Comparison of DDFV and DG Methods for Flow in Anisotropic Heterogeneous Porous Media

Abstract

We present a preliminary work to simulate gas injection in deep aquifers. Unsteady single-phase flows are considered. We compare Discrete Duality Finite Volume (DDFV, Discrete Duality Finite Volume) and Discontinuous Galerkin (DG, Discontinuous Galerkin) schemes applied to discretize the diffusive term. The second-order backward differentiation formula is used for the time-stepping method. On the one hand, the DDFV methods are easy to implement, ensure a preservation of physical properties and offer superconvergence in the L2-norm on a regular basis. On the other hand, the DG methods are flexible, allow arbitrary order of accuracy, and their ample theoretical foundation make them a reliable choice for many computational problems. We consider here the symmetric weighted interior penalty Galerkin method. Accuracy and robustness of these two schemes are tested and compared on various test cases, especially in anisotropic heterogeneous media.