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

•A linear, totally decoupled, and second-order scheme for the ternary CAC fluids.•The proposed scheme is highly efficient and is very easy to implement.•The discrete energy dissipation law of the numerical scheme is proven. Based on a time-dependent auxiliary variable approach, we propose linear, to...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 438; p. 127599
Main Authors: Tan, Zhijun, Yang, Junxiang, Chen, Jianjun, Kim, Junseok
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2023
Subjects:
Dissipation law
Finite difference method
Multigrid algorithm
Three-phase conservative allen–Cahn fluids
Three-phase conservative allen–Cahn fluids
Multigrid algorithm
Finite difference method
Dissipation law
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:•A linear, totally decoupled, and second-order scheme for the ternary CAC fluids.•The proposed scheme is highly efficient and is very easy to implement.•The discrete energy dissipation law of the numerical scheme is proven. Based on a time-dependent auxiliary variable approach, we propose linear, totally decoupled, 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 conserved, (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 decoupled equations need to be updated at each time step. We adopt the linear multigrid algorithm 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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2022.127599