Numerical solution of steady-state groundwater flow and solute transport problems: Discontinuous Galerkin based methods compared to the Streamline Diffusion approach

In this study, we consider the simulation of subsurface flow and solute transport processes in the stationary limit. In the convection-dominant case, the numerical solution of the transport problem may exhibit non-physical diffusion and under- and overshoots. For a higher order symmetric interior penalty discontinuous Galerkin (DG) discretization, we present a novel approach for reducing numerical under- and overshoots near sharp fronts, that are not resolved by the mesh, using a diffusive L2-projection. In the context of geostatistical inversion, where a small amount of oscillations is tolerated by a proper treatment of measurement errors, this may serve as an efficient alternative to adaptive mesh refinement. Furthermore, we realize a fast solver for the arising linear system by reordering the degrees of freedom in flow direction and exploiting the upwind character of the DG scheme. In 2-D and 3-D examples, we compare the DG-based method to the streamline diffusion approach with respect to computing time and their ability to resolve steep fronts.