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Journal of Scientific Computing

, Volume 48, Issue 1–3, pp 105–116 | Cite as

Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green–Naghdi Model

  • F. Chazel
  • D. Lannes
  • F. Marche
Article

Abstract

We investigate here the ability of a Green–Naghdi model to reproduce strongly nonlinear and dispersive wave propagation. We test in particular the behavior of the new hybrid finite-volume and finite-difference splitting approach recently developed by the authors and collaborators on the challenging benchmark of waves propagating over a submerged bar. Such a configuration requires a model with very good dispersive properties, because of the high-order harmonics generated by topography-induced nonlinear interactions. We thus depart from the aforementioned work and choose to use a new Green–Naghdi system with improved frequency dispersion characteristics. The absence of dry areas also allows us to improve the treatment of the hyperbolic part of the equations. This leads to very satisfying results for the demanding benchmarks under consideration.

Keywords

Green–Naghdi equations Splitting technique Hybrid method Hyperbolic systems Highorder well-balanced scheme WENO reconstruction Submerged bar Dispersive waves Nonlinear interactions 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Université de ToulouseUPS/INSA, IMT, CNRS UMR 5219ToulouseFrance
  2. 2.DMAEcole Normale Supérieure, et CNRS UMR 8553ParisFrance
  3. 3.I3MUniv. Montpellier 2 et CNRS UMR 5149MontpellierFrance

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