An unconditionally energy-stable second-order time-accurate numerical scheme for the coupled Cahn-Hilliard system in copolymer/homopolymer mixtures

Abstract

In this article, we present an unconditional energy stable numerical method for the coupled Cahn-Hilliard system for homopolymer and copolymer mixtures in two-and three-dimensional spaces. By combining a Crank- Nicolson-type method with a nonlinearly stabilized splitting method, a second-order accurate numerical scheme is constructed. To efficiently solve the discrete system, we use a fast iterative Fourier transform method. We prove the unconditional energy stability of the proposed method. Therefore, a large time step can be adopted. Various numerical experiments are performed to prove the performance of the proposed scheme.