Jean-Baptiste Clément

Czech Technical University in Prague | ČVUT · Department of Technical Mathematics (FS)

Flows in unsaturated porous media are modelled by the Richards’ equation which is a degenerate parabolic nonlinear equation. Its limitations and the challenges raised by its numerical solution are laid out. Getting robust, accurate and cost-effective results is difficult in particular because of moving sharp wetting fronts due to the nonlinear hydraulic properties. Richards’ equation is discretized by a discontinuous Galerkin method in space and backward differentiation formulas in time. The resulting numerical scheme is conservative, high-order and very flexible. Thereby, complex boundary conditions are included easily such as seepage condition or dynamic forcing. Moreover, an adaptive strategy is proposed. Adaptive time stepping makes nonlinear convergence robust and a block-based adaptive mesh refinement is used to reach required accuracy cost-effectively. A suitable a posteriori error indicator helps the mesh to capture sharp wetting fronts which are also better approximated by a discontinuity introduced in the solution thanks to a weighted discontinuous Galerkin method. The approach is checked through various test-cases and a 2D benchmark. Numerical simulations are compared with laboratory experiments of water table recharge/drainage and a largescale experiment of wetting, following reservoir impoundment of the multi-materials La Verne dam. This demanding case shows the potentiality of the strategy developed in this thesis. Finally, applications are handled to simulate groundwater flows under the swash zone of sandy beaches in comparison with experimental observations.