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.

中文翻译：

---

异构域中Richards方程的上游流动性有限体积

本文关注的是异构域中的Richards方程，该域的每个子域都是同质的，并且代表岩石类型。我们的第一个贡献是严格证明收敛到以细胞为中心的有限体积方案的弱解的收敛性，该方案具有上游流动性且无需Kirchhoff变换。我们的第二个贡献是以数字方式证明了在出现不连续性的子区域之间的界面处局部细化网格的相关性，以便为考虑中的方案计算的结果保持可接受的准确性。