Study Of Burgers Equation Based On Lattice Boltzmann Method

With the growing interest in nonlinear science, a lot of gas dynamics, traffic flow, heatconduction, and turbulence models may be changed into Burgers equation. This equation issimplified model of Navier-Stokes equation in flow mechanics and it is an important andfundamental partial differential equation. This problem can from shock, which makes itdifficult to solve Burgers equation. Therefore, the study of Burgers equation has importantmeanings.For the past two decades, the lattice Boltzmann method is developed as a newnumerical simulation method. It has many advantages, such as the simplicity of program,easiness to handle boundary, high efficiency of computation and so on. It has attracted thegreatest attention in computational fluid dynamics. It solved many problems that could notbe solved by traditional computational methods. The combination of lattice Boltzmannmethod with nonlinear partial differential equations has been proved to be an effectivemethod. We focus on the lattice Boltzmann model for solving Burgers Equation.This paper consists of four chapters. Chapter1is introduction. Firstly, we introducedevelopment history and study of lattice Boltzmann Method. Finally, the organizationalstructure of this work is given.In chapter2, we give a few of important models of lattice Boltzmann. Through theChapman-Enskog expansion method, the correct Navier-Stokes equations can be recovered.Finally, we introduce several methods of dealing with boundary conditions.In chapter3, we solve the one-dimensional and two-dimensional Burgers equation bylattice Boltzmann D1Q3and D2Q9models, respectively. We compared numerical resultsof lattice Boltzmann models to analytical solutions and numerical solutions gettingclassical methods. Numerical simulation results show that lattice Boltzmann method is aneffective numerical method for solving Burgers equation and the scheme is of secondnumerical accuracy and better stability. In chapter4, we summarize research work and point out shortages and unsolvedproblems of the thesis. In addition, the researching orientations are suggested in the future.