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

  • Authors:

  • Ryosuke Akoh;Satoshi Ii;Feng Xiao

  • Affiliations:

  • Department of Environmental Science and Technology, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan;Department of Mechanical Engineering, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-8656, Japan;Department of Environmental Science and Technology, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan and LHD, Institute of Mechanics, Chinese Academy of Sciences, ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

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.