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用格子Boltzmann方法模拟非线性热传导方程

刘芳 施卫平

刘芳, 施卫平. 用格子Boltzmann方法模拟非线性热传导方程[J]. 应用数学和力学, 2015, 36(11): 1158-1166. doi: 10.3879/j.issn.1000-0887.2015.11.004
引用本文: 刘芳, 施卫平. 用格子Boltzmann方法模拟非线性热传导方程[J]. 应用数学和力学, 2015, 36(11): 1158-1166. doi: 10.3879/j.issn.1000-0887.2015.11.004
LIU Fang, SHI Wei-ping. Simulation of the Nonlinear Heat Conduction Equation With the Lattice Boltzmann Method[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1158-1166. doi: 10.3879/j.issn.1000-0887.2015.11.004
Citation: LIU Fang, SHI Wei-ping. Simulation of the Nonlinear Heat Conduction Equation With the Lattice Boltzmann Method[J]. Applied Mathematics and Mechanics, 2015, 36(11): 1158-1166. doi: 10.3879/j.issn.1000-0887.2015.11.004

用格子Boltzmann方法模拟非线性热传导方程

doi: 10.3879/j.issn.1000-0887.2015.11.004
基金项目: 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)
详细信息
    作者简介:

    刘芳(1982—),女,辽宁铁岭人,讲师,博士(通讯作者. E-mail: fairfang@sina.com);施卫平(1963—),男,长春人,教授,博士(E-mail: shiwp@jlu.edu.cn).

  • 中图分类号: O241.8

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

Funds: The National Natural Science Foundation of China(11401046)
  • 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.
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出版历程
  • 收稿日期:  2015-07-10
  • 修回日期:  2015-08-20
  • 刊出日期:  2015-11-15

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