作　　者： ; ; ;

机构地区： 天津大学机械学院

出　　处： 《天津城市建设学院学报》 2006年第3期222-226,共5页

摘　　要： 构造了一维黏性Burgers方程的一个基于3-速格子模型的格子Boltzmann格式,分析了格式的单调性和稳定性,得到了格式的单调性条件,并证明了在此条件下,格式是L_∞稳定的；分析了平衡分布函数中含有的可调系数对格式性能的影响,研究表明：通过引入适当形式的平衡分布函数,采用简单的3-速格子,可以恢复宏观Burgers方程,通过与标准二阶精度的有限差分解的比较,证明了本文的LB格式是简单而有效的。 A lattice Boltzmann scheme based on the 3-bit lattice model for one-dimensional viscous Burgers equation is developed. Monotonicity and stability of the scheme are analyzed. The conditions of monotonicity are obtained, under which the stability of the scheme is proved in the L∞ norms. The effect of the adjustable coefficient in the equilibrium distribution function on the properties of the scheme is analyzed. It is showed that the macroscopic Burgers equation can be recovered by using the suitable equilibrium distribution function based on the relatively simple 3-bit lattice form. Furthermore, solutions computed via the lattice Bohzmann method are compared with those computed by a standard second-order finite difference method, which illustrates the LB scheme is simple and efficient.

关 键 词： 格子 方法 方程 平衡分布函数 单调性 稳定性

领　　域： [理学] [理学] [理学] [理学]