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A well-balanced positivity preserving two-dimensional shallow flow model with wetting and drying fronts over irregular topography

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Abstract

This paper presents an improved well-balanced Godunov-type 2-D finite volume model with structured grids to simulate shallow flows with wetting and drying fronts over an irregular topography. The intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for the water depth is implemented to resolve the stationary or wet/dry fronts. The bed slope source term is discretized using a central difference method to capture the static flow state over the irregular topography. Second-order accuracy in space is achieved by using the slope limited linear reconstruction method. With the proposed method, the model can avoid the partially wetting/drying cell problem and maintain the mass conservation. The proposed model is tested and verified against three theoretical benchmark tests and two experimental dam break flows. Further, the model is applied to predict the maximum water level and the flood arrival time at different gauge points for the Malpasset dam break event. The predictions agree well with the numerical results and the measurement data published in literature, which demonstrates that with the present model, a well-balanced state can be achieved and the water depth can be nonnegative when the Courant number is kept less than 0.25.

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Ningbo Institute of Technology, Zhejiang University, Ningbo, 315100, China

    Gang-feng Wu  (吴钢锋)

  2. Institute of Port, Coastal and Offshore Engineering, Ocean College, Zhejiang University, Hangzhou, 310058, China

    Zhi-guo He  (贺治国) & Liang Zhao  (赵亮)

  3. Institute of Hydraulic Structures and Water Environment, Zhejiang University, Hangzhou, 310058, China

    Guo-hua Liu  (刘国华)

Authors
  1. Gang-feng Wu  (吴钢锋)
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  2. Zhi-guo He  (贺治国)
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  3. Liang Zhao  (赵亮)
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  4. Guo-hua Liu  (刘国华)
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Corresponding author

Correspondence to Zhi-guo He  (贺治国).

Additional information

Project supported by Natural Science Foundation of Zhejiang Province (Grant No. LR16E090001), the Research Funding of Shenzhen City (Grant No. JCYJ20160425164642646) and the Zhejiang Province Science and Technology Research Funding (Grant No. 2015C03015).

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Wu, Gf., He, Zg., Zhao, L. et al. A well-balanced positivity preserving two-dimensional shallow flow model with wetting and drying fronts over irregular topography. J Hydrodyn 30, 618–631 (2018). https://doi.org/10.1007/s42241-018-0069-7

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  • DOI: https://doi.org/10.1007/s42241-018-0069-7

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