamic variables, without restriction on the density or viscosity of either fluid. When the two fluids have equal kinematic viscosities, these transforms can be inverted explicitly to express the fluid variables as integrals of Green's functions multiplied by initial data. In addition to normal modes, a set of continuum modes, not treated explicitly in the literature, makes an important contribution to the development of the fluid motion

  12. Quasi-Simultaneous Viscous-Inviscid Interaction for Transonic Airfoil Flow

    NARCIS (Netherlands)

    Veldman, Arthur E.P.

    2005-01-01

    Following Prandtl, a viscous-inviscid interaction (VII) method is presented, where the flow field is divided into a viscous shear layer and an inviscid outer region. Their coupling is performed with the quasi-simultaneous approach, making use of an appropriately chosen interaction law. Firstly, an

  13. Transient forced convection with viscous dissipation to power-law fluids in thermal entrance region of circular ducts with constant wall heat flux

    International Nuclear Information System (INIS)

    Dehkordi, Asghar Molaei; Mohammadi, Ali Asghar

    2009-01-01

    A numerical investigation was conducted on the transient behavior of a hydrodynamically, fully developed, laminar flow of power-law fluids in the thermally developing entrance region of circular ducts taking into account the effect of viscous dissipation but neglecting the effect of axial conduction. In this regard, the unsteady state thermal energy equation was solved by using a finite difference method, whereas the steady state thermal energy equation without wall heat flux was solved analytically as the initial condition of the former. The effects of the power-law index and wall heat flux on the local Nusselt number and thermal entrance length were investigated. Moreover, the local Nusselt number of steady state conditions was correlated in terms of the power-law index and wall heat flux and compared with literature data, which were obtained by an analytic solution for Newtonian fluids. Furthermore, a relationship was proposed for the thermal entrance length

  14. Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

    Science.gov (United States)

    Alfonso, Lester; Zamora, Jose; Cruz, Pedro

    2015-04-01

    The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

  15. Self-Similar Solutions for Viscous and Resistive Advection ...

    Indian Academy of Sciences (India)

    2016-01-27

    Jan 27, 2016 ... In this paper, self-similar solutions of resistive advection dominated accretion flows (ADAF) in the presence of a pure azimuthal magnetic field are investigated. The mechanism of energy dissipation is assumed to be the viscosity and the magnetic diffusivity due to turbulence in the accretion flow.

  16. Turbulence and turbulent drag reduction in swirling flow: Inertial versus viscous forcing.

    Science.gov (United States)

    Burnishev, Yuri; Steinberg, Victor

    2015-08-01

    We report unexpected results of a drastic difference in the transition to fully developed turbulent and turbulent drag reduction (TDR) regimes and in their properties in a von Karman swirling flow with counter-rotating disks of water-based polymer solutions for viscous (by smooth disks) as well as inertial (by bladed disks) forcing and by tracking just torque Γ(t) and pressure p(t) . For the viscous forcing, just a single TDR regime is found with the transition values of the Reynolds number (Re) Re turb c =Re TDR c ≃(4.8±0.2)×10(5) independent of ϕ , whereas for the inertial forcing two turbulent regimes are revealed. The first transition is to fully developed turbulence, and the second one is to the TDR regime with both Re turb c and Re TDR c depending on polymer concentration ϕ . Both regimes differ by the values of C f and C p , by the scaling exponents of the fundamental turbulent characteristics, by the nonmonotonic dependencies of skewness and flatness of the pressure PDFs on Re, and by the different frequency power spectra of p with the different dependencies of the main vortex peak frequency in the p power spectra on ϕ and Re. Thus our experimental results show the transition to the TDR regime in a von Karman swirling flow for the viscous and inertial forcings in a sharp contrast to the recent experiments [Phys. Fluids 10, 426 (1998); Phys. Rev. E 47, R28(R) (1993); and J. Phys.: Condens. Matter 17, S1195 (2005)] where the transition to TDR is observed in the same swirling flow with counter-rotating disks only for the viscous forcing. The latter result has led its authors to the wrong conclusion that TDR is a solely boundary effect contrary to the inertial forcing associated with the bulk effect, and this conception is currently rather widely accepted in literature.

  17. Numerical simulation of the RISOe1-airfoil dynamic stall

    Energy Technology Data Exchange (ETDEWEB)

    Bertagnolio, F.; Soerensen, N. [Risoe National Lab., Wind Energy and Atmospheric Physics Dept., Roskilde (Denmark)

    1997-12-31

    In this paper we are concerned with the numerical computation of the dynamic stall that occur in the viscous flowfield over an airfoil. These results are compared to experimental data that were obtained with the new designed RISOe1-airfoil, both for a motionless airfoil and for a pitching motion. Moreover, we present some numerical computations of the plunging and lead-lag motions. We also investigate the possibility of using the pitching motion to simulate the plunging and lead-lag situations. (au)

  18. Electrohydrodynamics of a viscous drop with inertia.

    Science.gov (United States)

    Nganguia, H; Young, Y-N; Layton, A T; Lai, M-C; Hu, W-F

    2016-05-01

    Most of the existing numerical and theoretical investigations on the electrohydrodynamics of a viscous drop have focused on the creeping Stokes flow regime, where nonlinear inertia effects are neglected. In this work we study the inertia effects on the electrodeformation of a viscous drop under a DC electric field using a novel second-order immersed interface method. The inertia effects are quantified by the Ohnesorge number Oh, and the electric field is characterized by an electric capillary number Ca_{E}. Below the critical Ca_{E}, small to moderate electric field strength gives rise to steady equilibrium drop shapes. We found that, at a fixed Ca_{E}, inertia effects induce larger deformation for an oblate drop than a prolate drop, consistent with previous results in the literature. Moreover, our simulations results indicate that inertia effects on the equilibrium drop deformation are dictated by the direction of normal electric stress on the drop interface: Larger drop deformation is found when the normal electric stress points outward, and smaller drop deformation is found otherwise. To our knowledge, such inertia effects on the equilibrium drop deformation has not been reported in the literature. Above the critical Ca_{E}, no steady equilibrium drop deformation can be found, and often the drop breaks up into a number of daughter droplets. In particular, our Navier-Stokes simulations show that, for the parameters we use, (1) daughter droplets are larger in the presence of inertia, (2) the drop deformation evolves more rapidly compared to creeping flow, and (3) complex distribution of electric stresses for drops with inertia effects. Our results suggest that normal electric pressure may be a useful tool in predicting drop pinch-off in oblate deformations.

