Home  About us  Contact
 

Diffusion Terms (diffusion + term)

Distribution by Scientific Domains
Engineering71%
Mathematics and Statistics21%

Selected Abstracts

Some results on the accuracy of an edge-based finite volume formulation for the solution of elliptic problems in non-homogeneous and non-isotropic media

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009
Darlan Karlo Elisiário de Carvalho
Abstract The numerical simulation of elliptic type problems in strongly heterogeneous and anisotropic media represents a great challenge from mathematical and numerical point of views. The simulation of flows in non-homogeneous and non-isotropic porous media with full tensor diffusion coefficients, which is a common situation associated with the miscible displacement of contaminants in aquifers and the immiscible and incompressible two-phase flow of oil and water in petroleum reservoirs, involves the numerical solution of an elliptic type equation in which the diffusion coefficient can be discontinuous, varying orders of magnitude within short distances. In the present work, we present a vertex-centered edge-based finite volume method (EBFV) with median dual control volumes built over a primal mesh. This formulation is capable of handling the heterogeneous and anisotropic media using structured or unstructured, triangular or quadrilateral meshes. In the EBFV method, the discretization of the diffusion term is performed using a node-centered discretization implemented in two loops over the edges of the primary mesh. This formulation guarantees local conservation for problems with discontinuous coefficients, keeping second-order accuracy for smooth solutions on general triangular and orthogonal quadrilateral meshes. In order to show the convergence behavior of the proposed EBFV procedure, we solve three benchmark problems including full tensor, material heterogeneity and distributed source terms. For these three examples, numerical results compare favorably with others found in literature. A fourth problem, with highly non-smooth solution, has been included showing that the EBFV needs further improvement to formally guarantee monotonic solutions in such cases. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A further work on multi-phase two-fluid approach for compressible multi-phase flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2008
Yang-Yao Niu
Abstract This paper is to continue our previous work Niu (Int. J. Numer. Meth. Fluids 2001; 36:351,371) on solving a two-fluid model for compressible liquid,gas flows using the AUSMDV scheme. We first propose a pressure,velocity-based diffusion term originally derived from AUSMDV scheme Wada and Liou (SIAM J. Sci. Comput. 1997; 18(3):633,657) to enhance its robustness. The scheme can be applied to gas and liquid fluids universally. We then employ the stratified flow model Chang and Liou (J. Comput. Physics 2007; 225:240,873) for spatial discretization. By defining the fluids in different regions and introducing inter-phasic force on cell boundary, the stratified flow model allows the conservation laws to be applied on each phase, and therefore, it is able to capture fluid discontinuities, such as the fluid interfaces and shock waves, accurately. Several benchmark tests are studied, including the Ransom's Faucet problem, 1D air,water shock tube problems, 2D shock-water column and 2D shock-bubble interaction problems. The results indicate that the incorporation of the new dissipation into AUSM+ -up scheme and the stratified flow model is simple, accurate and robust enough for the compressible multi-phase flows. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A higher-order predictor,corrector scheme for two-dimensional advection,diffusion equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008
Chuanjian Man
Abstract A higher-order accurate numerical scheme is developed to solve the two-dimensional advection,diffusion equation in a staggered-grid system. The first-order spatial derivatives are approximated by the fourth-order accurate finite-difference scheme, thus all truncation errors are kept to a smaller order of magnitude than those of the diffusion terms. Therefore, there is no need to add an artificial diffusion term to balance the unwanted numerical diffusion. For the time derivative, the fourth-order accurate Adams,Bashforth predictor,corrector method is applied. The stability analysis of the proposed scheme is carried out using the Von Neumann method. It is shown that the proposed algorithm has good stability. This method also shows much less spurious oscillations than current lower-order accurate numerical schemes. As a result, the proposed numerical scheme can provide more accurate results for long-time simulations. The proposed numerical scheme is validated against available analytical and numerical solutions for one- and two-dimensional transport problems. One- and two-dimensional numerical examples are presented in this paper to demonstrate the accuracy and conservative properties of the proposed algorithm by comparing with other numerical schemes. The proposed method is demonstrated to be a useful and accurate modelling tool for a wide range of transport problems. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A comparative study of efficient iterative solvers for generalized Stokes equations

