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

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

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

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
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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

A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations

¹College of Mathematics and Statistics, Jishou University, Jishou, Hunan 416000, P.R.China
²School of Mathematics and Statistics, Central South University, Changsha 410083, P.R.China

Funds: The National Natural Science Foundation of China（51974377）

摘要

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.
- Riemann-Liouville分数阶左导数 /
- 空间分数阶电报方程 /
- 格子Boltzmann模型 /
- Chapman-Enskog展开
Abstract: The lattice Boltzmann method (LBM) was applied to numerically solve Riemann-Liouville spatial fractional-order telegraph equations. Firstly, the integral term of the fractional-order operator was discretized and the order of convergence was analyzed. Then, a 1D and 3-velocity (D1Q3) LBM evolution model with modified functions was established. The expressions of equilibrium distribution functions and correction functions were deduced by means of the Chapman-Enskog multi-scale analysis and the Taylor expansion technique. Therefore, the macroscopic equation was exactly recovered from the established evolution model. Numerical results show the stability and effectiveness of the model.
- left Riemann-Liouville fractional derivative /
- spatial fractional-order telegraph equation /
- lattice Boltzmann model /
- Chapman-Enskog expansion

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参考文献(20)

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