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

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

2010-05-10

arxiv.org/abs/1005.1586v1

J.Comput.Phys.230:1479-1498,2011

Mathematics

Numerical Analysis

Scientific paper

10.1016/j.jcp.2010.11.015

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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