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

作者：Yang, Xiaofeng^*; Zhao, Jia^*; Wang, Qi; Shen, Jie

来源：Mathematical Models and Methods in Applied Sciences, 2017, 27(11): 1993-2030.

DOI：10.1142/S0218202517500373

• Second-order
• phase-field
• Cahn-Hilliard
• three-phase
• unconditional energy stability
• invariant energy quadratization

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 a linear symmetric, positive definite at each time step. We prove that the developed schemes are unconditionally energy stable and present various 2D and 3D numerical simulations to demonstrate the stability and the accuracy of the schemes.

• 出版日期2017-10
• 单位北京计算科学研究中心; 南开大学