A gradient scheme for the discretization of Richards equation

Abstract

We propose a finite volume method on general meshes for the discretization ofRichards equation, an elliptic—parabolic equationmodeling groundwater flow. The diffusion term, which can be anisotropic and heterogeneous, is discretized in a gradient scheme framework, which can be applied to a wide range of unstructured possibly non-matching polyhedral meshes in arbitrary space dimension. More precisely, we implement the SUSHI scheme which is also locally conservative. As is needed for Richards equation, the time discretization is fully implicit.We obtain a convergence result based upon energy-type estimates and the application of the Fréchet-Kolmogorov compactness theorem. We implement the scheme and present the results of a number of numerical tests.