Efficient linear, decoupled, and unconditionally stable scheme for a ternary Cahn-Hilliard type Nakazawa-Ohta phase-field model for tri-block copolymers

Abstract

We establish a ternary Cahn-Hilliard type Nakazawa-Ohta phase-field model for the triblock copolymer, and study its numerical approximation. The model is a highly coupled nonlinear system, consisting of two Cahn-Hilliard equations and two nonlocal equations. We solve the model by constructing a second-order accurate, time-marching scheme via the Scalar Auxiliary Variable (SAV) approach combined with the stabilization technique. At every time step, the scheme is composed of several decoupled type bi-Laplace equations, which makes it the first linear and fully-decoupled scheme. We further prove the unconditional energy stability rigorously and perform numerous numerical simulations in 2D and 3D to illustrate it numerically.