Gradient discretization of hybrid-dimensional Darcy flow in fractured porous media with discontinuous pressures at matrix–fracture interfaces

Abstract

We investigate the discretization of Darcy flow through fractured porous media on general polyhedral meshes. We consider a hybrid-dimensional model, invoking a complex network of planar fractures. The model accounts for matrix–fracture interactions and fractures acting either as drains or as barriers, i.e., we have to deal with pressure discontinuities at matrix–fracture interfaces. The numerical analysis is performed in the general framework of gradient discretizations which is extended to the model under consideration. Two families of schemes, namely the vertex approximate gradient scheme and the hybrid finite volume scheme, are detailed and shown to fit the gradient scheme framework, which yields, in particular, convergence. Numerical tests confirm the theoretical results.