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

TL;DR

This paper compares discontinuous Galerkin and streamline diffusion methods for simulating steady-state groundwater flow and solute transport, focusing on accuracy, efficiency, and handling steep concentration fronts.

Contribution

It introduces an adaptive refinement strategy and a diffusive $L^2$-projection to improve DG method accuracy and efficiency in subsurface flow simulations.

Findings

DG methods effectively resolve steep fronts in 2D and 3D.

The diffusive $L^2$-projection reduces numerical overshoots.

DG-based methods show competitive computation times.

Abstract

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 $L^2$-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.