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

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

1 EPOC - Environnements et Paléoenvironnements OCéaniques
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 DMA - Département de Mathématiques et Applications - ENS Paris
4 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Domaines: Analyse numérique [math.NA]; Physique Atmosphérique et Océanique [physics.ao-ph]

Philippe Bonneton, Florent Chazel, David Lannes, Fabien Marche, Marion Tissier. A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model. Journal of Computational Physics, 2010, 230 (4), pp.1479-1498. ⟨10.1016/j.jcp.2010.11.015⟩. ⟨hal-00482564⟩