Lattice Boltzmann model for a class of partial differential equations

Computer Engineering and Applications ›› 2016, Vol. 52 ›› Issue (3): 21-26.

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Lattice Boltzmann model for a class of partial differential equations

DAI Houping1，2, ZHENG Zhoushun2，3, DUAN Dandan2

1.School of Mathematics and Statistics, Jishou University, Jishou, Hunan 416000, China
2.School of Mathematics and Statistics, Central South University, Changsha 410083, China
3.State Key Laboratory of Porous Metal Materials, Xi’an 710016, China

Online:2016-02-01 Published:2016-02-03

一类偏微分方程的格子Boltzmann模型

戴厚平1，2，郑洲顺2，3，段丹丹2

1.吉首大学数学与统计学院，湖南吉首 416000
2.中南大学　数学与统计学院，长沙 410083
3.金属多孔材料国家重点实验室，西安 710016

Abstract

Abstract: 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.

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Key words: lattice Boltzmann model, convection-diffusion equation, Burgers&rsquo, equation, Modified-Burgers&rsquo, equation, D1Q3 model

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。

关键词: 格子Boltzmann模型, 对流扩散方程, Burgers方程, Modified-Burgers方程, D1Q3模型

DAI Houping1，2, ZHENG Zhoushun2，3, DUAN Dandan2. Lattice Boltzmann model for a class of partial differential equations[J]. Computer Engineering and Applications, 2016, 52(3): 21-26.

戴厚平1，2，郑洲顺2，3，段丹丹2. 一类偏微分方程的格子Boltzmann模型[J]. 计算机工程与应用, 2016, 52(3): 21-26.

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Lattice Boltzmann model for a class of partial differential equations

一类偏微分方程的格子Boltzmann模型

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