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2008
Maxim Larin
Abstract We consider a generalized Stokes equation with problem parameters ,,0 (size of the reaction term) and ,>0 (size of the diffusion term). We apply a standard finite element method for discretization. The main topic of the paper is a study of efficient iterative solvers for the resulting discrete saddle point problem. We investigate a coupled multigrid method with Braess,Sarazin and Vanka-type smoothers, a preconditioned MINRES method and an inexact Uzawa method. We present a comparative study of these methods. An important issue is the dependence of the rate of convergence of these methods on the mesh size parameter and on the problem parameters , and ,. We give an overview of the main theoretical convergence results known for these methods. For a three-dimensional problem, discretized by the Hood,Taylor ,,2,,,1 pair, we give results of numerical experiments. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Numerical studies of a nonlinear heat equation with square root reaction term

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2009
Ron Buckmire
Abstract Interest in calculating numerical solutions of a highly nonlinear parabolic partial differential equation with fractional power diffusion and dissipative terms motivated our investigation of a heat equation having a square root nonlinear reaction term. The original equation occurs in the study of plasma behavior in fusion physics. We begin by examining the numerical behavior of the ordinary differential equation obtained by dropping the diffusion term. The results from this simpler case are then used to construct nonstandard finite difference schemes for the partial differential equation. A variety of numerical results are obtained and analyzed, along with a comparison to the numerics of both standard and several nonstandard schemes. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

On discontinuous Galerkin methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2003
O. C. Zienkiewicz
Abstract Discontinuous Galerkin methods have received considerable attention in recent years for problems in which advection and diffusion terms are present. Several alternatives for treating the diffusion and advective fluxes have been introduced. This report summarizes some of the methods that have been proposed. Several numerical examples are included in the paper. These present discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for diffusion,reaction problems and advection,diffusion problems. We discuss the performance of various formulations with respect to accuracy as well as stability of the method. Copyright © 2003 John Wiley & Sons, Ltd. [source]

A higher-order predictor,corrector scheme for two-dimensional advection,diffusion equation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008
Chuanjian Man
Abstract A higher-order accurate numerical scheme is developed to solve the two-dimensional advection,diffusion equation in a staggered-grid system. The first-order spatial derivatives are approximated by the fourth-order accurate finite-difference scheme, thus all truncation errors are kept to a smaller order of magnitude than those of the diffusion terms. Therefore, there is no need to add an artificial diffusion term to balance the unwanted numerical diffusion. For the time derivative, the fourth-order accurate Adams,Bashforth predictor,corrector method is applied. The stability analysis of the proposed scheme is carried out using the Von Neumann method. It is shown that the proposed algorithm has good stability. This method also shows much less spurious oscillations than current lower-order accurate numerical schemes. As a result, the proposed numerical scheme can provide more accurate results for long-time simulations. The proposed numerical scheme is validated against available analytical and numerical solutions for one- and two-dimensional transport problems. One- and two-dimensional numerical examples are presented in this paper to demonstrate the accuracy and conservative properties of the proposed algorithm by comparing with other numerical schemes. The proposed method is demonstrated to be a useful and accurate modelling tool for a wide range of transport problems. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Coupling between shallow water and solute flow equations: analysis and management of source terms in 2D

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005
J. Murillo
Abstract A two-dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first order upwind technique is applied to solve the flux terms in both the flow and solute equations and the bed slope source terms and a centred discretization is applied to the diffusion and friction terms. The convenience of considering the fully coupled system of equations is indicated and the methodology is well explained. Three options are suggested and compared in order to deal with the diffusion terms. Some comparisons are carried out in order to show the performance in terms of accuracy and computational effort of the different options. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Low Reynolds number k,, model for near-wall flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005
M. M. Rahman
Abstract A wall-distance free k,, turbulence model is developed that accounts for the near-wall and low Reynolds number effects emanating from the physical requirements. The model coefficients/functions depend non-linearly on both the strain rate and vorticity invariants. Included diffusion terms and modified C,(1,2) coefficients amplify the level of dissipation in non-equilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Stability and accuracy of a semi-implicit Godunov scheme for mass transport

