运用格子Boltzmann方法求解空间分数阶方程  

The lattice Boltzmann method is used tosolve the spatial fractional order equation

作　　者：李康 张建影 LI Kang;ZHANG Jianying(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《长春工业大学学报》2023年第3期218-224,共7页Journal of Changchun University of Technology

基　　金：国家自然科学基金资助项目(11602033)。

摘　　要：研究了一类Riesz空间分数阶方程的数值求解问题,构造了格子Boltzmann方法(LBM)的D1Q3模型。对分数阶微积分算子进行处理,以便于构造格子Boltzmann模型。通过Chapman-Enskog多尺度展开得到一系列偏微分方程,并且计算出平衡态分布函数。通过数值模拟验证了该方法有效。A class of numerical solving problems of Riesz spatial fractional equations is studied,and the D1Q3 model of the lattice Boltzmann method(LBM)is constructed.Fractional calculus operators are processed to facilitate the construction of lattice Boltzmann models.A series of partial differential equations are obtained by Chapman-Enskog multiscale expansion,and the equilibrium distribution function is calculated.Numerical simulation verifies that the method is effective.

关 键 词：Riesz空间分数阶 格子BOLTZMANN方法 分数阶微积分算子 格子BOLTZMANN模型 

分 类 号：O242[理学—计算数学]