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arXiv · 1005.1586

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

Philippe Bonneton·Florent Chazel·David Lannes·Fabien Marche·Marion Tissier
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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.

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Philippe Bonneton, Florent Chazel, David Lannes, Fabien Marche, Marion Tissier. 2010-05-10. A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model. https://doi.org/10.1016/j.jcp.2010.11.015

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