A novel linear, unconditional energy stable scheme for the incompressible Cahn–Hilliard–Navier–Stokes phase-field model

Abstract

In this paper, we propose a linear, unconditional energy stable time discretization scheme for Cahn–Hilliard–Navier–Stokes model, which is a phase-field model for two-phase incompressible flow. Based on a Lagrange multiplier approach, our proposed scheme is linearized by using implicit–explicit treatments, and the computation of the velocity field u, the pressure p, the phase function ϕ are decoupled. Using the mathematical induction, the bound ‖ϕn‖L∞ is obtained. Rigorous error analysis for the variable u, p and ϕ are carried out in semi-discrete form. Finally, some numerical experiments are done to demonstrate the effectiveness for the proposed method.