二维空间分数阶反应扩散方程组的格子Boltzmann方法  

Lattice Boltzmann Method for Two-dimensional Fractional Reaction-Diffusion Equations

作　　者：冯舒婷 戴厚平[1] 宋通政 FENG Shuting;DAI Houping;SONG Tongzheng(School of Mathematics and Statistics,Jishou University,Jishou,Hunan 416000,China)

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《计算物理》2022年第6期666-676,共11页Chinese Journal of Computational Physics

基　　金：湖南省自然科学基金(2021JJ30548);湖南省教育厅科学研究重点项目(21A0329);吉首大学研究生校级科研基金(Jdy21014);吉首大学研究生科研创新项目(JGY2022075)资助

摘　　要：提出一种二维空间分数阶反应扩散方程组的格子Boltzmann方法,对方程组的分数阶积分项进行离散化处理。通过Chapman-Enskog多尺度技术和Taylor展开技术,从所建立的模型中恢复出二维空间分数阶反应扩散方程组,推导出各个速度方向上的平衡态分布函数。通过数值算例对所构造的LB模型进行检验,数值计算结果与算例的精确解吻合较好。A lattice Boltzmann method(LBM)for two⁃dimensional fractional reaction⁃diffusion equations involving Riemann⁃Liouville derivatives is proposed.Firstly,fractional integral terms in equations are discretized.Then,with Chapman⁃Enskog analysis and Taylor⁃expansion technology two⁃dimensional fractional reaction⁃diffusion equations are recovered from the LB model.Equilibrium state of distribution function in each velocity direction is derived.Finally,the LB model is tested with numerical examples.It was found that numerical results agree well with analytical solutions.

关 键 词：Riemann-Liouville分数阶导数 反应扩散方程组 格子BOLTZMANN方法 Chapman-Enskog多尺度技术 

分 类 号：O241.82[理学—计算数学]