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 an interior penalty discontinuous
Galerkin (DG) discretization, we present a h-adaptive refinement strategy
and, alternatively, a new efficient approach for reducing numerical under- and
overshoots using a diffusive L2-projection. Furthermore, we illustrate an
efficient 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 streamline
diffusion approach with respect to computing time and their ability to resolve
steep fronts