Numerical approximations for a three-component Cahn-Hilliard phase-field model based on the invariant energy quadratization method

Abstract

How to develop efficient numerical schemes while preserving energy stability at the discrete level is challenging for the three-component Cahn-Hilliard phase-field model. In this paper, we develop a set of first and second order temporal approximation schemes based on a novel ``Invariant Energy Quadratization'' approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to well-posed linear systems with symmetric, positive definite operators to be solved at each time step. We prove that the developed schemes are unconditionally energy stable rigorously and present various 2D and 3D numerical simulations to demonstrate the stability and the accuracy of the schemes.