用格子Boltzmann方法研究二维Burgers方程

给出了一个求解二维Burgers方程的格子Boltzmann方法.分析了相应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.研究表明,通过引入适当形式的平衡分布函数,采用简单的5速正方格子模型可以恢复宏观Burgers方程.通过与标准二阶精度的有限差分解的比较,证明了本文的格子Boltzmann方法(LBM)是简单而有效的.

Study of Two-dimensional Burgers Equation Using Lattice Boltzmann Method

A lattice Boltzmann method for solving two-dimensional nonlinear advection-diffusion equation,namely,the viscous Burgers equation is introduced.Monotonicity and stability of the scheme are analyzed.The conditions of Monotonic-ity are obtained,under which the stability of the scheme is proved in the L∞ norms.It is shown that the macroscopic Burgers equation can be recovered by using suitable equilibrium distribution function based upon relatively simple lattice form,i.e.two-dimensional 5-speed square lattice.Furthermore,it is proved that the Lattice Boltzmann method in this paper is simple and efficient by comparing the solutions computed via the Lattice Boltzmann method with those computed by a standard second-order finite difference method.