一类偏微分方程的格子Boltzmann模型

摘要

研究了对流扩散方程、Burgers方程和Modified-Burgers方程等具有相同形式的一类偏微分方程.并且构建了带修正函数项的D1Q3格子Boltzmann模型求解这类方程.为了能准确地恢复出此宏观方程,利用Chapman-Enskog展开和多尺度分析技术,推导出了各个方向的平衡态分布函数和修正函数的具体表达式.数值计算结果表明该模型是稳定、有效的.%The convection-diffusion equation, Burgers equation and Modified-Burgers equation, which are a class of partial differential equation that has the same form, are investigated. And the D1Q3 lattice Boltzmann model with modified terms is developed to numerically solve these equations. In order to recover the governing equation correctly, based on the Chapman-Enskog expansion and multi-scale technique, the specific expression of equilibrium distribution function and modified function are deduced. The numerical computation results show that the D1Q3 lattice Boltzmann model is stable and effective.