  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.
