Upstream mobility finite volumes for the Richards equation in heterogenous domains

Bassetto, Sabrina; Cancès, Clément; Enchéry, Guillaume; Tran, Quang-Huy

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1051/m2an/2021047

Title :

Upstream mobility finite volumes for the Richards equation in heterogenous domains

Author(s) :

Bassetto, Sabrina [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
IFP Energies nouvelles [IFPEN]
Cancès, Clément [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Enchéry, Guillaume [Auteur correspondant]
IFP Energies nouvelles [IFPEN]
Tran, Quang-Huy [Auteur]
Institut Jacques Monod [IJM (UMR_7592)]

Journal title :

ESAIM: Mathematical Modelling and Numerical Analysis

Pages :

2101-2139

Publisher :

EDP Sciences

Publication date :

2021-09

ISSN :

0764-583X

English keyword(s) :

Richards’ equation
heterogeneous domains
finite-volume schemes
mobility upwinding

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

This paper is concerned with the Richards equation in a heterogeneous domain, each subdomain of which is homogeneous and represents a rocktype. Our first contribution is to rigorously prove convergence toward a weak solution ...
Show more >This paper is concerned with the Richards equation in a heterogeneous domain, each subdomain of which is homogeneous and represents a rocktype. Our first contribution is to rigorously prove convergence toward a weak solution of cell-centered finite-volume schemes with upstream mobility and without Kirchhoff’s transform. Our second contribution is to numerically demonstrate the relevance of locally refining the grid at the interface between subregions, where discontinuities occur, in order to preserve an acceptable accuracy for the results computed with the schemes under consideration.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :