Linear and fully decoupled scheme for a hydrodynamics coupled phase-field surfactant system based on a multiple auxiliary variables approach

We propose a linear, fully decoupled, and energy stable finite difference scheme for solving a phase-field surfactant fluid system. Inspired by the idea of multiple scalar auxiliary variables (MSAV) approach, two scalar auxiliary variables are used to transform the original governing equations into their equivalent forms. Based on the equivalent system, a highly efficient scheme can be developed. In one time cycle, the proposed algorithm can be efficiently performed, i.e., the surfactant ψ is explicitly updated, then the phase-field function ϕ, velocity field u, and pressure field p can be computed by solving linear systems with constant coefficients. The energy dissipation law for a modified energy can be estimated by using the proposed method. Various computational simulations confirm that the proposed method is not only accurate and energy stable but also works well for simulating surfactant-laden droplet dynamics.