A Comparative Study of Two Allen-Cahn Models for Immiscible N-Phase Flows by Using a Consistent and Conservative Lattice Boltzmann Method

In this work, we conduct a detailed comparison between two second-orderconservative Allen-Cahn (AC) models [Model A: Zhenget al., Phys. Rev. E 101, 0433202(2020) andModel B: Mirjalili and Mani, J. Comput. Phys. 498, 112657 (2024)] for theimmiscibleN-phase flows. Mathematically, these two AC equations can be proved tobe equivalent under some approximate conditions. However, the effects of these ap-proximations 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 forN-phase flows, and present some numerical compar-isons of accuracy and stability between these two AC models. The results show thatboth two AC models have good performances in accuracy, but theModel Bis more sta-ble for the realistic complexN-phase flows, although there is an adjustable parameterin theModel A.