Decoupled, non-iterative, and unconditionally energy stable large time stepping method for the three-phase Cahn-Hilliard phase-field model

Abstract

In this paper, we consider numerical approximations for a three-phase phase-field model, where three fourth-order Cahn-Hilliard equations are nonlinearly coupled together through a Lagrange multiplier term and a sixth-order polynomial bulk potential. By combining the recently developed SAV approach with the linear stabilization technique, we arrive at a novel stabilized-SAV scheme. At each time step, the scheme requires solving only four linear biharmonic equations with constant coefficients, making it the first, to the best of the author's knowledge, totally decoupled, second-order accurate, linear, and unconditionally energy stable scheme for the model. We further prove the unconditional energy stability rigorously and demonstrate the stability and the accuracy of the scheme numerically through the comparisons with the non-stabilized SAV scheme for simulating numerous benchmark numerical examples in 2D and 3D.