Comparative study of the lattice Boltzmann models for Allen-Cahn and Cahn-Hilliard equations
Comparative study of the lattice Boltzmann models for Allen-Cahn and Cahn-Hilliard equations
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Allen-Cahn 和 Cahn-Hilliard 方程的格子玻尔兹曼模型的比较研究
DOI：
10.1103/physreve.94.033304
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发表时间：
2016
影响因子：
2.4
通讯作者：
Liang H.
中科院分区：
文献类型：
--
作者：
Wang H. L.;Chai Z. H.;Shi B. C.;Liang H.
本文对Allen-Cahn（A-C）和Cahn-Hilliard（C-H）方程的格子Boltzmann（LB）模型进行了比较研究。为此，首先提出了一种新的A-C方程LB模型，通过对平衡态分布函数和源项分布函数的精细设计，使A-C方程得到了正确的恢复。该模型中的梯度项可由分布函数的非平衡部分计算，从而可局部实现碰撞过程。然后对几个经典问题进行了详细的数值研究，并与最近发展起来的LB模型[H. Liang，Phys.Rev.E89，053320（2014）PLEEE 81539 -375510.1103/PhysRevE.89.053320]中描述的方法。结果表明，本文提出的A-C方程的LB模型具有更高的精度和更好的稳定性，并且在空间上具有二阶收敛速度，而以往的C-H方程的LB模型的收敛速度仅为1.5。
In this paper, a comparative study of the lattice Boltzmann (LB) models for the Allen-Cahn (A-C) and Cahn-Hilliard (C-H) equations is conducted. To this end, a new LB model for the A-C equation is first proposed, where the equilibrium distribution function and the source term distribution function are delicately designed to recover the A-C equation correctly. The gradient term in this model can be computed by the nonequilibrium part of the distribution function such that the collision process can be implemented locally. Then a detailed numerical study on several classical problems is performed to give a comparison between the present model for the A-C equation and the recently developed LB model [H. Liang , Phys. Rev. E 89, 053320 (2014)PLEEE81539-375510.1103/PhysRevE.89.053320] for the C-H equation in terms of tracking the interface of two-phase flow. The results show that the present LB model for the A-C equation is more accurate and more stable, and also has a second-order convergence rate in space, while the convergence rate of the previous LB model for the C-H equation is only about 1.5.