Volume 55, Number 5, September-October 2021
|Page(s)||2101 - 2139|
|Published online||13 October 2021|
Upstream mobility finite volumes for the Richards equation in heterogenous domains
IFP Energies nouvelles, 1 et 4 avenue de Bois Préau, 92852 Rueil-Malmaison Cedex, France
2 Inria, Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, 59000 Lille, France
* Corresponding author: email@example.com
Accepted: 18 August 2021
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.
Mathematics Subject Classification: 65M08 / 65M12 / 76S05
Key words: Richards’ equation / heterogeneous domains / finite-volume schemes / mobility upwinding
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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