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.
Keywords: Richards’ equation, heterogeneous domains, finite-volume schemes, mobility upwinding
@article{M2AN_2021__55_5_2101_0,
author = {Bassetto, Sabrina and Canc\`es, Cl\'ement and Ench\'ery, Guillaume and Tran, Quang-Huy},
title = {Upstream mobility finite volumes for the {Richards} equation in heterogenous domains},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2101--2139},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021047},
mrnumber = {4323405},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021047/}
}
TY - JOUR AU - Bassetto, Sabrina AU - Cancès, Clément AU - Enchéry, Guillaume AU - Tran, Quang-Huy TI - Upstream mobility finite volumes for the Richards equation in heterogenous domains JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2101 EP - 2139 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021047/ DO - 10.1051/m2an/2021047 LA - en ID - M2AN_2021__55_5_2101_0 ER -
%0 Journal Article %A Bassetto, Sabrina %A Cancès, Clément %A Enchéry, Guillaume %A Tran, Quang-Huy %T Upstream mobility finite volumes for the Richards equation in heterogenous domains %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2101-2139 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021047/ %R 10.1051/m2an/2021047 %G en %F M2AN_2021__55_5_2101_0
Bassetto, Sabrina; Cancès, Clément; Enchéry, Guillaume; Tran, Quang-Huy. Upstream mobility finite volumes for the Richards equation in heterogenous domains. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 2101-2139. doi: 10.1051/m2an/2021047
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