An energy-stable method for a phase-field surfactant model

Abstract

Two-phase systems with surfactants have extensive applications in scientific and industrial fields. In this paper, we consider a second-order time-accurate, highly efficient, and energy-stable scheme for a phase-field surfactant equation satisfying the energy boundedness. Because of the nonlinear and coupling terms in phase-field surfactant systems, it is not trivial to develop a totally decoupled and energy dissipation-preserving computational scheme. To address this challenge, we use an efficient variant of the scalar auxiliary variable (SAV) approach. The present method has the following merits: (i) The time-marching scheme is completely decoupled and the numerical implementation is efficient; (ii) the energy stability can be estimated in a straightforward manner; and (iii) various surfactant-laden dynamics can be well simulated. Various computational tests are conducted to validate the desired temporal accuracy, energy stability, and capability.