A double-layer reduced model for fault flow on slipping domains with hybrid finite volume scheme

TL;DR

This paper introduces a reduced co-dimension one model for fault flow in fractured porous media, employing a hybrid finite volume scheme with non-matching meshes to improve simulation accuracy and computational efficiency.

Contribution

It develops a mathematical framework for fault flow modeling using a reduced model and hybrid finite volume discretization, addressing mesh movement and non-matching grids.

Findings

Proves well-posedness of the continuous problem

Establishes convergence of the discretized scheme

Supports results with numerical tests

Abstract

In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than other characteristic sizes, can allow one part of the domain to slide past to the other. We propose a mathematical scheme where a reduced model for the fault flows is employed yielding a problem of co-dimension one. The hybrid finite volume method is used to obtain the discretized problem, which employs two different meshes for each fault, one associated with the porous-medium domain on each side of the fault. These two meshes can move with the corresponding domain, resulting in non-matching grids between the two parts of the fault. In an earlier paper a mathematical scheme was proposed where the numerical discretization considers the hybrid finite volume method. In this paper we focus on the well-posedness of the continuous problem, the convergence of the discretized problem, and with several numerical tests we support the theoretical findings.