Finite volume schemes for diffusion equations: introduction to and review of modern methods

J Droniou - Mathematical Models and Methods in Applied …, 2014 - World Scientific
We present Finite Volume methods for diffusion equations on generic meshes, that received
important coverage in the last decade or so. After introducing the main ideas and …

Control-volume distributed multi-point flux approximation coupled with a lower-dimensional fracture model

R Ahmed, MG Edwards, S Lamine… - Journal of …, 2015 - Elsevier
A cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-
volume formulation is presented for discrete fracture-matrix simulations. The grid is aligned …

A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

M Wheeler, G Xue, I Yotov - Numerische Mathematik, 2012 - Springer
In this paper, we develop a new mixed finite element method for elliptic problems on general
quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme …

Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity

G Lin, J Liu, L Mu, X Ye - Journal of computational physics, 2014 - Elsevier
This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy
flow computation. The WGFEMs are new numerical methods that rely on the novel concept …

Higher order FE–FV method on unstructured grids for transport and two-phase flow with variable viscosity in heterogeneous porous media

KS Schmid, S Geiger, KS Sorbie - Journal of Computational Physics, 2013 - Elsevier
This paper presents higher order methods for the numerical modeling of two-phase flow with
simultaneous transport and adsorption of viscosifying species within the individual phases in …

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

HA Friis, MG Edwards - Journal of Computational Physics, 2011 - Elsevier
A new family of cell-centered finite-volume schemes is presented for solving the general full-
tensor pressure equation of subsurface flow in porous media on arbitary unstructured …

An algebraic multiscale solver for the simulation of two-phase flow in heterogeneous and anisotropic porous media using general unstructured grids (AMS-U)

ACR de Souza, DKE de Carvalho… - Applied Mathematical …, 2022 - Elsevier
We introduce a new multiscale finite volume framework for the simulation of multi-phase flow
in heterogenous and anisotropic porous media on quite general unstructured grids that …

An introduction to multi-point flux (MPFA) and stress (MPSA) finite volume methods for thermo-poroelasticity

JM Nordbotten, E Keilegavlen - Polyhedral methods in geosciences, 2021 - Springer
In this chapter, we give a unified introduction to the MPFA-and MPSA-type finite volume
methods for Darcy flow and poro-elasticity, applicable to general polyhedral grids. This …

Pores resolving simulation of Darcy flows

PK Smolarkiewicz, CL Winter - Journal of Computational Physics, 2010 - Elsevier
A theoretical formulation and corresponding numerical solutions are presented for
microscopic fluid flows in porous media with the domain sufficiently large to reproduce …

[HTML][HTML] A nonlinear repair technique for the MPFA-D scheme in single-phase flow problems and heterogeneous and anisotropic media

ACR de Souza, DKE de Carvalho… - Journal of …, 2024 - Elsevier
Abstract A novel Flux Limited Splitting (FLS) non-linear Finite Volume (FV) method for
families of linear Control Volume Distributed Multi Point Flux Approximation (CVD-MPFA) …