Fluid Flow Simulation By Lattice Boltzmann Method

In this thesis, a method in computational fluid dynamics named Lattice Boltzmann methods(LBM) will be presented. It is a relatively young numerical simulation method, but it has draw the attention of many scholars from allover the world in recent years and it is still in continuous improvement. LBM contains a multi-disciplinary knowledge, there is fluid mechanics, statistical mechanics, heat and mass transfer and computational logic and so on.One of the most important theoretical idea is evolved from lattice gas automata theory(LGA). So it can be said that lattice gas automata theory is the pioneer of Lattice Boltzmann Method. The principle of fluid simulation used lattice gas automata is that entirely discrete the both time and space of the fluid and then solving the problem according to the discreted fluid particles by the rules of migrate and collision. That is the basic ideal of Lattice Boltzmann method. Furthermore, the HPP model and the FHP model provides important ideas to discrete velocity model of LBM.LBM is different from the traditional CFD method, it has the characteristics of continuous on macroscopic scale and discrete on microcosmic. So it is usually classified as a mesoscopic simulation method. The macroscopic results of the fuid obtained by statistical average a large number of discreted grid of the system. Because LBM has inherently parallel characteristics and the boundary conditions method is relative simple, it is easy to realize the program to do simulation. Compared with the traditional method of computational fluid dynamics, LBM has significant advantages, particularly in the field of microscale flow model simulation, multiphase multicomponent simulation and porous media flow and so on which is difficult to accomplish by many traditional method. With the continuous development of the discrete model and boundary conditions method, lattice Boltzmann method will be more and more better.This paper describes the derivation of the Boltzmann equation to the lattice Boltzmann equation, the basic idea of Boltzmann equations, including the conversion of macro and micro phenomena bases, control the flow of items and simplify the collision term is derived equations in 2D and 3D common discrete velocity model applications and settings, etc. at equilibrium equations and the pipe wall at the boundary conditions.The simulation work used Matlab software as a tool, simulated the two dimensional and three dimensional simulation of Poiseuille flow in a channel with different situation used lattice Bhatnagar-Gross-Krook(LBGK) model(D2Q9 and D3Q19) respectively. And we also consider the impact of external force in LBM, then compare the simulation results to have a further understanding the lattice Boltzmann method.