一维空间Riesz分数阶对流扩散方程的格子Boltzmann方法  

Lattice Boltzmann Method for One-dimensional Riesz Spatial Fractional Convection-Diffusion Equations

作　　者：魏雪丹 戴厚平[1] 李梦军 郑洲顺[2] WEI Xuedan;DAI Houping;LI Mengjun;ZHENG Zhoushun(College of Mathematics and Statistics,Jishou University,Jishou,Hunan 416000,China;School of Mathematics and Statistics,Central South University,Changsha,Hunan 410083,China)

机构地区：[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,湖南长沙410083

出　　处：《计算物理》2021年第6期683-692,共10页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(51974377)资助项目。

摘　　要：建立格子Boltzmann方法(LBM)的D1Q3演化模型,研究一类Riesz空间分数阶对流扩散方程的数值求解问题。对分数阶微积分算子中的积分项离散化处理,得到逼近的标准对流扩散方程。结合Taylor展式和ChapmanEnskog多尺度展开技术得到模型的各个方向上的平衡态分布函数,通过D1Q3演化模型正确恢复所要求解的宏观方程。数值算例验证该方法的有效性。A D1Q3 evolution model of lattice Boltzmann method(LBM)is established to numerically solve a class of spatial fractional convection-diffusion equation in Riesz sense.By discretizing the integral term of fractional order operator,the fractional convection-diffusion equation is transformed into a standard one with Riesz derivative.With Taylor expansion,Chapman-Enskog and multi-scales expansion,equilibrium distribution functions of the model are derived in all directions.Furthermore,the macroscopic equation to be solved is recovered correctly.Finally,numerical experiments are carried out to verify the model.

关 键 词：Riesz空间分数阶对流扩散方程 格子BOLTZMANN方法 Chapman-Enskog展开 

分 类 号：O241.82[理学—计算数学]