A Discontinuous Galerkin Method for Simulations of Transport Processes on the Pore Scale

Abstract

In the simulation of pore scale processes a good approximation to the geometrical shape of the solid phase is crucial to good quality of the numerical results, while on the other hand interest often focuses on a small number of unknowns. I will present a new approach for solving PDEs in complex domains. It is based on a Discontinuous Galerkin (DG) discretization on a structured grid, where the minimal number of unknowns is independent of the shape of the domain, while this new method still allows the provision of fine structures of the domains shape, even if their size is significantly smaller than the grid cell size. Its advantage for flow and transport simulation on the pore scale is that the resolution of the simulation can be chosen freely between very large domains, perhaps the size of several REVs, and very small domains, just the size of few sandcorns, without changing the discretization and without neglecting details in the shape of your domain. I give an overview of the new technique and exemplify this with the numerical simulation of solute transport in a 3D pore scale domain. This is intended only as an introduction and does not involve productive computations. Future applications might involve multiphase flow on the pore scale or even upscaling simulations.