用格子Boltzmann方法模拟非线性热传导方程  

Simulation of the Nonlinear Heat Conduction Equation With the Lattice Boltzmann Method

作　　者：刘芳[1] 施卫平[2] 

机构地区：[1]长春工业大学基础科学学院,长春130012 [2]吉林大学数学学院,长春130012

出　　处：《应用数学和力学》2015年第11期1158-1166,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11401046);吉林省教育厅"十二五"科学技术研究计划(2014-478)~~

摘　　要：对具有非线性源项和非线性扩散项的热传导方程建立格子Boltzmann求解模型.在演化方程中增加了两个关于源项分布函数的微分算子,对演化方程实施Chapman-Enskog展开.通过对演化方程的进一步改进,恢复出具有高阶截断误差的宏观方程.对不同参数选取下的非线性热传导方程进行了数值模拟,数值解与精确解吻合得很好.该模型也可以用于同类型的其他偏微分方程的数值计算中.A lattice Boltzmann model for the heat conduction equation with a nonlinear source term and a nonlinear diffusion term was presented. 2 differential operators related to the source term distribution function were added to the evolution equation, on which the Chapman-Enskog expansion was carried out. Then, through some further improvement of the evolution equation the macroscopic differential equation was recovered in 2 schemes with high-order truncation errors. Detailed numerical simulations of the nonlinear heat conduction equation with different parameter selections were performed. The numerical results agree well with the exact solutions. This model can also be directly used to numerically solve other partial differential equations in similar forms.

关 键 词：格子BOLTZMANN模型 非线性热传导方程 LBGK模型 非线性源项 

分 类 号：O35[理学—流体力学]