A Gradient Scheme for the Discretization of Richards Equation

Konstantin Brenner (1, 2) , Danielle Hilhorst (3) , Huy-Cuong Vu-Do (4)

1 COFFEE - COmplex Flows For Energy and Environment
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay
4 Vietnam National University of Hochiminh City

We propose a finite volume method on general meshes for the discretiza-tion of Richards equation, an elliptic-parabolic equation modeling 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 unstruc-tured 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.

Mots clés: Richards' equation; finite volume schemes; SUSHI scheme

Domaines: Mathématiques [math]

Konstantin Brenner, Danielle Hilhorst, Huy-Cuong Vu-Do. A Gradient Scheme for the Discretization of Richards Equation. The International Symposium of Finite Volumes for Complex Applications VII, Jun 2014, Berlin, Germany. ⟨10.1007/978-3-319-05591-6_53⟩. ⟨hal-01317588⟩