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.
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 1 D and 3-velocity(D1 Q3)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.
作者
李梦军
戴厚平
魏雪丹
郑洲顺
LI Mengjun;DAI Houping;WEI Xuedan;ZHENG Zhoushun(College of Mathematics and Statistics,Jishou University,Jishou,Hunan 416000,P.R.China;School of Mathematics and Statistics,Central South University,Changsha 410083,P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2021年第5期522-530,共9页
Applied Mathematics and Mechanics
基金
国家自然科学基金(51974377)。
作者简介
李梦军(1996—),男,硕士(E⁃mail:limengjun2020@126.com);通讯作者:戴厚平(1979—),男,副教授,博士(E⁃mail:daihouping@163.com).
