An efficiently linear and totally decoupled variant of SAV approach for the binary phase-field surfactant fluid model

In this work, an efficiently linear, totally decoupled, and unconditionally energy-stable time-marching scheme is developed for solving the Cahn-Hilliard (CH) type phase-field incompressible surfactant fluid model. The proposed scheme is based on a variant of scalar auxiliary variable (SAV) approach. By defining several time dependent auxiliary variables, the original governing equations are reformulated into equivalent forms which provide the foundation to construct the time-discretized numerical method. Different from the original SAV approach, the proposed method achieves totally decoupled computations of all variables. In each time step, the surfactant is explicitly calculated, then the phase-field function is updated by solving linear elliptic type equations. The velocity and pressure fields are calculated by the projection method. The time-discretized energy dissipation law is estimated in detail. The numerical validations indicate that the proposed method not only has desired energy stability but also works well for surfactant-laden droplets dynamics.