Conservation properties of embedded finite-element methods for flow in fractured porous media

Abstract

We present a simple finite element framework which enables numerical simulations of transport problems in fractured porous media based on equi-dimensional models, i.e., models where fractures are considered heterogeneities of the same geometrical dimension as the embedding background. The two main ingredients of the proposed framework are an adaptive mesh refinement strategy, and an algebraic flux correction stabilization. The proposed finite-element method for equi-dimensional models is inherently simple and can be easily implemented in any common simulation software, as it does not require the complicated management of different meshes and discretizations, which are necessary for numerical simulations based on hybrid-dimensional models, i.e., models where fractures are considered as heterogeneities of a lower geometrical dimension than the embedding background. Actually, our equi-dimensional approach provides a strategy to validate hybrid-dimensional models. Our adaptive approach is inherently conservative and naturally reduces the discretization error which, for problems with heterogeneities, is concentrated at the interfaces.

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