A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system

Daozhi Han, Xiaoming Wang

We propose a novel second order in time, decoupled and unconditionally stable numerical scheme for solving the Cahn-Hilliard-Darcy (CHD) system which models two-phase flow in porous medium or in a Hele-Shaw cell. The scheme is based on the ideas of second order convex- splitting for the Cahn-Hilliard equation and pressure-correction for the Darcy equation. We show that the scheme is uniquely solvable, unconditionally energy stable and mass-conservative. Ample numerical results are presented to gauge the efficiency and robustness of our scheme.