A discrete fracture-matrix approach based on Petrov-Galerkin immersed finite element for fractured porous media flow on nonconforming mesh

Abstract

In this paper, the Petrov-Galerkin immersed finite element method is developed for simulating flow in fractured porous media. We consider the hybrid-dimensional fracture model as an elliptic interface problem with multiple physical coupling interface conditions, and embed the information of low-dimensional fractures into the local functions of interface elements. The immersed finite element space is constructed by explicitly representing the local solution functions in the interface element. This approach addresses the limitation of conforming meshes. More importantly, it can capture both the continuity and discontinuity of pressure, making it effective for both conductive and blocking fractures. We provide a detailed illustration of how to construct local functions on triangular and rectangular meshes. Finally, numerical examples and benchmarks are presented to validate the effectiveness of our proposed method.