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

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-bystep 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.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

In this work, we study a phase-field fluid-surfactant system using conservative Allen-Cahn equations and Navier-Stokes equations. We propose a highly efficient numerical scheme based on scalar auxiliary variables, which decouple all the variables and allow for step-by-step updates. The method satisfies mass conservation, unique solvability, and modified energy dissipation. Tests are conducted to investigate surfactant-laden phase separation and its effects in two and three-dimensional spaces.