Efficient, decoupled, and second-order unconditionally energy stable numerical schemes for the coupled Cahn–Hilliard system in copolymer/homopolymer mixtures

Abstract

The numerical approximations for the coupled Cahn–Hilliard system describing the phase separation of the copolymer and homopolymer mixtures are considered in this paper. To develop easy to implement time marching schemes with unconditional energy stabilities, we use the Scalar Auxiliary Variable (SAV) approach for achieving two efficient, decoupled, and linear numerical schemes, where a new scalar auxiliary variable is introduced to reformulate the model. The schemes lead to decoupled linear equations with constant coefficients at each time step, and their unique solvability and unconditional energy stabilities are proved rigorously. Numerical examples are performed to demonstrate the accuracy and energy stability of the proposed schemes, and numerous benchmark simulations are also presented to show a variety of morphologies of pattern formations of the copolymer and homopolymer mixtures.