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High order well-balanced finite difference WENO schemes for shallow water flows along channels with irregular geometry

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  • Wang, Xiufang
  • Li, Gang
  • Qian, Shouguo
  • Li, Jiaojiao
  • Wang, Zhen

Abstract

In this paper, we present high order finite difference weighted essentially non-oscillatory (WENO) schemes for the shallow water flows along open channels with irregular geometry and over a non-flat bottom topography. The proposed schemes maintain the well-balanced property for the still water steady state solutions, namely preserve steady state at the discrete level, when there is a exact balance between the flux gradient and the source term. Compared with the traditional shallow water equations with constant cross section, the construction of the well-balanced schemes is not a trivial work due to the effect induced by the irregular geometry of the channels. To preserve the well-balanced property, we first reformulate the source term, then propose to construct the numerical fluxes by means of a flux modification technique, and finally discrete the source term with the help of a novel source term approximation. Benchmark numerical examples are applied to validate the good performances of the resulting schemes: well-balanced property, high order accuracy, and high resolution for the discontinuous solutions.

Suggested Citation

  • Wang, Xiufang & Li, Gang & Qian, Shouguo & Li, Jiaojiao & Wang, Zhen, 2019. "High order well-balanced finite difference WENO schemes for shallow water flows along channels with irregular geometry," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:363:y:2019:i:c:12
    DOI: 10.1016/j.amc.2019.124587
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    References listed on IDEAS

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    1. Li, Gang & Caleffi, Valerio & Qi, Zhengkun, 2015. "A well-balanced finite difference WENO scheme for shallow water flow model," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1-16.
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    Cited by:

    1. Qiao, Dianliang & Lin, Zhiyang & Guo, Mingmin & Yang, Xiaoxia & Li, Xiaoyang & Zhang, Peng & Zhang, Xiaoning, 2022. "Riemann solvers of a conserved high-order traffic flow model with discontinuous fluxes," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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