We investigate here the ability of a Green-Naghdi model to reproduce stronglynonlinear and dispersive wave propagation. We test in particular the behaviorof the new hybrid finite-volume and finite-difference splitting approachrecently developed by the authors and collaborators on the challengingbenchmark of waves propagating over a submerged bar. Such a configurationrequires a model with very good dispersive properties, because of thehigh-order harmonics generated by topography-induced nonlinear interactions. Wethus depart from the aforementioned work and choose to use a new Green-Naghdisystem with improved frequency dispersion characteristics. The absence of dryareas also allows us to improve the treatment of the hyperbolic part of theequations. This leads to very satisfying results for the demanding benchmarksunder consideration.
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