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

Mohamed Ali Debyaoui (1, 2) , Mehmet Ersoy (2)

1 IDP - Institut Denis Poisson
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

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.

Mots clés: Open channel flow; Euler equations; Asymptotic approximation; Serre-Green-Naghdi equations; Free surface shallow water equations; Non-hydrostatic pressure; Dispersive model; Finite volume

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

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⟩