A highly efficient variant of scalar auxiliary variable (SAV) approach for the phase-field fluid-surfactant model

Abstract

In this work, we study a phase-field fluid-surfactant system by applying two conservative Allen-Cahn equations and Navier-Stokes equations. A highly efficient variant of scalar auxiliary variable approach is applied in designing a second-order time-accurate numerical scheme. By introducing several scalar auxiliary variables, all variables are decoupled with each other and they can be updated in a step-by-step manner. The proposed method satisfies the mass conservation law, unique solvability and modified energy dissipation property. Several tests are performed to investigate the surfactant-laden phase-separation and the effect of surfactant in two dimensional and three dimensional space.