A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
For coastal engineers and modelers, this provides a practical numerical method for simulating nonlinear wave transformations, though it is an incremental improvement over existing splitting techniques.
The authors reformulate the Green-Naghdi model and propose a hybrid finite volume/finite difference splitting method, validated in 1D against analytical solutions and experimental data, accurately capturing shoaling, breaking, and run-up.
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.