  19. Null controllability of the viscous Camassa–Holm equation with ...

    Indian Academy of Sciences (India)

    In this paper, we study the null controllability of the viscous Camassa–. Holm equation on the one-dimensional torus. By using a moving distributed control, we obtain that the system is null controllable for a given data with certain regularity. Keywords. Viscous Camassa–Holm equation; null controllability; moving control;.

  20. 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.

  1. Hall current and Joule heating effects on peristaltic flow of viscous fluid in a rotating channel with convective boundary conditions

    Directory of Open Access Journals (Sweden)

    Tasawar Hayat

    Full Text Available The present article has been arranged to study the Hall current and Joule heating effects on peristaltic flow of viscous fluid in a channel with flexible walls. Both fluid and channel are in a state of solid body rotation. Convective conditions for heat transfer in the formulation are adopted. Viscous dissipation in energy expression is taken into account. Resulting differential systems after invoking small Reynolds number and long wavelength considerations are numerically solved. Runge-Kutta scheme of order four is implemented for the results of axial and secondary velocities, temperature and heat transfer coefficient. Comparison with previous limiting studies is shown. Outcome of new parameters of interest is analyzed. Keywords: Rotating frame, Hall current, Joule heating, Convective conditions, Wall properties

  2. One-dimensional reduction of viscous jets. I. Theory

    Science.gov (United States)

    Pitrou, Cyril

    2018-04-01

    We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model whose sections are circular. However, when including the first corrections, we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model since it amounts to selectively discard some corrections. However, in a fast rotating frame, we find that the dominant effects induced by inertial and Coriolis forces should be correctly described by rod models. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as xAct, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018), 10.1103/PhysRevE.97.043116].

  3. Kaluza-Klein Bulk Viscous Fluid Cosmological Models and the Validity of the Second Law of Thermodynamics in f(R, T) Gravity

    Science.gov (United States)

    Samanta, Gauranga Charan; Myrzakulov, Ratbay; Shah, Parth

    2017-04-01

    The authors considered the bulk viscous fluid in f(R, T) gravity within the framework of Kaluza-Klein space time. The bulk viscous coefficient (ξ) expressed as ξ = {ξ_0} + {ξ_1}{{\\dot a} \\over a} + {ξ_2}{{\\ddot a} \\over {\\dot a}}, where ξ0, ξ1, and ξ2 are positive constants. We take p=(γ-1)ρ, where 0≤γ≤2 as an equation of state for perfect fluid. The exact solutions to the corresponding field equations are given by assuming a particular model of the form of f(R, T)=R+2f(T), where f(T)=λT, λ is constant. We studied the cosmological model in two stages, in first stage: we studied the model with no viscosity, and in second stage: we studied the model involve with viscosity. The cosmological model involve with viscosity is studied by five possible scenarios for bulk viscous fluid coefficient (ξ). The total bulk viscous coefficient seems to be negative, when the bulk viscous coefficient is proportional to {ξ _2}{{\\ddot a} \\over {\\dot a}}, hence, the second law of thermodynamics is not valid; however, it is valid with the generalised second law of thermodynamics. The total bulk viscous coefficient seems to be positive, when the bulk viscous coefficient is proportional to ξ = {ξ _1}{{\\dot a} \\over a} + {ξ _2}{{\\ddot a} \\over {\\dot a}} and ξ = {ξ _0} + {ξ _1}{{\\dot a} \\over a} + {ξ _2}{{\\ddot a} \\over {\\dot a}}, so the second law of thermodynamics and the generalised second law of thermodynamics is satisfied throughout the evolution. We calculate statefinder parameters of the model and observed that it is different from the ∧CDM model. Finally, some physical and geometrical properties of the models are discussed.

  4. Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

    International Nuclear Information System (INIS)

    Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

    2007-01-01

    We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic

  5. Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

    Science.gov (United States)

    Ikeguchi, Mitsunori; Doi, Junta

    1995-09-01

    The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

  6. Numerical solution of ordinary differential equations

    CERN Document Server

    Fox, L

    1987-01-01

    Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...

  7. Simulations of the Yawed MEXICO Rotor Using a Viscous-Inviscid Panel Method

    DEFF Research Database (Denmark)

    Ramos García, Néstor; Sørensen, Jens Nørkær; Shen, Wen Zhong

    2014-01-01

    In the present work the viscous-inviscid interactive model MIRAS is used to simulate flows past the MEXICO rotor in yawed conditions. The solver is based on an unsteady three-dimensional free wake panel method which uses a strong viscous-inviscid interaction technique to account for the viscous...

  8. Surface perturbations of a shallow viscous fluid heated from below and the (2+1)-dimensional Burgers equation

    International Nuclear Information System (INIS)

    Kraenkel, R.A.; Pereira, J.G.; Manna, M.A.

