| 空间分数阶电报方程的格子Boltzmann方法 |
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| 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. |
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| 作者姓名： | 李梦军 戴厚平 魏雪丹 郑洲顺 |
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| 作者单位： | 1吉首大学 数学与统计学院, 湖南 吉首 416000 |
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| 基金项目： | 国家自然科学基金(51974377) |
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| 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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| 关 键 词： | 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 |
| 收稿时间： | 2020-10-15 |
A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations |
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| Affiliation: | 1College of Mathematics and Statistics, Jishou University, Jishou, Hunan 416000, P.R.China2School of Mathematics and Statistics, Central South University, Changsha 410083, P.R.China |
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| 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. |
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