流体动力学的格子Boltzmann方法及其具体实现

Using Lattice Boltzmann Model Simulate Fluid Mechanics Phenomena

格子气自动机和格子Ｂｏｌｔｚｍａｎｎ方法的迅速发展提供了一类求解流体力学问题的新方法。本文中，我们介绍了格子Ｂｏｌｔｚｍａｎｎ方法，解决了格子气方法中的缺点，通过选择适当平衡分布及其参数，导出了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，并得到了声速和粘性系数。最后在微机上模拟了平面平板中无障碍物流问题及绕矩形障碍块的流动问题。结果表明该模型有格子气方法及其它的数值方法所没有的优点，计算更精确和直观。

The recent development of lattice gas automata and Lattice Boltzmann method have provided new computational models for solving a class of mathematical physic problems.In this paper,lattice boltzmann method is introduced here and it solves the shortcomings of the lattice gas method.By choosing the parameters of the functions of the equilibrium distribution appropriately,we derive the Navier-Stokes equations,and we are able to obtain the sound speed,kinematic viscosity and bulk viscosity.At the end of this paper,the computer simulated results of the laminar flow and block flow by this method coincide with the traditional numerical results by Navier-Stokes equations.The numerical results show that the new method is efficient to resolve Navier-Stokes equations and has great prospects.