    1991-01-01

    The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)

  9. Viscous-shock-layer solutions with coupled radiation and ablation injection for earth entry

    Science.gov (United States)

    Gupta, Roop N.; Lee, Kam-Pui; Moos, James N.; Sutton, Kenneth

    1990-01-01

    Results are obtained for the forebody of a planetary exploration vehicle entering the earth's atmosphere. A viscous-shock-layer analysis is used assuming the flow to be laminar and in chemical equilibrium. Presented results include coupled radiation and ablation injection. This study further includes the effect of different transport and thermodynamic properties and radiation models. A Lewis number of 1.4 appears adequate for the radiation-dominated flows. Five velocities corresponding to different possible trajectory points at an altitude of 70 km have been further analyzed in detail. Sublimation and radiative equilibrium wall temperatures are employed for cases with and without coupled injection, respectively. For the cases analyzed here, the mass injection rates are small. However, the rates could become large if a lower altitude is used for aerobraking and/or the body size is increased. A comparison of the equilibrium results with finite-rate chemistry calculation shows the flowfield to be in chemical equilibrium.

  10. Magnetohydrodynamic mixed convective slip flow over an inclined porous plate with viscous dissipation and Joule heating

    Directory of Open Access Journals (Sweden)

    S. Das

    2015-06-01

    Full Text Available The combined effects of viscous dissipation and Joule heating on the momentum and thermal transport for the magnetohydrodynamic flow past an inclined plate in both aiding and opposing buoyancy situations have been carried out. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and the rate of heat transfer at the plate. The results show that there are significant effects of pertinent parameters on the flow fields.

  11. Numerical solution of the Schroedinger equation with a polynomial potential

    International Nuclear Information System (INIS)

    Campoy, G.; Palma, A.

    1986-01-01

    A numerical method for solving the Schroedinger equation for a potential expressed as a polynomial is proposed. The basic assumption relies on the asymptotic properties of the solution of this equation. It is possible to obtain the energies and the stationary state functions simultaneously. They analyze, in particular, the cases of the quartic anharmonic oscillator and a hydrogen atom perturbed by a quadratic term, obtaining its energy eigenvalues for some values of the perturbation parameter. Together with the Hellmann-Feynman theorem, they use their algorithm to calculate expectation values of x'' for arbitrary positive values of n. 4 tables

  12. Long-time behavior in numerical solutions of certain dynamical systems

    International Nuclear Information System (INIS)

    Vazquez, L.

    1987-01-01

    A general discretization of the ordinary nonlinear differential equations d 2 v/dt 2 =f(v) and dv/dt=g(v) is studied. The discrete scheme conserves the discrete analogous of a quantity that is conserved by the corresponding equations. This method is applied to two cases and no ''ghost solutions'' were observed for the long range calculation. In these cases we analyze the stability of the corresponding numerical scheme as a dynamical system and in the sense studied by Kuo Pen-Yu and Stetter. In particular we find a correspondence between both kinds of stability. (author)

  13. Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

    Directory of Open Access Journals (Sweden)

    Roman Cherniha

    2016-06-01

    Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.

  14. Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark’s Method with Netwon-Raphson Iteration Revisited

    Directory of Open Access Journals (Sweden)

    Markou A.A.

    2018-03-01

    Full Text Available Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

  15. Model of an electric field produced by viscous interaction in the plasma sheet of the magnetotail

    International Nuclear Information System (INIS)

    Erkaev, N.V.

    1996-01-01

    Two-dimensional model of flow in a plasma layer of magnetotail is considered with account of low viscosity. The general Ohm's law is used for electric current. The role of viscous forces is most sufficient in boundary layers, which expand with moving away along the flow and located along the boundaries of plasma layer and solar wind. Auto model solution, describing the distribution of potential and velocity in boundary layers was obtained. The solution for boundary layers dictates boundary conditions for determination of large-scale distribution of electric potential in plasma layer. 7 refs., 4 figs

  16. WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

    Science.gov (United States)

    Crevoisier, David; Voltz, Marc

    2013-04-01

    To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute

  17. LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION

    Directory of Open Access Journals (Sweden)

    Decio Levi

    2013-10-01

    Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.

  18. Thermal development of the laminar flow of a Bingham fluid between two plane plates with viscous dissipation

    Energy Technology Data Exchange (ETDEWEB)

    Boualit, A.; Boualit, S. [Unite de recherche appliquee en energies renouvelables, Ghardaia (Algeria); Zeraibi, N. [Universite de Boumerdes, Faculte des hydrocarbures dept. Transport et equipement, Boumerdes (Algeria); Amoura, M. [Universite des Sciences et de la Technologie Houari Boumedienne, Faculte de Physique, Dept. Energetique, Alger (Algeria)

    2011-01-15

    The thermal development of the hydrodynamically developing laminar flow of a viscoplastic fluid (fluid of Bingham) between two plane plates maintained at a constant temperature has been studied numerically. This analysis has shown the effect caused by inertia and the rheological behaviour of the fluid on the velocity, pressure and temperature fields. The effects of Bingham and Peclet numbers on the Nusselt values with the inclusion of viscous dissipation are also discussed. (authors)

  19. The application of finite element method for mhd viscous flow over a porous stretching sheet

    International Nuclear Information System (INIS)

    Mahmood, R.; Sajid, M.

    2007-01-01

    This work is concerned with the magnetohydrodynamic (MHD) viscous flow due to a porous stretching sheet. The similarity solution of the problem is obtained using finite element method. The physical quantities of interest like the fluid velocity and skin friction coefficient is obtained and discussed under the influence of suction parameter and Hartman number. It is evident from the results that MHD can be used to control the boundary layer thickness. (author)

  20. Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

    Science.gov (United States)

    Fikri, Fariz Fahmi; Nuraini, Nuning

    2018-03-01

    The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

  1. Analytical and numerical investigation of trolleybus vertical dynamics on an artificial test track

    Directory of Open Access Journals (Sweden)

    Polach P.

