A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

DOI10.1016/j.jcp.2010.09.012zbMath1427.76161OpenAlexW2008578983MaRDI QIDQ613993

Michael G. Edwards, Helmer André Friis

Publication date: 23 December 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.09.012

zbMATH Keywords

anisotropyfinite volumeunstructured griddecouplingM-matrixcell centeredcontrol-volumefull pressure continuity

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite volume methods applied to problems in fluid mechanics (76M12)

Related Items

Design of coupled finite volume schemes minimizing the grid orientation effect in reservoir simulation, A vertex scheme for two-phase flow in heterogeneous media, A new nonlinear finite volume scheme preserving positivity for diffusion equations, The VEM-based positivity-preserving conservative scheme for radiation diffusion problems on generalized polyhedral meshes, Mixed finite element methods for groundwater flow in heterogeneous aquifers, A simplified enhanced MPFA formulation for the elliptic equation on general grids, A cell-centered nonlinear finite volume scheme preserving fully positivity for diffusion equation, A positive scheme for diffusion problems on deformed meshes, Positivity‐preserving scheme without separated method for <scp>2D</scp> convection–diffusion equations on polygonal meshes, A nonlinear repair technique for the MPFA-D scheme in single-phase flow problems and heterogeneous and anisotropic media, An algebraic multiscale solver for the simulation of two-phase flow in heterogeneous and anisotropic porous media using general unstructured grids (AMS-U), CVD-MPFA full pressure support, coupled unstructured discrete fracture-matrix Darcy-flux approximations, An improved monotone finite volume scheme for diffusion equation on polygonal meshes, A monotone combination scheme of diffusion equations on polygonal meshes, Simulation of multi-component multi-phase fluid flow in two-dimensional anisotropic heterogeneous porous media using high-order control volume distributed methods, Construction of Nonlinear Weighted Method for Finite Volume Schemes Preserving Maximum Principle, Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance, A monotone finite volume scheme for advection–diffusion equations on distorted meshes, A family of multi‐point flux approximation schemes for general element types in two and three dimensions with convergence performance, Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems, A Monotone Finite Volume Scheme with Second Order Accuracy for Convection-Diffusion Equations on Deformed Meshes, Finite volume schemes for diffusion equations: Introduction to and review of modern methods, M-Adaptation in the mimetic finite difference method, Nonlinear finite volume scheme preserving positivity for 2D convection-diffusion equations on polygonal meshes, Modeling anisotropic diffusion using a departure from isotropy approach, Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance, Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model, Finite-volume scheme for anisotropic diffusion, Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids, A new multipoint flux approximation method with a quasi-local stencil (MPFA-QL) for the simulation of diffusion problems in anisotropic and heterogeneous media, A hybrid-dimensional discrete fracture model for non-isothermal two-phase flow in fractured porous media, Analysis of the nonlinear scheme preserving the maximum principle for the anisotropic diffusion equation on distorted meshes

Cites Work

• A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis
• A quasi-positive family of continuous Darcy-flux finite-volume schemes with full pressure support
• Quasi-positive families of continuous Darcy-flux finite volume schemes on structured and unstructured grids
• Approximation of 2D and 3D diffusion operators with variable full tensor coefficients on arbitrary meshes
• Finite volume discretization with imposed flux continuity for the general tensor pressure equation
• Control-volume mixed finite element methods
• The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
• Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes.
• A new method for numerical solution of checkerboard fields
• A finite-volume method with hexahedral multiblock grids for modeling flow in porous media
• An introduction to multipoint flux approximations for quadrilateral grids
• Unstructured, control-volume distributed, full-tensor finite volume schemes with flow based grids
• M-matrix flux splitting for general full tensor discretization operators on structured and unstructured grids
• Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes
• Finite volume scheme for highly anisotropic diffusion operators on unstructured meshes
• Computable scalar fields: A basis for PDE software
• Double-families of quasi-positive Darcy-flux approximations with highly anisotropic tensors on structured and unstructured grids
• Non-linear flux-splitting schemes with imposed discrete maximum principle for elliptic equations with highly anisotropic coefficients
• Higher Order Multidimensional Upwind Convection Schemes for Flow in Porous Media on Structured and Unstructured Quadrilateral Grids
• Convergence of multipoint flux approximations on quadrilateral grids
• Positive-definiteq-families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element method
• Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell-Centered Triangular Grids
• Higher-resolution convection schemes for flow in porous media on highly distorted unstructured grids
• Mixed and Hybrid Finite Element Methods
• Iterative Solution Methods
• Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences
• Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry
• Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods
• A Theorem on the Conductivity of a Composite Medium
• A Multipoint Flux Mixed Finite Element Method
• A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension
• Higher‐resolution hyperbolic‐coupled‐elliptic flux‐continuous CVD schemes on structured and unstructured grids in 2‐D
• Convergence study of a family of flux‐continuous, finite‐volume schemes for the general tensor pressure equation
• On the convergence of the multi‐point flux approximation O‐method: Numerical experiments for discontinuous permeability
• Use of coordinate-free numerics in elastic wave simulation.