A nine-point finite volume scheme for the simulation of diffusion in heterogeneous media

From MaRDI portal

Publication:1022311

Jump to:navigation, search

DOI10.1016/j.crma.2009.03.013zbMath1166.65051OpenAlexW2010038215MaRDI QIDQ1022311

Robert Eymard, Raphaèle Herbin, Léo Agélas

Publication date: 10 June 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.03.013

zbMATH Keywords

convergence finite difference method numerical examples diffusion equation non-conforming meshes multipoint flux approximation cell-centered symmetric scheme harmonic averaging points nine-point finite volume scheme

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items

General finite-volume framework for saddle-point problems of various physics, A new FV scheme and fast cell-centered multigrid solver for 3D anisotropic diffusion equations with discontinuous coefficients, Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology, A Family of Linearity-Preserving Schemes for Anisotropic Diffusion Problems on General Grids, A small stencil and extremum-preserving scheme for anisotropic diffusion problems on arbitrary 2D and 3D meshes, A reconstruction algorithm with flexible stencils for anisotropic diffusion equations on 2D skewed meshes, Interpolation-based second-order monotone finite volume schemes for anisotropic diffusion equations on general grids, A Finite Volume Scheme with the Discrete Maximum Principle for Diffusion Equations on Polyhedral Meshes, Presure boundary conditions in the collocated finite-volume method for the steady Navier-Stokes equations, A novel cell-centered finite volume scheme with positivity-preserving property for the anisotropic diffusion problems on general polyhedral meshes, Monotone corrections for generic cell-centered finite volume approximations of anisotropic diffusion equations, An extremum-preserving finite volume scheme for convection-diffusion equation on general meshes, Piecewise Linear Transformation in Diffusive Flux Discretizations, Finite volume method for coupled subsurface flow problems. II: Poroelasticity, A cost-effective nonlinear extremum-preserving finite volume scheme for highly anisotropic diffusion on Cartesian grids, with application to radiation belt dynamics, Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes, Unnamed Item, A robust, interpolation‐free and monotone finite volume scheme for diffusion equations on arbitrary quadrilateral meshes, A nonlinear convex combination in the construction of finite volume scheme satisfying maximum principle, An interpolation-free cell-centered discretization of the heterogeneous and anisotropic diffusion problems on polygonal meshes, Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem, Pressure-correction projection method for modelling the incompressible fluid flow in porous media, Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system, A positivity-preserving pyramid scheme for anisotropic diffusion problems on general hexahedral meshes with nonplanar cell faces, An extremum‐preserving finite volume scheme for three‐temperature radiation diffusion equations, A monotone diffusion scheme for 3D general meshes: application to radiation hydrodynamics in the equilibrium diffusion limit, The cell-centered positivity-preserving finite volume scheme for 3D anisotropic diffusion problems on distorted meshes, A linearity-preserving diamond scheme with extended least square interpolation for the heterogeneous and anisotropic diffusion problems on polyhedral meshes, A pyramid scheme for three-dimensional diffusion equations on polyhedral meshes, Monotone nonlinear finite-volume method for challenging grids, A stabilized linearity-preserving scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes, An improvement of the two-point flux approximation scheme on polygonal meshes, A family of linearity-preserving schemes for anisotropic diffusion problems on arbitrary polyhedral grids, A Positivity-Preserving Finite Volume Scheme for Heat Conduction Equation on Generalized Polyhedral Meshes, A New Interpolation for Auxiliary Unknowns of the Monotone Finite Volume Scheme for 3D Diffusion Equations, A Decoupled and Positivity-Preserving DDFVS cheme for Diffusion Problems on Polyhedral Meshes, A Nonlinear Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations, Finite volume schemes for diffusion equations: Introduction to and review of modern methods, A nine-point scheme with explicit weights for diffusion equations on distorted meshes, A nonlinear correction and maximum principle for diffusion operators discretized using cell-centered finite volume schemes, Collocated finite-volume method for the incompressible Navier-Stokes problem, Cell-centered finite-volume method for elastic deformation of heterogeneous media with full-tensor properties, Piecewise linear transformation in diffusive flux discretization, A positivity-preserving finite volume scheme with least square interpolation for 3D anisotropic diffusion equation, A second order in space combination of methods verifying a maximum principle for the discretization of diffusion operators, Cell-centered finite-volume method for heterogeneous anisotropic poromechanics problem, Nonlinear Finite-Volume Scheme for Complex Flow Processes on Corner-Point Grids, The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1022311&oldid=13020346"