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Pré-Publication, Document De Travail Année : 2020

A Generalised Serre-Green-Naghdi equations for variable rectangular open channel hydraulics and its finite volume approximation

Mohamed Ali Debyaoui

Résumé

We present a non-linear dispersive shallow water model which enters in the framework of section-averaged models. These new equations are derived up to the second order of the shallow water approximation starting from the three-dimensional incompressible and irrotational Euler system. The derivation is carried out in the case of non uniform rectangular section and it generalises the well-known one-dimensional Serre-Green-Naghdi (SGN) equations on uneven bottom. The obtained model is fully consistent with the Euler system. We propose a well-balanced finite volume approximation and we present some numerical results to show the influence of the section variation.
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Dates et versions

hal-02548837 , version 1 (20-04-2020)
hal-02548837 , version 2 (19-05-2020)

Identifiants

  • HAL Id : hal-02548837 , version 1

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Mohamed Ali Debyaoui, Mehmet Ersoy. A Generalised Serre-Green-Naghdi equations for variable rectangular open channel hydraulics and its finite volume approximation. 2020. ⟨hal-02548837v1⟩
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