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

摘要

In this study, we consider the simulation of subsurface flow and solutetransport processes in the stationary limit. In the convection-dominant case,the numerical solution of the transport problem may exhibit non-physicaldiffusion and under- and overshoots. For an interior penalty discontinuousGalerkin (DG) discretization, we present a $h$-adaptive refinement strategyand, alternatively, a new efficient approach for reducing numerical under- andovershoots using a diffusive $L^2$-projection. Furthermore, we illustrate anefficient way of solving the linear system arising from the DG discretization.In $2$-D and $3$-D examples, we compare the DG-based methods to the streamlinediffusion approach with respect to computing time and their ability to resolvesteep fronts.