A New Well-Balanced Finite Volume CWENO Scheme for Shallow Water Equations over Bottom Topography

Wei Guo, Ziming Chen, Shouguo Qian*, Gang Li*, Qiang Niu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


In this article, we develop a new well-balanced finite volume central weighted essentially non-oscillatory (CWENO) scheme for one- and two-dimensional shallow water equations over uneven bottom. The well-balanced property is of paramount importance in practical applications, where many studied phenomena can be regarded as small perturbations to the steady state. To achieve the well-balanced property, we construct numerical fluxes by means of a decomposition algorithm based on a novel equilibrium preserving reconstruction procedure and we avoid applying the traditional hydrostatic reconstruction technique accordingly. This decomposition algorithm also helps us realize a simple source term discretization. Both rigorous theoretical analysis and extensive numerical examples all verify that the proposed scheme maintains the well-balanced property exactly. Furthermore, extensive numerical results strongly suggest that the resulting scheme can accurately capture small perturbations to the steady state and keep the genuine high-order accuracy for smooth solutions at the same time.

Original languageEnglish
Pages (from-to)1515-1539
Number of pages25
JournalAdvances in Applied Mathematics and Mechanics
Issue number6
Publication statusPublished - 2023


  • CWENO scheme
  • decomposition algorithm
  • Shallow water equations
  • source term
  • well-balanced property


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