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

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.