Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
Journal of Computational Physics
High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
Journal of Computational Physics
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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.