Upstream mobility finite volumes for the Richards equation in heterogenous domains

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