Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 891-903.

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Moving-Water Equilibria Preserving Central Scheme for the Saint-Venant System

Yiming Luo1(),Dingfang Li1(),Min Liu1(),Jian Dong2,*()   

  1. 1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072
    2 College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073
  • Received:2021-01-11 Online:2022-06-26 Published:2022-05-09
  • Contact: Jian Dong;;;
  • Supported by:
    the National Key Research and Development Project(2017YFC0405901)


In this paper, we propose a second-order unstaggered central finite volume scheme for the Saint-Venant system. Classical central scheme can preserve still-water steady state solution by reconstructing conservative variables and the water level, but generates enormous numerical oscillation when considering moving-water steady state. We choose to reconstruct conservative variables and the energy, and design a new discretization of the source term to preserve moving-water equilibria and capture its small perturbations. In the end, several classical numerical experiments are performed to verify the proposed scheme which is convergent, well-balanced and robust.

Key words: Saint-Venant system, Unstaggered central scheme, Moving-water equilibria

CLC Number: 

  • O241.82