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Godunov-Type Scheme for Nonlinear Equations
by
Hui Bi
Dept. of Math, Harbin Institute of Technology, Harbin, China
Coauthors: Boying Wu
This paper presents a modified Godunov scheme for nonlinear equations. Generally, it is very difficult to simulate the appearance of shock wave. As an example to Burgers equation, it will form the shock wave as time. When Godunov scheme is used in solving the viscid Buegers equation, it will produce numerical oscillations. So we make proper modification in numerical flux, and adopt integral multistep method in diffusion terms for improving accuracy. The numerical experiment shows that this method not only controls the numerical oscillations very well, but also has higher accuracy than singlestep method. Further, we discuss the stability of the method as well as the computational stability sufficient condition of it.
Date received: February 5, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caws-02.