  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.
