Finite Difference Method Based On Godunov Scheme For Burgers Equation

This paper mainly researches about finite difference multi-step method, which is used in solving the Burgers equation based on the Godunov scheme. First, this paper introduces the history and development of Computational Fluid Dynamics and the researching significance of Burgers equation. And then it points out the difficulty in simulating Burgers equation---the appearance of shock in solutions. Secondly, this paper reviews the advancement and development of Godunov discontinuous decomposition method and introduces the work it does briefly.Then, this paper advances multi-step method that is to solve Burgers equation which based on Godunov scheme. This method mainly aims at first-order Godunov scheme. Because of that this form would produce numerical oscillations when solving viscid Burgers equation, so this paper makes proper modification from the point of integral and adopts integral multi-step method in diffusion terms for increasing precision. And then, this paper discusses the compatibility and stability of this equation further and advances computational stability sufficient condition of this method. The numerical experiment expresses that this method not only controls the numerical oscillations well and also increases the numerical precision more than single-step method.Thirdly, this paper introduces the properties of second-order Godunov scheme detailedly and solves Burgers equations from the advantage in using MUSCL form to control numerical oscillations and increase precision. The numerical examples expresses that this method could control the advancement of numerical oscillations well.Finally, this paper also uses MUSCL scheme semi-analysis method in space discrete and uses single point sub-domain precise integration method-- which was first advances by the academician Zhong Wanxie and first used in Structural mechanics--to solve Burgers equation in time coordination. Because of the nonlinear character of Burgers equation so that this paper makes nonlinear terms into linearity in the process of the form constitution. The numerical experiments...