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.

中文翻译：

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Allen-Cahn 方程的改进的多重松弛时间格子 Boltzmann 模型

两相流在科学和工程中都很重要。本文提出了一种D2Q5多弛豫-时间格子Boltzmann模型来求解Allen-Cahn方程，该方程是阶参数的对流-扩散方程。通过 Chapmann-Enskog 分析，可以从 D2Q5 MRT LB 模型中恢复宏观方程。然后，对几个经典问题进行了详细的数值研究，以比较当前的 AC 方程模型与以前的研究。结果表明，与单松弛时间LB模型相比，本模型具有更好的准确性和稳定性，并且比D2Q9 MRT LB模型具有更高的计算效率。此外，作为一项重要应用，