Unconditional Energy Stable Runge-Kutta Schemes for a Phase Field Model for Diblock Copolymers

A high-accuracy and unconditional energy stable numerical scheme for a phase field model for diblock copolymers (PF-BCP model) is developed. The PF-BCP model is reformulated into an equivalent model, which based on scaler auxiliary variable (SAV) formulation. After that a stable Runge-Kutta (RK) method and a Fourier-spectral method are applied to the SAV-reformulated PF-BCP model to discretize on the temporal and spatial dimensions respectively. The fully discretized numerical scheme is computed by fixed-point iterations. Meanwhile, the unconditional energy decay property is proved rigorously. Finally, we present the results of numerical experiments to show the accuracy and efficiency of the RK scheme used and discuss the influence of physical parameters and initial conditions on the phase separation in the simulation of the PF-BCP model. In addition, the energy decay property of the numerical solutions is verified.