Numerical Approximations for a Three Component Cahn-hilliard Phase-field Model Based on the Invariant Energy Quadratization Method

How to develop efficient numerical schemes while preserving the energy stability at the discrete level is a challenging issue for the three component Cahn-Hillard phase-field model. We develop in this paper first and second order temporal approximation schemes based on the “Invariant Energy Quadratization” method, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to a symmetric positive definite linear system to be solved at each time step. We rigorously prove that the proposed schemes are unconditional energy stable. Various 2D and 3D numerical simulations are presented to demonstrate the stability and the accuracy of the schemes.