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Superposition of local zoom models and simultaneous calibration for 1D–2D shallow water flows

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  • Marin, J.
  • Monnier, J.

Abstract

We address the problem of coupling 2D shallow water equations with 1D shallow water equations (St-Venant equations), as applied to river-floodplain flows. Mathematical coupling conditions are derived classicaly from the 3D Navier–Stokes equations by integrating over the vertical wet section, when overflowing occurs. It leads to extra source terms in the 1D equations. Next we assume to be in a variational data assimilation context, then the optimal control process allows to couple both models and assimilate data simultaneously (Joint Assimilation Coupling algorithms). Two different versions of JAC algorithms are presented and compared. In a numerical test case, we superimpose the local 2D model on the 1D global model. The results show the efficiency of the present simultaneous superposition–assimilation approach.

Suggested Citation

  • Marin, J. & Monnier, J., 2009. "Superposition of local zoom models and simultaneous calibration for 1D–2D shallow water flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 547-560.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:3:p:547-560
    DOI: 10.1016/j.matcom.2009.09.001
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    Cited by:

    1. Wenchao Qi & Chao Ma & Hongshi Xu & Zifan Chen & Kai Zhao & Hao Han, 2021. "A review on applications of urban flood models in flood mitigation strategies," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(1), pages 31-62, August.
    2. Karjoun, Hasan & Beljadid, Abdelaziz, 2024. "A well-balanced and positivity-preserving numerical model for overland flow under vegetation effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 273-293.

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