An adapted energy dissipation law-preserving numerical algorithm for a phase-field surfactant model

The phase-field surfactant model is popular to study the dynamics of surfactant-laden phase separation in a binary mixture. In this work, we numerically investigate the H-1-gradient flow based phase-field surfactant mathematical model using an energy dissipation-preserving numerical method. The proposed method adapts a Lagrange multiplier method. The present method not only preserves the unconditional stability, but also satisfies the original energy dissipation law, which is different from the modified energy dissipation laws estimated by the scalar auxiliary variable and invariant energy quadratization methods. An effective scheme is introduced to solve the weakly coupled discrete equations. In one time cycle, we only need to calculate four linear, fully decoupled discrete equations with constant coefficients and compute two nonlinear algebraic equations using Newton's iteration. The computational experiments indicate that the proposed method is accurate and satisfies the original energy stability. Moreover, the long-time behaviors of surfactant-laden phase separation can also be well simulated.