The Numerical Methods For Burgers Equation And Stability Analysis

This paper mainly studies the numerical methods for nonlinear Burgers equation, and corresponding stability analysis. The paper firstly introduces in detail the development history of the computational fluid dynamics and the significance of Burgers equation, and points out the difficulties of simulating Burgers equation -- shock in solution. Then, the paper simply introduces the use of three kinds of numerical methods (classic finite difference method, AGE method and LDG finite element method), development situation and basic ideas, and briefly introduced in this paper for the job.This paper will be divided into four chapters, 2-4 chapters is the work I do. In chapter 2, we discuss the difference method, using the central difference method to solve nonlinear Burgers equation. Because the x=0, function more violent,the meshes nearby (-h, h) are refinded,in order to suppress oscillation effectively, and prove the stability of the presented scheme.numerical results are provide to demonstrate the effectiveness of the method ,the effect of solution regarding toεis also analyzed.In chapter 3, we discussed numerical method for two-dimensional nonlinear Burgers equation. Firstly, we use AGE method and give formulation. Secondly, we prove that the central difference method is stability.In the fourth chapter, we discussed LDG finite element method for nonlinear Burgers equation, give the formulation, stability analysis, inequality in entropy is presented, and the algorithm of process.Anyhow, to solve nonlinear Burgers equation we give the classic finite difference method, AGE finite difference method and LDG finite element method ,analyze the related properties, and verifies the effectiveness of the proposed method.