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 …
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 …
porous media, written by a developer of numerical methods. The reader will learn how to …
[BOOK][B] The gradient discretisation method
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 …
(GDM) and to some of its applications. It is intended for masters students, researchers and …
A multipoint flux mixed finite element method
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 …
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 …
geosciences. This method is well suited for solving elliptic and parabolic partial differential …
A compact multipoint flux approximation method with improved robustness
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 …
formulations on general grids. Although these methods are general in the sense that they …
Monotonicity of control volume methods
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 …
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
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 …
finite element (MHFE) method for general-purpose compositional reservoir simulation. The …
A cell-centered diffusion scheme on two-dimensional unstructured meshes
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 …
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
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 …
quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme …