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空间分数阶电报方程的格子Boltzmann方法

李梦军 戴厚平 魏雪丹 郑洲顺

李梦军, 戴厚平, 魏雪丹, 郑洲顺. 空间分数阶电报方程的格子Boltzmann方法[J]. 应用数学和力学, 2021, 42(5): 522-530. doi: 10.21656/1000-0887.410311
引用本文: 李梦军, 戴厚平, 魏雪丹, 郑洲顺. 空间分数阶电报方程的格子Boltzmann方法[J]. 应用数学和力学, 2021, 42(5): 522-530. doi: 10.21656/1000-0887.410311
LI Mengjun, DAI Houping, WEI Xuedan, ZHENG Zhoushun. A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 522-530. doi: 10.21656/1000-0887.410311
Citation: LI Mengjun, DAI Houping, WEI Xuedan, ZHENG Zhoushun. A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 522-530. doi: 10.21656/1000-0887.410311

空间分数阶电报方程的格子Boltzmann方法

doi: 10.21656/1000-0887.410311
基金项目: 国家自然科学基金(51974377)
详细信息
    作者简介:

    李梦军(1996—),男,硕士(E-mail: limengjun2020@126.com);戴厚平(1979—),男,副教授,博士(通讯作者. E-mail: daihouping@163.com).

  • 中图分类号: O241.82

A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations

Funds: The National Natural Science Foundation of China(51974377)
  • 摘要: 应用格子Boltzmann方法(LBM)对RiemannLiouville空间分数阶电报方程进行了数值模拟研究.首先,将分数阶算子中的积分项进行离散化处理,并进行了收敛阶分析.然后,构建了带修正函数项的一维三速度(D1Q3)的LBM演化模型.利用ChapmanEnskog多尺度技术和Taylor展开技术,推导出各平衡态分布函数和修正函数的具体表达式,准确地从所建的演化模型恢复出宏观方程.最后,数值计算结果表明该模型是稳定、有效的.
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出版历程
  • 收稿日期:  2020-10-15
  • 修回日期:  2021-04-06
  • 刊出日期:  2021-05-01

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