Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (2): 372-385.

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Research on the Application of Central Scheme in Saint-Venant System

Jian Dong()   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072
  • Received:2017-09-14 Online:2019-04-26 Published:2019-05-05
  • Supported by:
    国家自然科学基金(11001211);国家自然科学基金(11371023);国家重大研发计划(2016YFC0402207)

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

CLC Number: 

  • O241.82
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