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004
Scott F. Bradford
Abstract Semi-implicit, Godunov-type models are adapted for solving the two-dimensional, time-dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor,corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second-order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax-Wendroff, Warming-Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank,Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi-discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi-implicit schemes. Some linear, two-dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Employment of the second-moment turbulence closure on arbitrary unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004
B. BasaraArticle first published online: 12 JAN 200
Abstract The paper presents a finite-volume calculation procedure using a second-moment turbulence closure. The proposed method is based on a collocated variable arrangement and especially adopted for unstructured grids consisting of ,polyhedral' calculation volumes. An inclusion of 23k in the pressure is analysed and the impact of such an approach on the employment of the constant static pressure boundary is addressed. It is shown that this approach allows a removal of a standard but cumbersome velocity,pressure ,Reynolds stress coupling procedure known as an extension of Rhie-Chow method (AIAA J. 1983; 21: 1525,1532) for the Reynolds stresses. A novel wall treatment for the Reynolds-stress equations and ,polyhedral' calculation volumes is presented. Important issues related to treatments of diffusion terms in momentum and Reynolds-stress equations are also discussed and a new approach is proposed. Special interpolation practices implemented in a deferred-correction fashion and related to all equations, are explained in detail. Computational results are compared with available experimental data for four very different applications: the flow in a two-dimensional 180o turned U-bend, the vortex shedding flow around a square cylinder, the flow around Ahmed Body and in-cylinder engine flow. Additionally, the performance of the methodology is assessed by applying it to different computational grids. For all test cases, predictions with the second-moment closure are compared to those of the k,,model. The second-moment turbulence closure always achieves closer agreement with the measurements. A moderate increase in computing time is required for the calculations with the second-moment closure. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Accurate model of InxGa1,xAsyP1,y/InP active waveguides for optimal design of switches

INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 2 2003
V. Petruzzelli
Abstract Both the longitudinal and transverse charge diffusion terms in the rate equations as well as the spreading effect of the injected charge in the active layer are taken into account for a complete model of active twin ridge InGaAsP/InP-waveguides. A dedicated computer code, relying on an optimized beam propagation method (BPM) based on the method of lines (MoL,BPM), is written. The computer code is used for the optimal design of a travelling-wave switch and to simulate the bidirectional propagation for the design of a Fabry,Perot switch. This last switch version is more compact with respect to the travelling wave (TW) version because a reduction of the switch length of about 20% is gained. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Solutions to a nonlinear Poisson,Nernst,Planck system in an ionic channel

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2010
L. Hadjadj
Abstract A limiting one-dimensional Poisson,Nernst,Planck (PNP) equations is considered, when the three-dimensional domain shrinks to a line segment, to describe the flows of positively and negatively charged ions through open ion channel. The new model comprises the usual drift diffusion terms and takes into account for each phase, the bulk velocity defined by (4) including the water bath for ions. The existence of global weak solution to this problem is shown. The proof relies on the use of certain embedding theorem of weighted sobolev spaces together with Hardy inequality. Copyright © 2010 John Wiley & Sons, Ltd. [source]

Mathematical modeling for the ionic inclusion process inside conducting polymer-based thin-films

POLYMER ENGINEERING & SCIENCE, Issue 11 2008
Saptarshi Majumdar
Ionic inclusion inside thin conducting polymer (CP) film is a major and common feature for actuator as well as membrane-based drug release. In this study, an electro-active polymeric thin-film system has been conceptualized. PNP-electro-neutrality (Poisson,Nernst, Planck) based modeling framework with customized boundary conditions is used to depict the electrochemical phenomena. In dynamic model, kinetics of probable redox reactions is included along with electro-migration and diffusion terms in the overall PNP framework. At steady state, interfacial voltage seems to hold the critically important role, while ionic migration and reaction kinetics play very crucial roles in determining the dynamics of such systems. The validated model predicts that lowering in the standard potential of the polymeric electrode accelerates the process of ionic ingress. Higher ionic flux is obtained using slower voltage scan. Variation of diffusivity shows the large spectrum of relatively unexplored dynamics for such electro-active thin-film-based system. The significance is in designing actuator- or membrane-based controlled molecular release systems. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers [source]