分数阶Navier-Stokes方程的格子Boltzmann方法
The lattice Boltzmann method for the fractional Navier-Stokes equation
王雨欣 1张建影1
作者信息
- 1. 长春工业大学 数学与统计学院,吉林 长春 130012
- 折叠
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D1 Q3 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.
Abstract
For the numerical solution problem of fractional Navier-Stokes equation,the equation is first discretized.Then the D1 Q3 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 to two numerical 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Key words
Caputo fractional-order derivative/lattice Boltzmann method/fractional Navier-Stokes equation/equilibrium state distribution function引用本文复制引用
基金项目
国家自然科学基金资助项目(11602033)
出版年
2024
NETL
NSTL
万方数据