A multi-moment finite volume formulation for shallow water equations on unstructured mesh

Ryosuke Akoh, Satoshi Ii, Feng Xiao

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


A novel and accurate finite volume method has been presented to solve the shallow water equations on unstructured grid in plane geometry. In addition to the volume integrated average (VIA moment) for each mesh cell, the point values (PV moment) defined on cell boundary are also treated as the model variables. The volume integrated average is updated via a finite volume formulation, and thus is numerically conserved, while the point value is computed by a point-wise Riemann solver. The cell-wise local interpolation reconstruction is built based on both the VIA and the PV moments, which results in a scheme of almost third order accuracy. Efforts have also been made to formulate the source term of the bottom topography in a way to balance the numerical flux function to satisfy the so-called C-property. The proposed numerical model is validated by numerical tests in comparison with other methods reported in the literature.

Original languageEnglish
Pages (from-to)4567-4590
Number of pages24
JournalJournal of Computational Physics
Issue number12
Publication statusPublished - Jun 2010
Externally publishedYes


  • Finite volume method
  • High order scheme
  • Hydraulic simulation
  • Multi-moment
  • Shallow water equations
  • Unstructured grid

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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