Wang Lei, Shi Baochang, Chai Zhenhua
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 Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):043311. doi: 10.1103/PhysRevE.92.043311. Epub 2015 Oct 30.
In this paper, a regularized lattice Boltzmann model for a class of nonlinear convection-diffusion equations with variable coefficients is proposed. The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments. The Chapman-Enskog analysis shows that the nonlinear convection-diffusion equations can be recovered correctly. Numerical tests, including Fokker-Planck equations, Buckley-Leverett equation with discontinuous initial function, nonlinear convection-diffusion equation with anisotropic diffusion, are carried out to validate the present model, and the results show that the present model is more accurate than some available lattice Boltzmann models. It is also demonstrated that the present model is more stable than the traditional single-relaxation-time model for the nonlinear convection-diffusion equations.
本文提出了一种用于一类变系数非线性对流扩散方程的正则化格子玻尔兹曼模型。本模型的主要思想是引入一组仅根据宏观矩定义的预碰撞分布函数。查普曼-恩斯科格分析表明，非线性对流扩散方程能够被正确恢复。进行了数值试验，包括福克-普朗克方程、具有不连续初始函数的巴克利-莱弗里特方程、具有各向异性扩散的非线性对流扩散方程，以验证本模型，结果表明本模型比一些现有的格子玻尔兹曼模型更精确。还证明了对于非线性对流扩散方程，本模型比传统的单松弛时间模型更稳定。
