Efficient, non-iterative, and decoupled numerical scheme for a new modified binary phase-field surfactant system

Abstract

We consider in this paper numerical approximations of a Cahn-Hilliard binary phase-field fluid-surfactant model. By adding a quartic form of the gradient potential, we first modify the commonly used total free energy into a form which is bounded from below and establish the energy law for the new system. Then we develop a stabilized-SAV scheme that combines the SAV approach with the stabilization technique, where a crucial linear stabilization term is added to enhance the stability thus allowing large time steps. With many desired properties such as a second-order in time, totally decoupled, linear, and non-iterative, this scheme is unconditionally energy stable and requires solving only four decoupled and linear biharmonic equations with constant coefficients at each time step. We further prove the energy stability and present numerous 2D and 3D numerical simulations to demonstrate the accuracy and stability of the developed scheme