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Modified Shallow Water Equations for significantly varying seabeds: Modified Shallow Water Equations

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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Submitted on : Tuesday, April 26, 2016 - 9:50:14 AM
Last modification on : Friday, November 6, 2020 - 3:34:25 AM
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Denys Dutykh, Didier Clamond. Modified Shallow Water Equations for significantly varying seabeds: Modified Shallow Water Equations. Applied Mathematical Modelling, Elsevier, 2016, 40 (23-24), pp.9767-9787. ⟨10.1016/j.apm.2016.06.033⟩. ⟨hal-00675209v6⟩

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