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A well-balanced finite difference WENO scheme for shallow water flow model

Author

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  • Li, Gang
  • Caleffi, Valerio
  • Qi, Zhengkun

Abstract

In this paper, we are concerned with shallow water flow model over non-flat bottom topography by high-order schemes. Most of the numerical schemes in the literature are developed from the original mathematical model of the shallow water flow. The novel contribution of this study consists in designing a finite difference weighted essentially non-oscillatory (WENO) scheme based on the alternative formulation of the shallow water flow model, denoted as “pre-balanced’’ shallow water equations and introduced in Rogers et al. (2003) [23]. This formulation greatly simplifies the achievement of the well-balancing of the present scheme. Rigorous numerical analysis as well as extensive numerical results all verify that the current scheme preserves the exact conservation property. It is important to note that this resulting scheme also maintains the non-oscillatory property near discontinuities and keeps high-order accuracy for smooth solutions at the same time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:1-16
    DOI: 10.1016/j.amc.2015.04.054
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    Citations

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    Cited by:

    1. Zhizhuang Zhang & Xiangyu Zhou & Gang Li & Shouguo Qian & Qiang Niu, 2023. "A New Entropy Stable Finite Difference Scheme for Hyperbolic Systems of Conservation Laws," Mathematics, MDPI, vol. 11(12), pages 1-18, June.
    2. Li, Gang & Li, Jiaojiao & Qian, Shouguo & Gao, Jinmei, 2021. "A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. 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.
    4. Xiaoxu Zhao & Baining Wang & Gang Li & Shouguo Qian, 2024. "A Path-Conservative ADER Discontinuous Galerkin Method for Non-Conservative Hyperbolic Systems: Applications to Shallow Water Equations," Mathematics, MDPI, vol. 12(16), pages 1-21, August.

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