Discontinuous Galerkin Method for Steady-State Richards Equation

Jean-Baptiste Clément (1, 2) , Mehmet Ersoy (1) , Frederic Golay (1) , Damien Sous (2, 3)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 MIO - Institut méditerranéen d'océanologie
3 SIAME - Laboratoire des Sciences de l'Ingénieur Appliquées à la Mécanique et au génie Electrique

This work is devoted to the numerical simulation of flows in partially saturated porous media. We describe the Richards equation governing the subsurface flow and discuss its range of applicability. A discontinuous Galerkin formulation is used to approximate the steady-state Richards equation. To this end, we present the mathematical framework and a procedure for solving the nonlinear equation. Numerical tests are carried out to highlight properties of the discontinuous Galerkin method and a test case is compared to experimental data to validate the model.

Keywords: Discontinuous Galerkin method; Richards equation; Nonlinear resolution; Unsaturated porous media

Domains: Engineering Sciences [physics]; Mechanics [physics.med-ph]; Fluids mechanics [physics.class-ph]; Mathematics [math]; Analysis of PDEs [math.AP]

Jean-Baptiste Clément, Mehmet Ersoy, Frederic Golay, Damien Sous. Discontinuous Galerkin Method for Steady-State Richards Equation. Topical Problems of Fluid Mechanics 2019, Feb 2019, Prague, Czech Republic. pp.53-62, ⟨10.14311/TPFM.2019.008⟩. ⟨hal-02075109⟩