A fully-decoupled second-order-in-time and unconditionally energy stable scheme for a phase-field model of two phase flow with variable density

TL;DR

This paper introduces a second-order, fully decoupled, energy-stable numerical scheme for two-phase flow modeling with variable density, improving computational efficiency and stability in phase-field simulations.

Contribution

The paper proposes a novel decoupling Constant Scalar Auxiliary Variable (D-CSAV) method that simplifies computations and guarantees unconditional energy stability for complex two-phase flow models.

Findings

The scheme is unconditionally energy stable.

It requires solving only three linear elliptic systems per time step.

Extensive benchmarks confirm accuracy and efficiency.

Abstract

In this paper, we develop a second-order, fully decoupled, and energy-stable numerical scheme for the Cahn-Hilliard-Navier-Stokes model for two phase flow with variable density and viscosity. We propose a new decoupling Constant Scalar Auxiliary Variable (D-CSAV) method which is easy to generalize to schemes with high order accuracy in time. The method is designed using the "zero-energy-contribution" property while maintaining conservative time discretization for the "non-zero-energy-contribution" terms. Our algorithm simplifies to solving three independent linear elliptic systems per time step, two of them with constant coefficients. The update of all scalar auxiliary variables is explicit and decoupled from solving the phase field variable and velocity field. We rigorously prove unconditional energy stability of the scheme and perform extensive benchmark simulations to demonstrate accuracy and efficiency of the method.