空间分数阶对流方程的格子Boltzmann方法

doi:10.13438/j.cnki.jdzk.2022.02.004

吉首大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (2): 17-22.DOI: 10.13438/j.cnki.jdzk.2022.02.004

空间分数阶对流方程的格子Boltzmann方法

魏雪丹,李梦军,戴厚平

(吉首大学数学与统计学院,湖南吉首 416000)

出版日期:2022-03-25 发布日期:2022-07-14
通讯作者: 戴厚平(1979—),男,湖南邵阳人,吉首大学数学与统计学院副教授,博士,主要从事微分方程数值解研究.
作者简介:魏雪丹(1994—),女,甘肃张掖人,吉首大学数学与统计学院硕士研究生,主要从事微分方程数值解研究
基金资助:
湖南省自然科学基金资助项目(2021JJ30548);吉首大学研究生科研创新项目(JGY202140)

Lattice Boltzmann Method for Spatial Fractional Convection Equations

WEI Xuedan,LI Mengjun,DAI Houping

(School of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2022-03-25 Published:2022-07-14

摘要/Abstract

摘要：建立了格子Boltzmann模型来数值求解空间分数阶对流方程. 通过积分中值定理和线性插值方法将分数阶导数离散化,并结合Taylor展式和Chapman-Enskog多尺度展开推导出各方向上的平衡态分布函数. 对于一维和二维问题,数值算例验证了格子Boltzmann方法的有效性.

关键词： 分数阶对流方程, Caputo分数阶导数, Chapman-Enskog 展开, 格子Boltzmann模型

Abstract: Lattice Boltzmann model is established to numerically solve spatial fractional convection equations. Through integral mean value theorem and linear interpolation method,the fractional derivative was discretized,and the equilibrium distribution functions in each direction were derived by combining Taylor expansion and Chapman-Enskog multi-scale expansion.Numerical results verify the effectiveness of the constructed model via one-dimensional and two-dimensional problems.

Key words: fractional convection equations, Caputo fractional derivative, Chapman-Enskog expansion, lattice Boltzmann model

魏雪丹, 李梦军, 戴厚平. 空间分数阶对流方程的格子Boltzmann方法[J]. 吉首大学学报（自然科学版）, 2022, 43(2): 17-22.

WEI Xuedan, LI Mengjun, DAI Houping. Lattice Boltzmann Method for Spatial Fractional Convection Equations[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(2): 17-22.

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空间分数阶对流方程的格子Boltzmann方法

Lattice Boltzmann Method for Spatial Fractional Convection Equations

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