    2009-12-01

    Full Text Available Two virtual models of the ŠKODA 21 Tr low-floor trolleybus intended for the investigation of vertical dynamic properties during the simulation of driving on an uneven road surface are presented in the article. In order to solve analytically vertical vibrations, the trolleybus model formed by the system of four rigid bodies with seven degrees of freedom coupled by spring-damper elements is used. The influence of the asymmetry of a sprung mass, a linear viscous damping and a general kinematic excitation of wheels are incorporated in the model. The analytical approach to solving the ŠKODA 21 Tr low-floor trolleybus model vibrations is a suitable complement of the model based on a numerical solution. Vertical vibrations are numerically solved on the trolleybus multibody model created in the alaska simulation tool. Both virtual trolleybus models are used for the simulations of driving on the track composed of vertical obstacles. Conclusion concerning the effects of the usage of the linear and the nonlinear spring-damper elements characteristics are also given.

  2. Viscous fingering of HCI through gastric mucin

    Science.gov (United States)

    Bhaskar, K. Ramakrishnan; Garik, Peter; Turner, Bradley S.; Bradley, James Douglas; Bansil, Rama; Stanley, H. Eugene; Lamont, J. Thomas

    1992-12-01

    THE HCI in the mammalian stomach is concentrated enough to digest the stomach itself, yet the gastric epithelium remains undamaged. One protective factor is gastric mucus, which forms a protective layer over the surface epithelium1-4 and acts as a diffusion barrier5,6 Bicarbonate ions secreted by the gastric epithelium7 are trapped in the mucus gel, establishing a gradient from pH 1-2 at the lumen to pH 6-7 at the cell surface8-10. How does HCI, secreted at the base of gastric glands by parietal cells, traverse the mucus layer without acidifying it? Here we demonstrate that injection of HCI through solutions of pig gastric mucin produces viscous fingering patterns11-18 dependent on pH, mucin concentration and acid flow rate. Above pH 4, discrete fingers are observed, whereas below pH 4, HCI neither penetrates the mucin solution nor forms fingers. Our in vitro results suggest that HCI secreted by the gastric gland can penetrate the mucus gel layer (pH 5-7) through narrow fingers, whereas HC1 in the lumen (pH 2) is prevented from diffusing back to the epithelium by the high viscosity of gastric mucus gel on the luminal side.

  3. Bulk viscous matter-dominated Universes: asymptotic properties

    Energy Technology Data Exchange (ETDEWEB)

    Avelino, Arturo [Departamento de Física, Campus León, Universidad de Guanajuato, León, Guanajuato (Mexico); García-Salcedo, Ricardo [Centro de Investigacion en Ciencia Aplicada y Tecnologia Avanzada - Legaria del IPN, México D.F. (Mexico); Gonzalez, Tame [Departamento de Ingeniería Civil, División de Ingeniería, Universidad de Guanajuato, Guanajuato (Mexico); Nucamendi, Ulises [Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Ciudad Universitaria, CP. 58040 Morelia, Michoacán (Mexico); Quiros, Israel, E-mail: avelino@fisica.ugto.mx, E-mail: rigarcias@ipn.mx, E-mail: tamegc72@gmail.com, E-mail: ulises@ifm.umich.mx, E-mail: iquiros6403@gmail.com [Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Corregidora 500 S.R., Universidad de Guadalajara, 44420 Guadalajara, Jalisco (Mexico)

    2013-08-01

    By means of a combined use of the type Ia supernovae and H(z) data tests, together with the study of the asymptotic properties in the equivalent phase space — through the use of the dynamical systems tools — we demonstrate that the bulk viscous matter-dominated scenario is not a good model to explain the accepted cosmological paradigm, at least, under the parametrization of bulk viscosity considered in this paper. The main objection against such scenarios is the absence of conventional radiation and matter-dominated critical points in the phase space of the model. This entails that radiation and matter dominance are not generic solutions of the cosmological equations, so that these stages can be implemented only by means of unique and very specific initial conditions, i. e., of very unstable particular solutions. Such a behavior is in marked contradiction with the accepted cosmological paradigm which requires of an earlier stage dominated by relativistic species, followed by a period of conventional non-relativistic matter domination, during which the cosmic structure we see was formed. Also, we found that the bulk viscosity is positive just until very late times in the cosmic evolution, around z < 1. For earlier epochs it is negative, been in tension with the local second law of thermodynamics.

  4. Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta

    Directory of Open Access Journals (Sweden)

    Andresa Pescador

    2016-04-01

    Full Text Available This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.

  5. A mass conservative numerical solution of vertical water flow and mass transport equations in unsaturated porous media

    International Nuclear Information System (INIS)

    Lim, S.C.; Lee, K.J.

    1993-01-01

    The Galerkin finite element method is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solutes in unsaturated porous media. Numerical approximations based on different forms of the governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in an unsaturated flow problem. Solutions given by a simple Galerkin method based on the h-based Richards equation yield a large mass balance error and an underestimation of the infiltration depth. With the employment of the ROMV (restoration of main variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV method shows good mass conservation in water flow analysis, whereas it seems to have a minor effect on mass transport. However, it may relax the time-step size restriction and so ensure an improved calculation output. (author)

  6. Viscous fingering with permeability heterogeneity

    International Nuclear Information System (INIS)

    Tan, C.; Homsy, G.M.

    1992-01-01

    Viscous fingering in miscible displacements in the presence of permeability heterogeneities is studied using two-dimensional simulations. The heterogeneities are modeled as stationary random functions of space with finite correlation scale. Both the variance and scale of the heterogeneities are varied over modest ranges. It is found that the fingered zone grows linearly in time in a fashion analogous to that found in homogeneous media by Tan and Homsy [Phys. Fluids 31, 1330 (1988)], indicating a close coupling between viscous fingering on the one hand and flow through preferentially more permeable paths on the other. The growth rate of the mixing zone increases monotonically with the variance of the heterogeneity, as expected, but shows a maximum as the correlation scale is varied. The latter is explained as a ''resonance'' between the natural scale of fingers in homogeneous media and the correlation scale

  7. Different nonideality relationships, different databases and their effects on modeling precipitation from concentrated solutions using numerical speciation codes

    Energy Technology Data Exchange (ETDEWEB)

    Brown, L.F.; Ebinger, M.H.

