A Generalised Serre-Green-Naghdi equations for variable rectangular open channel hydraulics and its finite volume approximation - Archive ouverte HAL Access content directly
Book Sections Year : 2021

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

Abstract

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 and versions

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

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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. Muñoz-Ruiz M.L., Parés C., Russo G. (eds) Recent Advances in Numerical Methods for Hyperbolic PDE Systems. SEMA SIMAI Springer Series, vol 28. Springer, 2021, 978-3-030-72850-2. ⟨10.1007/978-3-030-72850-2_11⟩. ⟨hal-02548837v2⟩
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