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

TL;DR

This paper introduces a novel splitting numerical method for the Green-Naghdi model, effectively capturing complex wave phenomena like breaking and run-up in shallow water simulations.

Contribution

A new hybrid finite volume and finite difference splitting approach tailored for the Green-Naghdi model, improving numerical resolution of nonlinear dispersive waves.

Findings

Accurately models wave shoaling and breaking.

Handles dry areas and wave run-up effectively.

Validated with analytical and experimental data.

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.