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

•We propose a novel stabilized SAV approach for solving the phase field model for tri-block copolymers.•The proposed schemes are second-order accurate, provably unconditionally energy stable, non-iterative.•The added linear stabilization term is shown to be crucial enhance the stability while keeping the required accuracy.•One only need to solve three decoupled linear equations at each time step.•We further prove the unconditional energy stabilities rigorously and present numerious 2D and 3D simulations. 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.