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arXiv · 1411.1432

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

A. Q. T. Ngo·P. Bastian·O. Ippisch
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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.

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A. Q. T. Ngo, P. Bastian, O. Ippisch. 2014-11-05. Numerical solution of steady-state groundwater flow and solute transport problems: Discontinuous Galerkin based methods compared to the Streamline Diffusion approach. https://doi.org/10.1016/j.cma.2015.06.008

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