An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen-Cahn fluids

초록

Based on a time-dependent auxiliary variable approach, we propose linear, totally decou-pled, and energy dissipative methods for the three-phase conservative Allen-Cahn (CAC) fluid system. The three-phase CAC equation has been extensively applied in the simulation of multi-component fluid flows because of the following advantages: (i) Total mass is con-served, (ii) Topological change of the interface can be implicitly captured. Compared with the ternary Cahn-Hilliard (CH) model, the CAC-type model is simple to solve. When we solve the CAC model by using the classical scalar auxiliary variable (SAV) approach, extra computational time is needed because we must decouple the local and non-local variables. The variant of SAV approach considered in the present study not only leads to linear and energy stable schemes, but also achieves highly efficient computation. Linear and decou-pled equations need to be updated at each time step. We adopt the linear multigrid al-gorithm to speed up the convergence. Extensive numerical experiments with and without fluid flows are conducted to validate the temporal accuracy, mass conservation, and energy law.(c) 2022 Elsevier Inc. All rights reserved.

키워드