Upstream mobility Finite Volumes for the Richards equation in\n heterogenous domains

2021/01/20 by Sabrina Bassetto, Clément Cancès, Bassetto, Sabrina +5 · 1 citation
Computer Science · Engineering · Mathematics · #65M08 #65M12 #76S05 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2101.08077

openalex publication_date 2021/01/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the Richards equation in a heterogeneous domain,\neach subdomain of which is homogeneous and represents a rocktype. Our first\ncontribution is to rigorously prove convergence toward a weak solution of\ncell-centered finite-volume schemes with upstream mobility and without\nKirchhoff's transform. Our second contribution is to numerically demonstrate\nthe relevance of locally refining the grid at the interface between subregions,\nwhere discontinuities occur, in order to preserve an acceptable accuracy for\nthe results computed with the schemes under consideration.\n

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