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.

翻译：本文涉及不同领域的理查斯等式,每个子领域都是同质的,代表着一种岩石类型。我们的第一个贡献是严格证明,在不改变基尔希霍夫的情况下,以细胞为主的、以上游流动为主的有限容量计划的解决办法是薄弱的。我们的第二个贡献是从数字上表明,在出现不连续性的次区域间界面上当地改进电网的相关性,以便保持所考虑的计划计算结果的可接受的准确性。