A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
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.
Keywords
Cite
@article{arxiv.1005.1586,
title = {A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model},
author = {Philippe Bonneton and Florent Chazel and David Lannes and Fabien Marche and Marion Tissier},
journal= {arXiv preprint arXiv:1005.1586},
year = {2011}
}