Decoupled, energy stable schemes for a phase-field surfactant model

In this paper, we construct several linear, decoupled and energy stable schemes for a phase-field surfactant model, in which the free energy functional contains a fourth-order Ginzburg–Landau double well potential, a logarithmic Flory–Huggins potential and two nonlinear coupling terms. Several scalar auxiliary variables (SAV) are introduced to transform the governing system into an equivalent form, allowing the nonlinear potentials to be treated efficiently and semi-explicitly. At each time step, the schemes involve solving only two linear elliptic differential equations, and computations of two phase-field variables are totally decoupled. Moreover, the local concentration of surfactants can be obtained in an “explicit” way. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient, easy-to-implement and unconditionally energy stable.