Improved multiple-relaxation-time lattice Boltzmann model for Allen–Cahn equation

Abstract

Two-phase flow is important in both science and engineering. In this paper, a D2Q5 multi-relaxation-time lattice Boltzmann model is proposed for solving Allen–Cahn equation, which is a convection–diffusion equation for the order parameter. Through Chapmann–Enskog analysis, the macroscopic equations can be recovered from the D2Q5 MRT LB model. Then, a detailed numerical study on several classical problems is performed to give a comparison between the present model for the AC equation and the previous study. The results show that the present model gets better accuracy and has better stability than that of single-relaxation-time LB model, and has higher computational efficiency than that of D2Q9 MRT LB model. Furthermore, as an important application, the model is also used to study the deformation field problem because of its excellent ability to cope with complex and changeable boundaries.