A Finite-Volume Moving-Mesh Method for Two-phase Flow in Fracturing Porous Media

TL;DR

This paper introduces a finite-volume moving-mesh method for simulating two-phase flow in fractured porous media with dynamic fracture geometries, improving accuracy and conservation in modeling complex flow scenarios.

Contribution

It develops a novel reduced model and a conforming moving-mesh discretization for two-phase flow in time-dependent fractured media, enhancing simulation flexibility and accuracy.

Findings

The method is fully conservative and allows arbitrary facet movement.

Numerical tests demonstrate the scheme's performance and accuracy.

The modeling error of the reduced model is thoroughly investigated.

Abstract

Flow in fractured porous media is modeled frequently by discrete fracture-matrix approaches where fractures are treated as dimensionally reduced manifolds. Generalizing earlier work we focus on two-phase flow in time-dependent fracture geometries including the fracture's aperture. We present the derivation of a reduced model for immiscible two-phase flow in porous media. For the reduced model we present a fully conforming finite-volume discretization coupled with a moving-mesh method. This method permits arbitrary movement of facets of the triangulation while being fully conservative. In numerical examples we show the performance of the scheme and investigate the modeling error of the reduced model.