Wave evolution over submerged sills: tests of a high-order Boussinesq model

Gobbi, Mauricio F.; Kirby, James T.

doi:10.1016/s0378-3839(99)00015-0

Cited by 121 publications

(80 citation statements)

References 18 publications

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“…The basis (24) have arbitrary polynomial orders k 1 in the horizontal plane and k 2 in the vertical plane. This makes it possible to tune the orders of the approximations to balance accuracy and efficiency needs in simulations.…”

Section: Nodal Prismatic Lagrange Finite Elements In Two Space Dimensmentioning

confidence: 99%

A stabilised nodal spectral element method for fully nonlinear water waves

Engsig-Karup

Eskilsson

Bigoni

2016

Journal of Computational Physics

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We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed and irregular dispersive wave propagation. The benefit of using a high-order -possibly adapted -spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.1

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Section: Nodal Prismatic Lagrange Finite Elements In Two Space Dimensmentioning

confidence: 99%

A stabilised nodal spectral element method for fully nonlinear water waves

Engsig-Karup

Eskilsson

Bigoni

2016

Journal of Computational Physics

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“…In our model, the long waves are slowed down by strong bathymetric variations since fluid particles are constrained to follow the seabed. We note also that a similar factor was previously introduced in [30] to account for steepness in the bathymetry. In our case it appears naturally as a property of the model.…”

Section: Hyperbolic Structurementioning

confidence: 84%

Modified shallow water equations for significantly varying seabeds

Dutykh

Clamond²

2016

Applied Mathematical Modelling

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Abstract. In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow water ansatz and imposing some constraints. Our derivation procedure does not explicitly involve any small parameter and is straightforward. The novel system is a non-dispersive non-hydrostatic extension of the classical Saint-Venant equations. A key feature of the new model is that, like the classical NSWE, it is hyperbolic and thus similar numerical methods can be used. We also propose a finite volume discretisation of the obtained hyperbolic system. Several test-cases are presented to highlight the added value of the new model. Some implications to tsunami wave modelling are also discussed.

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“…Boussinesq-type equations are widely used for the description of the non-linear breaking and non-breaking wave propagation in the nearshore or long wave propagation in the open sea (Gobbi and Kirby, 1999;Gobbi et al, 2000;AtaieAshtiani and Najafi Jilani, 2007;Fuhrman and Madsen, 2009;Zhou and Teng, 2009;Zhou et al, 2011). Over the years, the classical Boussinesq equations have been extended so as to be able to include higher-order nonlinear terms, which can describe better the propagation of highly nonlinear waves in the shoaling zone.…”

Section: Boussinesq Equations For Breaking/non-breaking Waves and Tsumentioning

confidence: 99%

Simulation of tsunami generation, propagation and coastal inundation in the Eastern Mediterranean

2015

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Abstract. In the present work, an advanced tsunami generation, propagation and coastal inundation 2-DH model (i.e. 2-D Horizontal model) based on the higher-order Boussinesq equations -developed by the authors -is applied to simulate representative earthquake-induced tsunami scenarios in the Eastern Mediterranean. Two areas of interest were selected after evaluating tsunamigenic zones and possible sources in the region: one at the southwest of the island of Crete in Greece and one at the east of the island of Sicily in Italy. Model results are presented in the form of extreme water elevation maps, sequences of snapshots of water elevation during the propagation of the tsunamis, and inundation maps of the studied low-lying coastal areas. This work marks one of the first successful applications of a fully nonlinear model for the 2-DH simulation of tsunami-induced coastal inundation; acquired results are indicative of the model's capabilities, as well of how areas in the Eastern Mediterranean would be affected by eventual larger events.

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Wave evolution over submerged sills: tests of a high-order Boussinesq model

Cited by 121 publications

References 18 publications

A stabilised nodal spectral element method for fully nonlinear water waves

A stabilised nodal spectral element method for fully nonlinear water waves

Modified shallow water equations for significantly varying seabeds

Simulation of tsunami generation, propagation and coastal inundation in the Eastern Mediterranean

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