    1996-08-01

    Four simple precipitation problems are solved to examine the use of numerical equilibrium codes. The study emphasizes concentrated solutions, assumes both ideal and nonideal solutions, and employs different databases and different activity-coefficient relationships. The study uses the EQ3/6 numerical speciation codes. The results show satisfactory material balances and agreement between solubility products calculated from free-energy relationships and those calculated from concentrations and activity coefficients. Precipitates show slightly higher solubilities when the solutions are regarded as nonideal than when considered ideal, agreeing with theory. When a substance may precipitate from a solution dilute in the precipitating substance, a code may or may not predict precipitation, depending on the database or activity-coefficient relationship used. In a problem involving a two-component precipitation, there are only small differences in the precipitate mass and composition between the ideal and nonideal solution calculations. Analysis of this result indicates that this may be a frequent occurrence. An analytical approach is derived for judging whether this phenomenon will occur in any real or postulated precipitation situation. The discussion looks at applications of this approach. In the solutes remaining after the precipitations, there seems to be little consistency in the calculated concentrations and activity coefficients. They do not appear to depend in any coherent manner on the database or activity-coefficient relationship used. These results reinforce warnings in the literature about perfunctory or mechanical use of numerical speciation codes.

  8. Dynamically Adapted Mesh Construction for the Efficient Numerical Solution of a Singular Perturbed Reaction-diffusion-advection Equation

    Directory of Open Access Journals (Sweden)

    Dmitry V. Lukyanenko

    2017-01-01

    Full Text Available This  work develops  a theory  of the  asymptotic-numerical investigation of the  moving fronts  in reaction-diffusion-advection models.  By considering  the  numerical  solution  of the  singularly perturbed Burgers’s  equation  we discuss a method  of dynamically  adapted mesh  construction that is able to significantly  improve  the  numerical  solution  of this  type of equations.  For  the  construction we use a priori information that is based  on the  asymptotic analysis  of the  problem.  In  particular, we take  into account the information about  the speed of the transition layer, its width  and structure. Our algorithms  are able to reduce significantly complexity and enhance stability of the numerical  calculations in comparison  with classical approaches for solving this class of problems.  The numerical  experiment is presented to demonstrate the effectiveness of the proposed  method.The article  is published  in the authors’  wording. 

  9. Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

    Directory of Open Access Journals (Sweden)

    SURE KÖME

    2014-12-01

    Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

  10. Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

    Science.gov (United States)

    D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

    2018-05-01

    In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

  11. Urease Plays an Important Role in the Chemotactic Motility of Helicobacter pylori in a Viscous Environment

    OpenAIRE

    Nakamura, Hiroki; Yoshiyama, Hironori; Takeuchi, Hiroaki; Mizote, Tomoko; Okita, Kiwamu; Nakazawa, Teruko

    1998-01-01

    Helicobacter pylori exhibits chemotactic responses to urea, flurofamide, acetohydroxamic acid, and sodium bicarbonate. In buffer, the chemotactic activities of a urease-positive strain were higher than those of the isogenic urease-negative strain. Moreover, the chemotactic activities of the urease-positive strain were increased in a viscous solution containing 3% polyvinylpyrrolidone, whereas those of the urease-negative mutant were not. These results are in accordance with the fact that the ...

  12. Viscous fingering effects in solvent displacement of heavy oil

    Energy Technology Data Exchange (ETDEWEB)

    Cuthiell, D. [Suncor Energy, Fort McMurray, AB (Canada); Kissel, G.; Jackson, C.; Frauenfeld, T.W.J.; Fisher, D. [Alberta Research Council, Devon, AB (Canada); Rispler, K. [Saskatchewan Research Council, Saskatoon, SK (Canada)

    2004-07-01

    Vapour Extraction (VAPEX) is a solvent-based process that is analogous to steam-assisted gravity drainage (SAGD) for the recovery of heavy oil. A cyclic solvent process is preferred for thin reservoirs, particularly primary-depleted reservoirs. In a cyclic steam stimulation process, a solvent is injected into the reservoir for a period of time before oil is produced from the well. Viscous fingering is a phenomena that characterizes several solvent-based processes for the recovery of heavy oil. A combined experimental and simulation study was conducted to characterize viscous fingering under heavy oil recovery conditions (high ratio of oil to solvent viscosity). Four experiments were conducted in heavy oil-saturated sand packs. Three involved injection of a miscible, liquid solvent at the bottom of the sand pack. The heavy oil in these experiments was displaced upwardly. The fourth experiment involved top-down injection of a gaseous solvent. The miscible liquid displacement was dominated by one solvent finger which broke through to a producing well at the other end of the sand pack. Breakthrough times were similar to that at lower viscosity. The fourth experiment showed fingering along with features of a gravity-driven VAPEX process. Key features of the experiment and realistic fingering patterns were numerically simulated using a commercial reservoir simulator. It was emphasized that accurate modelling of dispersion is necessary in matching the observed phenomena. The simulations should include the capillary effects because of their significance for gaseous fingering and the VAPEX processes. 17 refs., 2 tabs., 20 figs.

  13. Multiresolution strategies for the numerical solution of optimal control problems

    Science.gov (United States)

    Jain, Sachin

    There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a

  14. Numerical analysis

    CERN Document Server

    Rao, G Shanker

    2006-01-01

    About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...

