Robust Discretization of Flow in Fractured Porous Media

TL;DR

This paper introduces a novel discretization method for modeling flow in fractured porous media, combining mixed finite element and mortar methods to handle complex geometries and ensure mass conservation.

Contribution

The paper presents a new discretization approach that employs normal fluxes as mortar variables, effectively coupling flow in fractures with surrounding media and handling complex geometries.

Findings

Method is optimally convergent in theory.

Handles complex, non-matching grids and fracture intersections.

Applicable in 2D and 3D scenarios.

Abstract

Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our formulation is novel in that it employs the normal fluxes as the mortar variable within the mixed finite element framework, resulting in a formulation that couples the flow in the fractures with the surrounding domain with a strong notion of mass conservation. The proposed discretization handles complex, non-matching grids, and allows for fracture intersections and termination in a natural way, as well as spatially varying apertures. The discretization is applicable to both two and three spatial dimensions. A priori analysis shows the method to be optimally convergent with respect to the chosen mixed finite element spaces, which is sustained by numerical examples.