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, 2024)
In this work, we conduct a detailed comparison between two second-orderconservative 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 theimmiscible $N$-phase flows. Mathematically, these two AC equations can be proved tobe equivalent under some approximate conditions. However, the effects of these approximations are unclear from the theoretical point of view, and would be considerednumerically. To this end, we propose a consistent and conservative lattice Boltzmannmethod 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 thatboth 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 parameterin the Model A.
Keywords: Model comparisons; Allen-Cahn models; $N$-phase flows; lattice Boltzmann method.