  15. Effect of viscous dissipation and radiation in an annular cone

    International Nuclear Information System (INIS)

    Ahmed, N. J. Salman; Kamangar, Sarfaraz; Khan, T. M. Yunus; Azeem

    2016-01-01

    The viscous dissipation is an effect due to which heat is generated inside the medium. The presence of radiation further complicates the heat transfer behavior inside porous medium. The present paper discusses the combined effect of viscous dissipation and radiation inside a porous medium confined in an annular cone with inner radius r_i. The viscous dissipation and radiation terms are included in the energy equation thereby solving the coupled momentum and energy equations with the help of finite element method. The results are presented in terms of isothermal and streamline indicating the thermal and fluid flow behavior of porous medium. It is found that the combination of viscous dissipation and radiation parameter and the cone angle has significant effect on the heat transfer and fluid flow behavior inside the porous medium. The fluid velocity is found to increase with the increase in Raleigh number

  16. Effect of viscous dissipation and radiation in an annular cone

    Energy Technology Data Exchange (ETDEWEB)

    Ahmed, N. J. Salman; Kamangar, Sarfaraz [Centre for Energy Sciences, Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 Malaysia (Malaysia); Khan, T. M. Yunus, E-mail: yunus.tatagar@gmail.com [Centre for Energy Sciences, Dept. of Mechanical Engineering, University of Malaya, Kuala Lumpur, 50603 Malaysia (Malaysia); Dept. of Mechanical Engineering, BVB College of Engineering & Technology, Hubli (India); Azeem [Dept. of Computer System & Technology, University of Malaya, Kuala Lumpur (Malaysia)

    2016-06-21

    The viscous dissipation is an effect due to which heat is generated inside the medium. The presence of radiation further complicates the heat transfer behavior inside porous medium. The present paper discusses the combined effect of viscous dissipation and radiation inside a porous medium confined in an annular cone with inner radius r{sub i}. The viscous dissipation and radiation terms are included in the energy equation thereby solving the coupled momentum and energy equations with the help of finite element method. The results are presented in terms of isothermal and streamline indicating the thermal and fluid flow behavior of porous medium. It is found that the combination of viscous dissipation and radiation parameter and the cone angle has significant effect on the heat transfer and fluid flow behavior inside the porous medium. The fluid velocity is found to increase with the increase in Raleigh number.

  17. Numerical study for Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions

    Directory of Open Access Journals (Sweden)

    Tasawar Hayat

    Full Text Available The current investigation presents Darcy-Forchheimer flow of viscous fluid caused by a curved stretching sheet. Flow for porous space is characterized by Darcy-Forchheimer relation. Concept of homogeneous and heterogeneous reactions is also utilized. Heat transfer for Cattaneo–Christov theory characterizing the feature of thermal relaxation is incorporated. Nonlinear differential systems are derived. Shooting algorithm is employed to construct the solutions for the resulting nonlinear system. The characteristics of various sundry parameters are studied and discussed. Skin friction coefficient and heat transfer rate are numerically described. Keywords: 2D flow, Curved stretching surface, Darcy-Forchheimer porous medium, Cattaneo-Christov heat flux, Homogeneous-heterogeneous reactions

  18. h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems

    Science.gov (United States)

    Botti, L.; Colombo, A.; Bassi, F.

    2017-10-01

    In this work we exploit agglomeration based h-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature h-coarsened mesh sequences are generated by recursive agglomeration of a fine grid, admitting arbitrarily unstructured grids of complex domains, and agglomeration based discontinuous Galerkin discretizations are employed to deal with agglomerated elements of coarse levels. Both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated. For the sake of efficiency coarse grid operators are inherited through element-by-element L2 projections, avoiding the cost of numerical integration over agglomerated elements. Specific care is devoted to the projection of viscous terms discretized by means of the BR2 dG method. We demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels. The numerical solution of steady and unsteady, linear and non-linear problems is considered tackling challenging 2D test cases and 3D real life computations on parallel architectures. Significant execution time gains are documented.

  19. Grad-Shafranov reconstruction: overview and improvement of the numerical solution used in space physics

    Energy Technology Data Exchange (ETDEWEB)

    Ojeda Gonzalez, A.; Domingues, M.O.; Mendes, O., E-mail: ojeda.gonzalez.a@gmail.com [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil); Kaibara, M.K. [Universidade Federal Fluminense (GMA/IME/UFF), Niteroi, RJ (Brazil); Prestes, A. [Universidade do Vale do Paraiba (IP and D/UNIVAP), Sao Jose dos Campos, SP (Brazil). Lab. de Fisica e Astronomia

    2015-10-15

    The Grad-Shafranov equation is a Poisson's equation, i.e., a partial differential equation of elliptic type. The problem is depending on the initial condition and can be treated as a Cauchy problem. Although it is ill-posed or ill-conditioned, it can be integrated numerically. In the integration of the GS equation, singularities with large values of the potential arise after a certain number of integration steps away from the original data line, and a filter should be used. The Grad-Shafranov reconstruction (GSR) technique was developed from 1996 to 2000 for recovering two-dimensional structures in the magnetopause in an ideal MHD formulation. Other works have used the GSR techniques to study magnetic flux ropes in the solar wind and in the magnetotail from a single spacecraft dataset; posteriorly, it was extended to treat measurements from multiple satellites. From Vlasov equation, it is possible to arrive at the GS-equation in function of the normalized vector potential. A general solution is obtained using complex variable theory. A specific solution was chosen as benchmark case to solve numerically the GS equation.We propose some changes in the resolution scheme of the GS equation to improve the solution. The result of each method is compared with the solution proposed by Hau and Sonnerup (J. Geophys. Res. 104(A4), 6899-6917 (1999)). The main improvement found in the GS resolution was the need to filter Bx values at each y value. (author)

  20. Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.

    Science.gov (United States)

    Esmaeeli, Hadi S; Farnam, Yaghoob; Bentz, Dale P; Zavattieri, Pablo D; Weiss, Jason

    2017-02-01

    This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained.

