Modeling Fractures and Barriers as Interfaces for Flow in Porous Media

TLDR

Fractured porous media are examined at a scale where individual fractures can be modeled separately. The authors present interface‑based flow models that account for interactions between fractures and the surrounding porous matrix. The model admits a unique solution, with error estimates converging at O(max{h,d}) in the L2 norm, and numerical experiments validate these theoretical predictions.

Abstract

We consider a fractured porous medium that is studied at a scale such that the fractures can be modeled individually. Models for flow in which the fractures are interfaces between subdomains are presented. These models take into account interactions between the fractures and the surrounding porous medium. Existence and uniqueness of the solution to the model problem are proved. Error estimates show convergence as $\mathcal{O}(\max\{h,d\})$ in the L2 norm, where h is the mesh size and d the fracture width. Numerical experiments confirm the theoretical results.