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Numerical Simulations of Water Wave Propagation and Flooding

In: Proceedings of the Conference on Applied Mathematics and Scientific Computing

Author

Listed:
  • Luka Sopta

    (University of Rijeka)

  • Nelida Črnjarić-Žic

    (University of Rijeka)

  • Senka Vuković

    (University of Rijeka)

  • Danko Holjević

    (Croatian Waters)

  • Jerko Škifić

    (University of Rijeka)

  • Siniša Družeta

    (University of Rijeka)

Abstract

In this paper we present main points in the process of application of numerical schemes for hyperbolic balance laws to water wave propagation and flooding. The appropriate mathematical models are the one-dimensional open channel flow equations and the two-dimensional shallow water equations. Therefore good simulation results can only be obtained with well-balanced numerical schemes such as the ones developed by Bermùdez and Vázquez, Hubbard and García-Navarro, LeVeque, etc. as well as the ones developed by the authors of this paper. We also propose a modification of the well-balanced Q-scheme for the two-dimensional shallow water equations that solves the wetting and drying problem. Finally, we present numerical results for three simulation tasks: the CADAM dam break experiment, the water wave propagation in the Toce river, and the catastrophic dam break on the Malpasset river.

Suggested Citation

  • Luka Sopta & Nelida Črnjarić-Žic & Senka Vuković & Danko Holjević & Jerko Škifić & Siniša Družeta, 2005. "Numerical Simulations of Water Wave Propagation and Flooding," Springer Books, in: Zlatko Drmač & Miljenko Marušić & Zvonimir Tutek (ed.), Proceedings of the Conference on Applied Mathematics and Scientific Computing, pages 293-304, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-3197-7_22
    DOI: 10.1007/1-4020-3197-1_22
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