Volume 6 Issue 1
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Zhi-li WANG, Yan-fen GENG. 2013: Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids. Water Science and Engineering, 6(1): 91-105. doi: 10.3882/j.issn.1674-2370.2013.01.007
Citation: Zhi-li WANG, Yan-fen GENG. 2013: Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids. Water Science and Engineering, 6(1): 91-105. doi: 10.3882/j.issn.1674-2370.2013.01.007
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Two-dimensional shallow water equations with porosity and their numerical scheme on unstructured grids

doi: 10.3882/j.issn.1674-2370.2013.01.007
  • 1.

    State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210024, P. R. China

  • 2.

    School of Transportation, Southeast University, Nanjing 210096, P. R. China

Funds:  This work was supported by the National Natural Science Foundation of China (Grants No. 50909065 and 51109039) and the National Basic Research Program of China (973 Program, Grant No. 2012CB417002).
More Information
  • Corresponding author: Yan-fen GENG
  • Received Date: 2011-12-05
  • Rev Recd Date: 2012-05-09
    Abstract
  •  In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosity source term appears in the momentum equation. The numerical model of the shallow water equations with porosity is presented with the finite volume method on unstructured grids and the modified Roe-type approximate Riemann solver. The source terms of the bed slope and porosity are both decomposed in the characteristic direction so that the numerical scheme can exactly satisfy the conservative property. The present model was tested with a dam break with discontinuous porosity and a flash flood in the Toce River Valley. The results show that the model can simulate the influence of obstructions, and the numerical scheme can maintain the flux balance at the interface with high efficiency and resolution.

     

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