  1. Bulk viscous Zel'dovich fluid model and its asymptotic behavior

    Energy Technology Data Exchange (ETDEWEB)

    Nair, K.R.; Mathew, Titus K. [Cochin University of Science and Technology, Department of Physics, Kochi (India)

    2016-10-15

    In this paper we consider a flat FLRW universe with bulk viscous Zel'dovich fluid as the cosmic component. Considering the bulk viscosity as characterized by a constant bulk viscous coefficient, we analyze the evolution of the Hubble parameter. Type Ia Supernovae data is used for constraining the model and for extracting the constant bulk viscous parameter and present the Hubble parameter. We also present the analysis of the scale factor, equation of state, and deceleration parameter. The model predicts the later time acceleration and is also compatible with the age of the universe as given by the oldest globular clusters. Study of the phase-space behavior of the model shows that a universe dominated by bulk viscous Zel'dovich fluid is stable. But the inclusion of a radiation component in addition to the Zel'dovich fluid makes the model unstable. Hence, even though the bulk viscous Zel'dovich fluid dominated universe is a feasible one, the model as such fails to predict a prior radiation dominated phase. (orig.)

  2. Viscous dipping, application to the capture of fluids in living organisms

    Science.gov (United States)

    Lechantre, Amandine; Michez, Denis; Damman, Pascal

    Some insects, birds and mammals use flower nectar as their energy resources. For this purpose, they developed specific skills to ingest viscous fluids. Depending on the sugar content, i.e., the viscosity, different strategies are observed in vivo. Indeed, butterflies use simple suction for low viscosity nectars; hummingbirds have a tongue made from two thin flexible sheets that bend to form a tube when immersed in a fluid; other animals exhibit in contrast complex papillary structures. We focus on this last method generally used for very viscous nectars. More specifically, bees and bats possess a tongue decorated with microstructures that, according to biologists, would be optimized for fluid capture by viscous dipping. In this talk, we will discuss this assumption by comparing physical models of viscous dipping to in vivo measurements. To mimic the tongue morphology, we used various rod shapes obtained by 3D printing. The influence of the type and size of lateral microstructures was then investigated and used to build a global framework describing viscous dipping for structured rods/tongues.

  3. Coalescence of two equal cylinders: exact results for creeping viscous plane flow driven by capillarity

    International Nuclear Information System (INIS)

    Hopper, R.W.

    1984-01-01

    The coalescence of two equal viscous cylinders under the influence of capillarity is of interest in the theory of sintering. Although the flow in typical cylinder coalescence experiments is not planar, the plane-flow case is of general interest and is a good approximation in the early stage. An essentially exact analytic solution giving the shape as a function of time for slow plane flow is presented in simple closed form. 16 references, 2 figures, 1 table

  4. Viscous damping of toroidal angular momentum in tokamaks

    Energy Technology Data Exchange (ETDEWEB)

    Stacey, W. M. [Georgia Tech Fusion Research Center, Atlanta, Georgia 30332 (United States)

    2014-09-15

    The Braginskii viscous stress tensor formalism was generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry in order to provide a representation for the viscous damping of toroidal rotation in tokamaks arising from various “neoclassical toroidal viscosity” mechanisms. In the process, it was verified that the parallel viscosity contribution to damping toroidal angular momentum still vanishes even in the presence of toroidal asymmetries, unless there are 3D radial magnetic fields.

  5. Stokes’ and Lamb's viscous drag laws

    International Nuclear Information System (INIS)

    Eames, I; Klettner, C A

    2017-01-01

    Since Galileo used his pulse to measure the time period of a swinging chandelier in the 17th century, pendulums have fascinated scientists. It was not until Stokes' (1851 Camb. Phil. Soc. 9 8–106) (whose interest was spurred by the pendulur time pieces of the mid 19th century) treatise on viscous flow that a theoretical framework for the drag on a sphere at low Reynolds number was laid down. Stokes' famous drag law has been used to determine two fundamental physical constants—the charge on an electron and Avogadro's constant—and has been used in theories which have won three Nobel prizes. Considering its illustrious history it is then not surprising that the flow past a sphere and its two-dimensional analog, the flow past a cylinder, form the starting point of teaching flow past a rigid body in undergraduate level fluid mechanics courses. Usually starting with the two-dimensional potential flow past a cylinder, students progress to the three-dimensional potential flow past a sphere. However, when the viscous flow past rigid bodies is taught, the three-dimensional example of a sphere is first introduced, and followed by (but not often), the two-dimensional viscous flow past a cylinder. The reason why viscous flow past a cylinder is generally not taught is because it is usually explained from an asymptotic analysis perspective. In fact, this added mathematical complexity is why the drag on a cylinder was only solved in 1911, 60 years after the drag on a sphere. In this note, we show that the viscous flow past a cylinder can be explained without the need to introduce any asymptotic analysis while still capturing all the physical insight of this classic fluid mechanics problem. (paper)

  6. Thermal radiation from an evolving viscous quark gluon plasma

    International Nuclear Information System (INIS)

    Mitra, Sukanya; Mohanty, Payal; Sarkar, Sourav; Alam, Jan-E

    2013-01-01

    The effects of viscosity on the space-time evolution of quark gluon plasma produced in nuclear collisions at relativistic heavy ion collider energies have been studied. The entropy generated due to the viscous motion of the fluid has been taken into account in constraining the initial temperature by the final multiplicity (measured at the freeze-out point). The viscous effects on the photon spectra has been introduced consistently through the evolution dynamics and phase space factors of all the participating partons/hadrons in the production process. In contrast to some of the recent calculations the present work includes the contribution from the hadronic phase. A small change in the transverse momentum (p T ) distribution of photons is observed due to viscous effects. (author)

  7. A Blast Wave Model With Viscous Corrections

    International Nuclear Information System (INIS)

    Yang, Z; Fries, R J

    2017-01-01

    Hadronic observables in the final stage of heavy ion collision can be described well by fluid dynamics or blast wave parameterizations. We improve existing blast wave models by adding shear viscous corrections to the particle distributions in the Navier-Stokes approximation. The specific shear viscosity η/s of a hadron gas at the freeze-out temperature is a new parameter in this model. We extract the blast wave parameters with viscous corrections from experimental data which leads to constraints on the specific shear viscosity at kinetic freeze-out. Preliminary results show η/s is rather small. (paper)

  8. A Blast Wave Model With Viscous Corrections

    Science.gov (United States)

    Yang, Z.; Fries, R. J.

