Discontinuous Galerkin Method for Modeling Flow and Reactive Transport in Porous Media

Abstract

An important example of an intradomain (i.e. within a specified physical system) multifield problems in the management of water resources is the transport of radionuclides, chemicals, and/or biological species through soil and aquifers. The simulation of such processes with chemical interactions is inherently ill-conditioned due to widely varying scales. Species can be present at trace amounts, equilibrium constants and other parameters can vary over perhaps 50–100 orders of maginitude, the time period of interest can involve millions of years, and the porous media can involve many orders of variablility in permeability.

In this paper we analyze a discontinuous Galerkin method for flow and reactive transport in porous media and apply it to the simulation of a far field nuclear waste management problem. The problem is characterized by large discontinous jumps in permeability, effective porosity, and diffusivity; and by the need to model small levels of concentration of the radioactive constituents. Theoretical derivation shows that optimal a priori error estimates in the energy norm can be obtained for concentration and pressure. Numerical computation of a benchmark case demonstrates the importance of the locally conservative property and low numerical diffusion for DG. Methods to optimize the numerical performance of DG such as the use of a slope limiter are also discussed.