A NUMERICAL STUDY OF A MICRO-MACRO SCALE MODEL FOR A TWO-PHASE STOKES-CAHN-HILLIARD SYSTEM IN A POROUS MEDIUM

Phase-field models, which account for a finite interfacial thickness, provide a powerful approach to capturing the movement of fluid interfaces. In this paper, we focus on the numerical simulation of two-phase incompressible Stokes flow, governed by the Stokes-Cahn-Hilliard system, within a porous medium. We validate a homogenized model previously derived from a heterogeneous microscopic framework using two-scale convergence. Numerical solutions are computed using a semidiscrete finite element scheme, capturing the dynamics of phase separation and interface stabilization, which demonstrates the agreement between the macroscopic and microscopic descriptions. In other words, we discuss how the solutions to the above equations approach the original sharp-interface model as the interfacial thickness ε tends to zero.