Conservative numerical methods for the reinterpreted discrete fracture model on non-conforming meshes and their applications in contaminant transportation in fractured porous media

Abstract

The discrete fracture model (DFM) has been widely used to simulate fluid flow in fractured porous media. Traditional DFM is considered to be limited on conforming meshes, hence significant difficulty may arise in generating high-quality unstructured meshes due to the complexity of the fracture networks. Recently, Xu and Yang reinterpreted DFM and demonstrated that it can actually be extended to non-conforming meshes without any essential changes. However, the continuous Galerkin (CG) method was applied and the local mass conservation was missing. This paper is a follow-up work, and we apply the interior penalty discontinuous Galerkin (IPDG) method and enriched Galerkin (EG) method for the pressure equation. With the numerical fluxes, the local mass is conservative. As an application, we combine the reinterpreted DFM (RDFM) with the incompressible miscible displacements in porous media. The bound-preserving techniques are applied to the coupled system. We can theoretically guarantee that the concentration is between 0 and 1. Finally, several numerical experiments are given to demonstrate the good performance of the RDFM based on the above two methods on non-conforming meshes and the effectiveness of the bound-preserving technique.