Efficient and energy stable scheme for the hydrodynamically coupled three components Cahn-Hilliard phase-field model using the stabilized-Invariant Energy Quadratization (S-IEQ) Approach

Abstract In this paper, we consider numerical approximations for solving the hydrodynamically coupled three components Cahn-Hilliard phase-field model. By combining the Invariant Energy Quadratization approach with the stabilization technique, and the projection method for the Navier-Stokes equations, we obtain a linear, second-order, and unconditionally energy stable time marching scheme. We present rigorous proofs for the well-posedness of the obtained linear system and the unconditional energy stability. Various 2D and 3D numerical simulations are implemented to demonstrate the stability and accuracy of the scheme thereafter.