A comparative study of two Allen-Cahn models for immiscible $N$-phase flows by using a consistent and conservative lattice Boltzmann method

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Main Authors: Zhan, Chengjie, Liu, Xi, Chai, Zhenhua, Shi, Baochang
Format: Preprint
Published: 2023
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author Zhan, Chengjie
Liu, Xi
Chai, Zhenhua
Shi, Baochang
author_facet Zhan, Chengjie
Liu, Xi
Chai, Zhenhua
Shi, Baochang
contents In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [\emph{Model A}: Zheng \emph{et al.}, Phys. Rev. E 101, 0433202 (2020) and \emph{Model B}: Mirjalili and Mani, (2023)] for the immiscible $N$-phase flows. Mathematically, these two AC equations can be proved to be equivalent under some approximate conditions. However, the effects of these approximations are unclear from the theoretical point of view, and would be considered numerically. To this end, we propose a consistent and conservative lattice Boltzmann method for the AC models for $N$-phase flows, and present some numerical comparisons of accuracy and stability between these two AC models. The results show that both two AC models have good performances in accuracy, but the \emph{Model B} is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the \emph{Model A}.
format Preprint
id arxiv_https___arxiv_org_abs_2306_06983
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle A comparative study of two Allen-Cahn models for immiscible $N$-phase flows by using a consistent and conservative lattice Boltzmann method
Zhan, Chengjie
Liu, Xi
Chai, Zhenhua
Shi, Baochang
Fluid Dynamics
Mathematical Physics
In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [\emph{Model A}: Zheng \emph{et al.}, Phys. Rev. E 101, 0433202 (2020) and \emph{Model B}: Mirjalili and Mani, (2023)] for the immiscible $N$-phase flows. Mathematically, these two AC equations can be proved to be equivalent under some approximate conditions. However, the effects of these approximations are unclear from the theoretical point of view, and would be considered numerically. To this end, we propose a consistent and conservative lattice Boltzmann method for the AC models for $N$-phase flows, and present some numerical comparisons of accuracy and stability between these two AC models. The results show that both two AC models have good performances in accuracy, but the \emph{Model B} is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the \emph{Model A}.
title A comparative study of two Allen-Cahn models for immiscible $N$-phase flows by using a consistent and conservative lattice Boltzmann method
topic Fluid Dynamics
Mathematical Physics
url https://arxiv.org/abs/2306.06983