@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0228},
url = {http://global-sci.org/intro/article_detail/cicp/23460.html}
}