Chai Zhenhua, Shi Baochang
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China.
Phys Rev E. 2020 Aug;102(2-1):023306. doi: 10.1103/PhysRevE.102.023306.
In this paper, we first present a unified framework of multiple-relaxation-time lattice Boltzmann (MRT-LB) method for the Navier-Stokes and nonlinear convection-diffusion equations where a block-lower-triangular-relaxation matrix and an auxiliary source distribution function are introduced. We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansion, and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes and nonlinear convection-diffusion equations from the MRT-LB method and show that from mathematical point of view, these four analysis methods can give the same equations at the second-order of expansion parameters. Finally, we give some elements that are needed in the implementation of the MRT-LB method and also find that some available LB models can be obtained from this MRT-LB method.
在本文中，我们首先提出了一种用于纳维 - 斯托克斯方程和非线性对流扩散方程的多松弛时间格子玻尔兹曼（MRT - LB）方法的统一框架，其中引入了一个块下三角松弛矩阵和一个辅助源分布函数。然后，我们对四种常用的分析方法（查普曼 - 恩斯科格分析、麦克斯韦迭代、直接泰勒展开和递推方程方法）进行了比较，这些方法已被用于从MRT - LB方法中获得宏观纳维 - 斯托克斯方程和非线性对流扩散方程，并表明从数学角度来看，这四种分析方法在展开参数的二阶项上可以给出相同的方程。最后，我们给出了MRT - LB方法实现中所需的一些要素，并且还发现可以从这种MRT - LB方法中获得一些现有的LB模型。
