Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

TL;DR

This paper evaluates a new Green-Naghdi model with enhanced dispersion properties for simulating strongly nonlinear waves over complex topography, demonstrating its effectiveness through challenging benchmark tests.

Contribution

The authors develop and test a Green-Naghdi model with improved frequency dispersion and hyperbolic treatment, advancing the simulation of nonlinear dispersive waves over submerged topography.

Findings

Accurately reproduces wave propagation over submerged bars

Improved dispersion characteristics enhance model performance

Effective handling of hyperbolic equations without dry areas

Abstract

We investigate here the ability of a Green-Naghdi model to reproduce strongly nonlinear and dispersive wave propagation. We test in particular the behavior of the new hybrid finite-volume and finite-difference splitting approach recently developed by the authors and collaborators on the challenging benchmark of waves propagating over a submerged bar. Such a configuration requires a model with very good dispersive properties, because of the high-order harmonics generated by topography-induced nonlinear interactions. We thus depart from the aforementioned work and choose to use a new Green-Naghdi system with improved frequency dispersion characteristics. The absence of dry areas also allows us to improve the treatment of the hyperbolic part of the equations. This leads to very satisfying results for the demanding benchmarks under consideration.