The hybrid-dimensional Darcy's law: a non-conforming reinterpreted discrete fracture model (RDFM) for single-phase flow in fractured media

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Department of Mathematical Sciences


In this paper, we propose a novel discrete fracture model for flow simulation of fractured porous media containing flow blocking barriers on non-conforming meshes. The methodology of the approach is to modify the traditional Darcy's law into the hybrid-dimensional Darcy's law where fractures and barriers are represented as Dirac-δ functions contained in the permeability tensor and resistance tensor, respectively. As a natural extension of the previous discrete fracture model [21] for highly conductive fractures, this model is able to account for the influence of both highly conductive fractures and blocking barriers accurately on non-conforming meshes. The local discontinuous Galerkin (LDG) method is employed to accommodate the form of the hybrid-dimensional Darcy's law and the nature of the pressure/flux discontinuity. The performance of the model is demonstrated by several numerical tests.

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Journal of Computational Physics