A numerical method for a model of two-phase flow in a coupled free flow and porous media system

In this article, we study two-phase fluid flow in coupled free flow and porous media regions. The model consists of coupled Cahn–Hilliard and Navier–Stokes equations in the free fluid region and the two-phase Darcy law in the porous medium region. We propose a Robin–Robin domain decomposition method for the coupled Navier–Stokes and Darcy system with the generalized Beavers–Joseph–Saffman condition on the interface between the free flow and the porous media regions. Numerical examples are presented to illustrate the effectiveness of this method.