Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟

计算物理 ›› 2015, Vol. 32 ›› Issue (6): 639-648.

Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟

段雅丽¹, 陈先进¹, 孔令华²

1. 中国科学技术大学数学科学学院, 安徽合肥 230026;
2. 江西师范大学数学与信息科学学院, 江西南昌 330022

收稿日期:2014-11-05 修回日期:2015-02-01 出版日期:2015-11-25 发布日期:2015-11-25
作者简介:Duan Yali(1973-),female,Shanxi,associate professor,PhD,major in numerical solution of PDEs,E-mail:ylduan01@ustc.edu.
基金资助:
Supported by the NSFC(11101399,10901074);Fundamental Research Funds for Central Universities(WK0010000022)

Lattice Boltzmann Model for Compound Burgers-Korteweg-de Vries Equation

DUAN Yali¹, CHEN Xianjin¹, KONG Linghua²

1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China;
2. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

Received:2014-11-05 Revised:2015-02-01 Online:2015-11-25 Published:2015-11-25
Supported by:
Supported by the NSFC(11101399,10901074);Fundamental Research Funds for Central Universities(WK0010000022)

摘要/Abstract

摘要： 针对Burgers-Korteweg-de Vries(cBKdV)复合方程提出一种格子Boltzmann模型.通过恰当地处理色散项u_xxx并运用Chapman-Enskog展开从格子Boltzmann方程推导出宏观方程,从而得到联系微观量与宏观量的局部平衡分布函数.对不同微分方程进行数值实验,数值解与解析解非常吻合,相比于其它数值结果,该格子Boltzmann模型的数值结果更精确,说明该数值模型的高效性.

关键词: 格子Boltzmann模型, Burgers-KdV复合方程, Chapman-Enskog展开

Abstract: We develop a lattice Boltzmann model for compound Burgers-Korteweg-de Vries (cBKdV) equation. By properly treating dispersive term u_xxx and applying Chapman-Enskog expansion, the governing equation is recovered correctly from lattice Boltzmann equation and local equilibrium distribution functions are obtained. Numerical experiments show that our results agree well with exact solutions and have better numerical accuracy compared with previous numerical results. This hence indicates that the model is satisfactory and efficient.

Key words: Lattice Boltzmann model, Compound Burgers-KdV equation, Chapman-Enskog expansion

中图分类号:

O241.8

段雅丽, 陈先进, 孔令华. Burgers-Korteweg-de Vries复合方程的格子Boltzmann方法模拟[J]. 计算物理, 2015, 32(6): 639-648.

DUAN Yali, CHEN Xianjin, KONG Linghua. Lattice Boltzmann Model for Compound Burgers-Korteweg-de Vries Equation[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 32(6): 639-648.

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