基于一维渗流方程的格子Boltzmann模型

Lattice Boltzmann model based on one-dimensional seepage equation

针对分数阶渗流方程的数值求解问题,提出了格子Boltzmann方法(LBM)的D1Q3模型。首先对分数阶微积分算子进行处理,以便于构造格子Boltzmann模型;然后通过Taylor展开和Chapman-Enskog多尺度展开技术恢复出宏观方程;最后推导出各个方向上的平衡态分布函数的表达式。根据两个数值例子的计算结果以及误差分析,验证了理论分析的有效性。

A D1Q3 model based on the lattice Boltzmann method(LBM)is proposed for the numerical solution of fractional order seepage equations.Firstly,the fractional calculus operators are processed to facilitate the construction of lattice Boltzmann models;Then,the macroscopic equations were restored using Taylor expansion and Chapman-Enskog multi-scale expansion techniques;Finally,the expression of the equilibrium distribution function in each direction is derived.The effectiveness of the theoretical analysis was verified based on the calculation results of two numerical examples and error analysis.