Efficient decoupled second-order numerical scheme for the flow-coupled Cahn–Hilliard phase-field model of two-phase flows

Abstract

We construct in this paper a fully-decoupled and second-order accurate numerical scheme for solving the Cahn–Hilliard–Navier–Stokes phase-field model of two-phase incompressible flows. A full decoupling method is used by introducing several nonlocal variables and their ordinary differential equation to deal with the nonlinear and coupling terms. By combining with some effective methods to handle the Navier–Stokes equation, we obtain an efficient and easy-to-implement numerical scheme in which one only needs to solve several fully-decoupled linear elliptic equations with constant coefficients at each time step. We further prove the unconditional energy stability and solvability rigorously, and present various numerical simulations in 2D and 3D to demonstrate the efficiency and stability of the proposed scheme, numerically.