A CIP/multi-moment finite volume method for shallow water equations with source terms

R. Akoh, S. Ii, F. Xiao

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


A novel finite volume method has been presented to solve the shallow water equations. In addition to the volume-integrated average (VIA) for each mesh cell, the surface-integrated average (SIA) is also treated as the model variable and is independently predicted. The numerical reconstruction is conducted based on both the VIA and the SIA. Different approaches are used to update VIA and SIA separately. The SIA is updated by a semi-Lagrangian scheme in terms of the Riemann invariants of the shallow water equations, while the VIA is computed by a flux-based finite volume formulation and is thus exactly conserved. Numerical oscillation can be effectively avoided through the use of a non-oscillatory interpolation function. The numerical formulations for both SIA and VIA moments maintain exactly the balance between the fluxes and the source terms. 1D and 2D numerical formulations are validated with numerical experiments.

Original languageEnglish
Pages (from-to)2245-2270
Number of pages26
JournalInternational Journal for Numerical Methods in Fluids
Issue number12
Publication statusPublished - Apr 30 2008
Externally publishedYes


  • CIP
  • Finite volume method
  • High-order accuracy
  • Method of characteristics
  • Multi-moment
  • Shallow water equations
  • Source terms

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics


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