Hybrid-Dimensional Finite Volume Discretizations for Fractured Porous Media

TL;DR

This paper extends finite volume discretizations for flow in fractured porous media using a hybrid-dimensional approach, addressing challenges at fracture intersections and coupling, and demonstrating robustness and accuracy through numerical simulations.

Contribution

It introduces a hierarchical finite volume framework with a Schur complement technique for fracture intersection cell elimination, enhancing robustness and flexibility.

Findings

Effective handling of fracture intersections in 2D and 3D simulations

Robustness of the method demonstrated with heterogeneous and anisotropic permeability

Flexible hierarchical framework facilitates implementation and coupling

Abstract

Over the last decade, finite volume discretizations for flow in porous media have been extended to handle situations where fractures dominate the flow. These discretizations have successfully been combined with the discrete fracture-matrix models to yield mass conservative methods capable of explicitly incorporating the impact of fractures and their geometry. When combined with a hybrid-dimensional formulation, two central concerns are the restrictions arising from small cell sizes at fracture intersections and the coupling between fractures and matrix. Focusing on these aspects, we demonstrate how finite volume methods effectively can be extended to handle fractures, providing generalizations of previous work. We address the finite volume methods applying a general hierarchical formulation, facilitating implementation with extensive code reuse and providing a natural framework for coupling of different subdomains. Furthermore, we demonstrate how a Schur complement technique may be used to obtain a robust and versatile method for fracture intersection cell elimination. We investigate the accuracy of the proposed elimination method through a series of numerical simulations in 3D and 2D. The simulations, performed on fractured domains containing permeability heterogeneity and anisotropy, also demonstrate the flexibility of the hierarchical framework.