    2017-04-01

    Hadronic observables in the final stage of heavy ion collision can be described well by fluid dynamics or blast wave parameterizations. We improve existing blast wave models by adding shear viscous corrections to the particle distributions in the Navier-Stokes approximation. The specific shear viscosity η/s of a hadron gas at the freeze-out temperature is a new parameter in this model. We extract the blast wave parameters with viscous corrections from experimental data which leads to constraints on the specific shear viscosity at kinetic freeze-out. Preliminary results show η/s is rather small.

  9. Mathematical and numerical study of nonlinear hyperbolic equations: model coupling and nonclassical shocks

    International Nuclear Information System (INIS)

    Boutin, B.

    2009-11-01

    This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)

  10. 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.

  11. A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo in Natural Waters

    Science.gov (United States)

    Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

  12. Fully-developed heat transfer in annuli with viscous dissipation

    Energy Technology Data Exchange (ETDEWEB)

    Coelho, P.M. [Universidade do Porto, Porto (Portugal). Centro de Estudos de Fenomenos de Transporte, DEMEGI, Faculdade de Engenharia; Pinho, F.T. [Universidade do Porto, Porto (Portugal). Centro de Estudos de Fenomenos de Transporte, Faculdade de Engenharia

    2006-09-15

    For Newtonian concentric annular flows analytical solutions are obtained under imposed asymmetric constant wall heat fluxes as well as under imposed asymmetric constant wall temperatures, taking into account viscous dissipation and for fluid dynamic and thermally fully-developed conditions. Results for the special case of the heat flux ratio for identical wall temperatures and the critical Brinkman numbers marking changes of sign in wall heat fluxes are also derived. Equations are presented for the Nusselt numbers at the inner and outer walls, bulk temperature and normalised temperature distribution as a function of all relevant non-dimensional numbers. Given the complexity of the derived equations, simpler exact expressions are presented for the Nusselt numbers for ease of use, with their coefficients given in tables as a function of the radius ratio. (author)

  13. The new high resolution method of Godunov`s type for 3D viscous flow calculations

    Energy Technology Data Exchange (ETDEWEB)

    Yershov, S.V.; Rusanov, A.V. [Ukranian National Academy of Sciences, Kahrkov (Ukraine)

    1996-12-31

    The numerical method is suggested for the calculations of the 3D viscous compressible flows described by the thin-layer Reynolds-averaged Navier-Stokes equations. The method is based on the Godunov`s finite-difference scheme and it uses the ENO reconstruction suggested by Harten to achieve the uniformly high-order accuracy. The computational efficiency is provided with the simplified multi grid approach and the implicit step written in {delta} -form. The turbulent effects are simulated with the Baldwin - Lomax turbulence model. The application package FlowER is developed to calculate the 3D turbulent flows within complex-shape channels. The numerical results for the 3D flow around a cylinder and through the complex-shaped channels show the accuracy and the reliability of the suggested method. (author)

  14. The new high resolution method of Godunov`s type for 3D viscous flow calculations

    Energy Technology Data Exchange (ETDEWEB)

    Yershov, S V; Rusanov, A V [Ukranian National Academy of Sciences, Kahrkov (Ukraine)

    1997-12-31

    The numerical method is suggested for the calculations of the 3D viscous compressible flows described by the thin-layer Reynolds-averaged Navier-Stokes equations. The method is based on the Godunov`s finite-difference scheme and it uses the ENO reconstruction suggested by Harten to achieve the uniformly high-order accuracy. The computational efficiency is provided with the simplified multi grid approach and the implicit step written in {delta} -form. The turbulent effects are simulated with the Baldwin - Lomax turbulence model. The application package FlowER is developed to calculate the 3D turbulent flows within complex-shape channels. The numerical results for the 3D flow around a cylinder and through the complex-shaped channels show the accuracy and the reliability of the suggested method. (author)

  15. Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

    International Nuclear Information System (INIS)

    Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

    2008-01-01

    Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

  16. A numerical solution of a singular boundary value problem arising in boundary layer theory.

    Science.gov (United States)

    Hu, Jiancheng

    2016-01-01

    In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

  17. Horizontally viscous effects in a tidal basin: extending Taylor's problem

    NARCIS (Netherlands)

    Roos, Pieter C.; Schuttelaars, H.M.

    2009-01-01

    The classical problem of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, pp. 148–181) of Kelvin wave reflection in a semi-enclosed rectangular basin of uniform depth is extended to account for horizontally viscous effects. To this end, we add horizontally viscous terms to the hydrodynamic model

  18. Influence of viscous dissipation and radiation on MHD Couette flow ...

    African Journals Online (AJOL)

    The overall analysis of the study of these parameters in various degrees show an increase in the velocity profile of the fluid, while radiation parameter decreases the temperature profile; viscous dissipation and Reynolds number increase the temperature profile of the fluid. Key word: Couette flow, viscous dissipation, ...

  19. A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts

    NARCIS (Netherlands)

    Rienstra, S.W.; Eversman, W.

    2001-01-01

    An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite-element solution solving the same potential flow equations. The test geometry taken is representative of a high-bypass

  20. Convergence of finite differences schemes for viscous and inviscid conservation laws with rough coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Karlsen, Kenneth Hvistendal; Risebro, Nils Henrik

    2000-09-01

    We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a ''rough'' coefficient function k(x). we show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations as well as new convergence results for their finite difference approximations. In the inviscid case, we also provide a rate of convergence. Our convergence proofs are based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. (author)