格子玻尔兹曼方法及其在大气湍流研究中的应用

文章的目的是对格子玻尔兹曼方法进行系统的介绍，格子玻尔兹曼方法(Lattice Boltzmann Method)的出现直接来源于20世纪60年代的元胞自动机(Cellular Automata)思想，而这一方法用于解决流动现象时，又可以追溯到19世纪的分子运动论，求解的是Boltzmann提出的玻尔兹曼输运方程，因此将这一方法称为格子玻尔兹曼方法，之前也被称为格子气自动机(Lattice Gas Automaton)。该方法多用于研究复杂现象，如材料晶体凝聚时的生长过程、城市土地利用的演化等方面。在20世纪70年代由Hardy、Pomeau和Pazzis建立了第一个用于研究流体运动的格子气自动机，此后，这一方法被广泛用来模拟各种流动问题，诸如二相流、孔隙介质中的渗流等，并根据这一方法开发了相应的商业软件PowerFlow。同时，格子玻尔兹曼方法由于其在微观水平描述运动的特点，成为研究湍流的一个很好的数值计算工具，特别是用其进行直接数值模拟(DNS)计算，成为继传统的差分法、有限体积法和谱方法之后的又一有力的手段。而作为大气运动的一个主要现象的大气湍流，比普通湍流更加复杂，在这里着重介绍了大气湍流的特点和应用格子玻尔兹曼方法模拟湍流的发展过程。

The Application of Lattice Boltzmann Method in the Atmospheric Turbulence Study

The objective of this paper is to systemically introduce the lattice Bohzmann method from its mathematic and physical bases, and to investigate broadly its application in every field. The lattice Bohzmann method based on the idea of cellular automaton was proposed by John von Neumann in the 1960g. The cellular automaton simulates the parallelizable character of the brain and constructs the dynamic evolvement system. That starts a new direction to solve the complex problems. When it is used to solve the flow problem, it combines with the molecule kinetic theory of nineteenth century to solve Boltzmann transport equation. It means to study the flow by simulating the molecules movement in the flow. So it is also called lattice Boltzmann method, or lattice gas automaton. From investigation, it can be seen that the application fields are very broad. For example, it is used to simulate the crystal agglomeration, the evolvement of city land use, the traffic flow, the seismic wave, the spread of fire in the forest, the prevalence of virus and the spread of public opinion. By this method, good results are obtained. In the 1970g, Hardy, Pomeau and Pazzis built the first lattice gas automaton to simulate flow. Then, because it can explain flow from microcosmic level, it is very suitable to solve complex flow such as multiphase flow, porous flow and snow grain transport in the wind. Moreover, PowerFlow the commercial software was developed based on the lattice Bohzmann method. For turbulence, which is the old problem-turbulence, many methods are used and LBM now gradually becomes a new way to directly simulate it because it can calculate in the molecule level. The atmospheric turbulence is more complex then usual turbulence. Here, we especially introduce the atmospheric turbulence character and give an elementary project to simulate by LBM.