A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model

Philippe Bonneton; Florent Chazel; David Lannes; Fabien Marche; Marion Tissier

hal-00482564, version 1

A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model

Philippe Bonneton ¹, Florent Chazel ( Author to contact preferably ) ², David Lannes () ³, Fabien Marche () ⁴, Marion Tissier ¹

Journal of Computational Physics 230, 4 (2010) 1479-1498

Abstract: The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up.

1: Environnements et Paléoenvironnements OCéaniques (EPOC)
CNRS : UMR5805 – INSU – Université Sciences et Technologies - Bordeaux I – Ecole Pratique des Hautes Etudes – Observatoire Aquitain des Sciences de l'Univers
2: Institut de Mathématiques de Toulouse (IMT)
Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219
3: Département de Mathématiques et Applications (DMA)
CNRS : UMR8553 – Ecole normale supérieure de Paris - ENS Paris
4: Institut de Mathématiques et de Modélisation de Montpellier (I3M)
CNRS : UMR5149 – Université Montpellier II - Sciences et techniques

hal-00482564, version 1
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From: Florent Chazel <>
Submitted on: Monday, 10 May 2010 17:22:48
Updated on: Tuesday, 12 March 2013 14:26:04

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arXiv: 1005.1586

DOI: 10.1016/j.jcp.2010.11.015

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