Richards' equation describes flows in variably saturated porous media. Its solution is challenging since it is a parabolic equation with nonlinearities and degeneracies. In particular, many real-life problems are demanding because they can involve steep/heterogeneous hydraulics properties, dynamic boundary conditions or moving sharp wetting fronts. In this regard, the aim is to design a robust and efficient numerical method to solve Richards’ equation. Towards this direction, the work presented here deals with Discontinuous Galerkin methods which are very flexible discretization schemes. They are combined with BDF methods to get high-order solutions. Built upon these desirable features, an adaptive mesh refinement strategy is proposed to improve Richards’ equation simulations. Examples such as the impoundment of a multi-material dam or the groundwater dynamics of sandy beaches illustrate the abilities of the... more