A reinterpreted discrete fracture model for Darcy–Brinkman flow in fractured porous media and its extension on nonconforming meshes

Document Type

Article

Publication Date

4-2026

Department

Department of Mathematical Sciences

Abstract

A novel hybrid-dimensional model for Darcy–Brinkman flow in fractured porous media is proposed, inherently compatible with non-conforming grids. Building upon the reinterpreted discrete fracture model (RDFM) for Darcy flow, which introduces a Dirac–δ function to unify matrix-fracture flow, we develop the hybrid-dimensional RDFM for Darcy–Brinkman flow. We also rigorously establish its mathematical equivalence with the classical interface model. For numerical discretization, a hybrid scheme combining Local Discontinuous Galerkin (LDG) and standard Galerkin finite element methods (FEM) is employed. This approach overcomes key limitations of the LDG method in modeling one-dimensional fractures, such as difficulties with numerical flux selection and auxiliary variable specification, while maintaining computational efficiency. To solve the resulting coupled system, we introduce a pseudo-time and advance the solution in time toward a stationary state. Validation through coupled tracer transport simulations confirms the model's robustness and applicability on non-matching grids.

Publication Title

Advances in Water Resources

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