Richards' equation is used to simulate flows in unsaturated porous media but it remains challenging to solve cost-effectively for complex cases. An adaptive strategy is proposed to deal with sharp wetting fronts. It is based on weighted discontinuous Galerkin methods and adaptive mesh refinement. The reservoir impoundment of La Verne dam is a demanding case because there are several materials, stiff hydraulic properties, dynamic boundary condition and seepage. The comparison of results with experimental data highlights the potential of the solving strategy.