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Volume 36, Issue 3
A Comparative Study of Two Allen-Cahn Models for Immiscible $N$-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method

Chengjie Zhan, Xi Liu, Zhenhua Chai & Baochang Shi

DOI: 10.4208/cicp.OA-2023-0228

Commun. Comput. Phys., 36 (2024), pp. 850-876.

Published online: 2024-10

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  • Abstract

In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [Model A: Zheng et al., Phys. Rev. E 101, 0433202 (2020) and Model B: Mirjalili and Mani, J. Comput. Phys. 498, 112657 (2024)] 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 Model B is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the Model A.

  • Keywords

Model comparisons, Allen-Cahn models, $N$-phase flows, lattice Boltzmann method.

  • AMS Subject Headings

76T30,76D05,76B45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-36-850, author = {Zhan , ChengjieLiu , XiChai , Zhenhua and Shi , Baochang}, title = {A Comparative Study of Two Allen-Cahn Models for Immiscible $N$-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method}, journal = {Communications in Computational Physics}, year = {2024}, volume = {36}, number = {3}, pages = {850--876}, abstract = {

In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [Model A: Zheng et al., Phys. Rev. E 101, 0433202 (2020) and Model B: Mirjalili and Mani, J. Comput. Phys. 498, 112657 (2024)] 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 Model B is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the Model A.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0228}, url = {http://global-sci.org/intro/article_detail/cicp/23460.html} }
TY - JOUR T1 - A Comparative Study of Two Allen-Cahn Models for Immiscible $N$-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method AU - Zhan , Chengjie AU - Liu , Xi AU - Chai , Zhenhua AU - Shi , Baochang JO - Communications in Computational Physics VL - 3 SP - 850 EP - 876 PY - 2024 DA - 2024/10 SN - 36 DO - http://doi.org/10.4208/cicp.OA-2023-0228 UR - https://global-sci.org/intro/article_detail/cicp/23460.html KW - Model comparisons, Allen-Cahn models, $N$-phase flows, lattice Boltzmann method. AB -

In this work, we conduct a detailed comparison between two second-order conservative Allen-Cahn (AC) models [Model A: Zheng et al., Phys. Rev. E 101, 0433202 (2020) and Model B: Mirjalili and Mani, J. Comput. Phys. 498, 112657 (2024)] 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 Model B is more stable for the realistic complex $N$-phase flows, although there is an adjustable parameter in the Model A.

Zhan , ChengjieLiu , XiChai , Zhenhua and Shi , Baochang. (2024). A Comparative Study of Two Allen-Cahn Models for Immiscible $N$-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method. Communications in Computational Physics. 36 (3). 850-876. doi:10.4208/cicp.OA-2023-0228
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