Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model
For researchers in coastal engineering and wave modeling, this work demonstrates an improved numerical model for strongly nonlinear and dispersive waves, though it is an incremental improvement over existing methods.
The authors tested a Green-Naghdi model with improved dispersion characteristics on wave propagation over a submerged bar, achieving very satisfying results for this challenging benchmark.
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.