Simulation of Two-Phase Flow in Models with Micro-porous Material

The paper presents an original numerical algorithm to simulate coupled two-phase fluid flow in domains containing open pores and microporous material. To simulate the coupled flow we use the time-dependent Navier-Stokes-Brinkman equation. The transport of the phases is governed by the Cahn-Hilliard equation in the open pores and by the Buckley-Leverett equation in the porous material. We suggested a unified finite-difference approximation of the two transport equations, that satisfy the natural conjugation conditions. However, Cahn-Hilliard requires an additional boundary condition, that must be satisfied at the interface to ensure the wetting angle.