Wang H L, Chai Z H, Shi B C, Liang H
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China.
Phys Rev E. 2016 Sep;94(3-1):033304. doi: 10.1103/PhysRevE.94.033304. Epub 2016 Sep 23.
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 et al., 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.
本文对用于艾伦 - 卡恩（A - C）方程和卡恩 - 希尔德里克（C - H）方程的格子玻尔兹曼（LB）模型进行了比较研究。为此，首先提出了一种用于A - C方程的新LB模型，其中平衡分布函数和源项分布函数经过精心设计，以正确恢复A - C方程。该模型中的梯度项可通过分布函数的非平衡部分来计算，从而使碰撞过程能够在局部实现。然后，针对几个经典问题进行了详细的数值研究，以便在追踪两相流界面方面，对本文提出的A - C方程模型与最近开发的用于C - H方程的LB模型[H. Liang等人，《物理评论E》89，053320（2014）PLEEE81539 - 375510.1103/PhysRevE.89.053320]进行比较。结果表明，本文提出的用于A - C方程的LB模型更准确、更稳定，并且在空间上具有二阶收敛率，而之前用于C - H方程的LB模型的收敛率仅约为1.5。
