Robust Discretization of Flow in Fractured Porous Media
This work addresses the challenge of accurately modeling flow in fractured porous media for geoscience and engineering applications, offering a robust method that handles complex fracture networks.
The paper proposes a new discretization for flow in fractured porous media using mixed finite element and mortar methods, achieving optimal convergence and strong mass conservation for complex geometries including non-matching grids and fracture intersections.
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.