关键词: Saint-Venant方程组, 有限体积法, 和谐性, 保正性

Abstract:

Shallow water wave equations have high requirements for their numerical schemes. In practical applications, we are more concerned with the behavior in the vicinity of the steady-state solution, especially when the dry and wet fronts occur in the computation area. In this case, not only the scheme is required to be well-balanced, but also the water depth needs to be kept non-negative, at the same time, the scheme is required with high resolution. Therefore, it is difficult to design a numerical scheme that is both well-balanced and positivity preserving. The core of the dissertation is to summarize and study the central schemes of the concerned shallow water wave equations:the KP scheme, the BCKN scheme and the T scheme. We investigate their advantages and disadvantages. We use the one-dimensional shallow water wave equations to show the applications of the each scheme to some examples.

Key words: Saint-Venant equations, Finite volume method, Well-Balanced, Positivity preserving