计算机应用 ›› 2013, Vol. 33 ›› Issue (09): 2432-2435.DOI: 10.11772/j.issn.1001-9081.2013.09.2432

• 先进计算 • 上一篇    下一篇

基于格子Boltzmann方法的一维Burgers方程的数值模拟

兰中周1,2,乐励华1,2,高云1,2   

  1. 1. 东华理工大学 理学院, 南昌 330013
    2. 东华理工大学 理学院, 南昌 330013
  • 收稿日期:2013-03-26 修回日期:2013-05-09 出版日期:2013-09-01 发布日期:2013-10-18
  • 通讯作者: 乐励华
  • 作者简介:兰中周(1985-),男,河南濮阳人,硕士研究生,主要研究方向:格子Boltzmann方法及其科学计算;
    乐励华(1965-),男,江西抚州人,教授,主要研究方向:复杂流动的格子Boltzmann建模、计算机仿真;
    高云(1986-),女,河南信阳人,硕士,主要研究方向:格子Boltzmann方法及其科学计算。

Numerical simulation of one-dimensional Burgers' equation based on lattice Boltzmann method

LAN Zhongzhou,LE Lihua,GAO Yun   

  1. School of Science, East China Institute of Technology, Nanchang Jiangxi 330013, China
  • Received:2013-03-26 Revised:2013-05-09 Online:2013-10-18 Published:2013-09-01
  • Contact: LE Lihua

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摘要： 基于格子Boltzmann方法(LBM)的一维Burgers方程的数值解法,已有2-bit和4-bit模型。文中通过选择合适的离散速度模型构造出恰当的平衡态分布函数; 然后, 利用单松弛的格子Bhatnagar-Gross-Krook模型、Chapman-Enskog展开和多尺度技术, 提出了用于求解一维Burgers方程的3-bit的格子Boltzmann模型，即D1Q3模型，并进行了数值实验。实验结果表明，该方法的数值解与解析解吻合的程度很好,且误差比现有文献中的误差更小,从而验证了格子Boltzamnn模型的有效性。

关键词: 格子Boltzmann方法, Burgers方程, Chapman-Enskog展开, 3-bit格子, 格子BGK模型

Abstract: For the numerical simulation of one-dimensional Burgers' equation based on Lattice Boltzmann method, there had been 2-bit and 4-bit models. In this paper, an equilibrium distribution function was constructed by choosing the proper kind of discrete velocity model. And then, using Lattice Bhatnagar-Gross-Krook (LBGK) model, Chapman-Enskog expansion and multiscale technique, a 3-bit Lattice Boltzmann Method (LBM) called D1Q3 model was proposed for the one-dimensional Burgers equation. Some numerical experiments were carried out and the numerical results were in good agreement with analytical solutions, therefore the effectiveness of the new method was verified.

Key words: Lattice Boltzmann Method (LBM), Burgers equation, Chapman-Enskog expansion, 3-bit lattice, Lattice Bhatnagar-Gross-Krook (LBGK) model

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