分数阶Navier-Stokes方程的格子Boltzmann方法  

The lattice Boltzmann method for the fractional Navier-Stokes equation

作　　者：王雨欣 张建影 WANG Yuxin;ZHANG Jianying(School of Mathematics&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》2024年第3期265-271,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：对于分数阶Navier-Stokes方程的数值求解问题,首先将该方程进行离散化处理,然后构造D1Q3格子Boltzmann模型,并采用Taylor展开和Chapman-Enskog多尺度展开等技术恢复宏观方程,同时推导出该模型平衡态分布函数的表达式。最后根据一维的两个数值算例对方程进行数值模拟以及误差分析,并将得到的数值解与精确解进行比较,从而验证格子Boltzmann方法的准确性与有效性。For the numerical solution problem of fractional Navier-Stokes equation,the equation is first discretized.Then the D1Q3 lattice Boltzmann model is constructed.The macroscopic equation is recovered by Taylor expansion and Chapman-Enskog multi-scale expansion techniques.At the same time,the expression of the equilibrium state distribution function of the model is derived.Finally,according tOtwOnumerical examples of one-dimensional,the equation is numerically simulated and its error is analyzed.The obtained numerical solution is compared with the exact solution.Thus,the accuracy and effectiveness of the lattice Boltzmann method are verified.

关 键 词：CAPUTO分数阶导数 格子BOLTZMANN方法 分数阶Navier-Stokes方程 平衡态分布函数 

分 类 号：O242[理学—计算数学]