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 …

[BOOK][B] An introduction to reservoir simulation using MATLAB/GNU Octave: User guide for the MATLAB Reservoir Simulation Toolbox (MRST)

KA Lie - 2019 - books.google.com
This book provides a self-contained introduction to the simulation of flow and transport in
porous media, written by a developer of numerical methods. The reader will learn how to …

[BOOK][B] The gradient discretisation method

J Droniou, R Eymard, T Gallouët, C Guichard, R Herbin - 2018 - Springer
This monograph is dedicated to the presentation of The Gradient Discretisation Method
(GDM) and to some of its applications. It is intended for masters students, researchers and …

A multipoint flux mixed finite element method

MF Wheeler, I Yotov - SIAM Journal on Numerical Analysis, 2006 - SIAM
We develop a mixed finite element method for single phase flow in porous media that
reduces to cell-centered finite differences on quadrilateral and simplicial grids and performs …

Mixed finite elements for solving 2‐D diffusion‐type equations

A Younes, P Ackerer, F Delay - Reviews of Geophysics, 2010 - Wiley Online Library
Mixed finite elements are a numerical method becoming more and more popular in
geosciences. This method is well suited for solving elliptic and parabolic partial differential …

A compact multipoint flux approximation method with improved robustness

I Aavatsmark, GT Eigestad, BT Mallison… - … Methods for Partial …, 2008 - Wiley Online Library
Multipoint flux approximation (MPFA) methods were introduced to solve control‐volume
formulations on general grids. Although these methods are general in the sense that they …

Monotonicity of control volume methods

JM Nordbotten, I Aavatsmark, GT Eigestad - Numerische Mathematik, 2007 - Springer
Robustness of numerical methods for multiphase flow problems in porous media is
important for development of methods to be used in a wide range of applications. Here, we …

A fully implicit mimetic finite difference scheme for general purpose subsurface reservoir simulation with full tensor permeability

AS Abushaikha, KM Terekhov - Journal of Computational Physics, 2020 - Elsevier
In the previous article Abushaikha et al.(2017)[1], we presented a fully-implicit mixed hybrid
finite element (MHFE) method for general-purpose compositional reservoir simulation. The …

A cell-centered diffusion scheme on two-dimensional unstructured meshes

J Breil, PH Maire - Journal of Computational Physics, 2007 - Elsevier
We propose a new cell-centered diffusion scheme on unstructured meshes. The main
feature of this scheme lies in the introduction of two normal fluxes and two temperatures on …

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 …