The Theoretic Research On The LBGK Method Of Computational Fluid Dynamics

Lattice BGK (LBGK) method is a very novel numerical method. It develops on the basis of the lattice gas automaton. The successful simulations of fluid flow by the LBGK method have demonstrated its wide applications in the computational fluid dynamics. For example, LBGK method has been applied in the simulations of the mass diffusion, heat-transfer, flow in porous media, multi-phase flow ,multicomponent flows,magnet-hydrodynamics,the flow with surface and instability. Now, it has the advancement in the simulation in the compress flow.It is very worthwhile to research LBGK method which is a new numerical method. Through the research to the LBGK method, it can promote the development of computational fluid dynamics and the comprehension of the microcosmic world .It boosts the development of correlative field , such as physics and computer .LBGK method adapts to the calculation on a large scale,which improve the speed and precision .It can deal with the complex flow and the turbulent flow.The research of LBGK method can promote the advancement and prosperity of fluid mechanics. It is no doubt that the research of lattice BGK has the important theoretic and practical value.Because of many reasons,LBGK method hasn't been widly applied in the research in our country.I study the method from the theoretic aspect and do the fundamental research in model,boundary condition ,precision,stability aspect.It can give people the clear and full understanding of LBGK method.This thesis summarizes up all kinds of the LBGK method, especially the model of the two-phase and multicomponent fluid. At the same time, this thesis focuses on the theoretical research on the LBGK method and discusses the inner relation between the LBGK and the N-S equations.The relationship among the selection of velocity group , the forms of equilibrium distribution functions,and the macroscopic N-S equations is clearly revealed.LBGK method has many advantages, such as easy dealing with the complex boundary conditions and high amenability to parallel computing. Of course, it has some disadvantage, especially the instability. So I put forth a new method toimprove the stability of LBGK method.The main work of the paper is followed:First, the basic theory and many models of LBGK method are introduced and discussed.Second, the relation between the LBGK method and the N-S equations is reaveled through a new method. I clearly explained the reasonable aspect and the problem of LBGK method.Finally, the stability of LBGK method is analyzed and the new method to improve the stability of LBGK method is proposed. That is, The equilibrium distribution function takes the form of logarithm in order to insure the equilibrium distribution function being the positive number, which can improve the stability of LBGK method.This paper's aim is to analyze LBGK method in every aspect and to do some fundamental research on this method for the improvement of its application in computational fluid dynamics.