A variant of stabilized-scalar auxiliary variable (S-SAV) approach for a modified phase-field surfactant model

In this article, we develop a new linear, decoupled, second-order accurate, and energy stable numerical method for a modified phase-field surfactant model (Xu et al., 2020). The proposed scheme is a simple and efficient variant of stabilized-scalar auxiliary variable (S-SAV) method. The proposed scheme not only retains all advantages of S-SAV method but also simplifies the solution algorithm. The phase-field, surfactant, and auxiliary variables are totally decoupled in time, thus we can solve the whole system in a step-by-step manner. The phase-field function ϕ and surfactant ψ can be separately updated by solving two linear semi-implicit systems with constant coefficients and then the auxiliary variable is directly updated in an explicit way. We analytically prove the energy stability and the unique solvability of the proposed method. The numerical experiments show the desired temporal accuracy and energy stability. We numerically investigate the proper stabilization coefficients for the present scheme with specific parameters. Furthermore, various two- and three-dimensional benchmark tests are performed to study the dynamics of surfactant-laden phase separation.