An improved scalar auxiliary variable (SAV) approach for the phase-field surfactant model

Abstract

In this work, we develop a new linear, decoupled numerical scheme for the typical phasefield surfactant model. An improved scalar auxiliary variable (SAV) approach is used to discretize the governing equations in time. Different from the classical SAV approach, this improved form can calculate the phase field function phi, surfactant function psi, and auxiliary variables in a step-by-step manner, i.e., the auxiliary variables are treated totally explicitly, thus we can directly calculate phi and psi instead of computing the inner products. At each time step, the surfactant psi can be directly obtained by an explicit way, then phi is updated by solving a linear system with constant coefficient. Therefore, the implementation of this improved SAV approach is easier than the classical SAV approach. The energy stability in first-order case can be analytically proved by using the our method. The numerical experiments show that our proposed method not only achieves desired firstand second-order accuracy but also satisfies the desired discrete energy dissipation law even if some larger time steps are used. Furthermore, the coarsening dynamics with different average concentrations can be well simulated by using our method. The co-continuous and drop patterns are generated in the even compositions case and uneven compositions case, respectively. (c) 2020 Elsevier Inc. All rights reserved.