Generalised Serre–Green–Naghdi equations for open channel and for natural river hydraulics

Debyaoui, Mohamed Ali; Ersoy, Mehmet

doi:10.3233/asy-201647

Cited by 4 publications

(5 citation statements)

References 35 publications

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“…Only few papers (to the author's knowledge) refer to an extension of the Serre equations to channel flows with arbitrary channel cross section. A recent attempt was made by Debyaoui and Ersoy (2020) using the traditional asymptotic expansion method, leading to a complex formulation after long computations.…”

Section: Aim Of Present Workmentioning

confidence: 99%

“…The variational method proposed by Clamond and Dutykh (2012) proved to be efficient in finding a system of Serre equations for arbitrary cross-sectional channels, given by ( 24), ( 40) and ( 45), the derivation being significantly easier than it would be by using the more traditional asymptotic expansion approach as in Debyaoui and Ersoy (2020). The global family of travelling waves (63) including solitary waves with celerity (64) are formally written for arbitrary shape of the cross section through the bottom/bank elevation 𝑑 (𝑦).…”

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confidence: 99%

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Serre Equations in Channels and Rivers of Arbitrary Cross Section

Violeau

2023

J. Hydraul. Eng.

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A variational approach is used to derivate a set of Serre equations for fully nonlinear, dispersive waves in channels of arbitrary cross-section. A family of travelling waves is found, as well as the relation between amplitude and celerity of solitary waves. An upper bound is proposed for the solitary wave amplitude as a function of the Froude number in trapezoidal cross-sectional canals, showing good agreement with an existing theory. For waves of moderate amplitude, cnoidal waves result with a soliton limit; the latter waves and their properties (celerity, wave number) are written as functions of the channel bank slope and channel bank curvature. The theoretical findings are in agreement with well-established results of the literature, in particular with more recent Boussinesq-type theories. A validation is proposed against existing experimental data.

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Section: Aim Of Present Workmentioning

confidence: 99%

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confidence: 99%

Serre Equations in Channels and Rivers of Arbitrary Cross Section

Violeau

2023

J. Hydraul. Eng.

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“…For the sake of completeness, skipping the technical details, we present the outline of the derivation. Interested readers can found the details in [6].…”

Section: Dimensionless Euler Equationsmentioning

confidence: 99%

“…However, for small or moderate transitions, the solutions of these equations are not able to catch undular bores induced by a non-hydrostatic pressure distribution [17]. Up to our knowledge, the first section-averaged dispersive shallow water equations for quite general assumptions on the geometry of the channel was proposed in [6], thus allowing for the application of the resulting equations to natural rivers with arbitrarily shaped cross-sections. This model reads…”

Section: Introductionmentioning

confidence: 99%

A Generalised Serre-Green-Naghdi Equations for Variable Rectangular Open Channel Hydraulics and Its Finite Volume Approximation

Debyaoui

Ersoy

2021

SEMA SIMAI Springer Series

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We present a non-linear dispersive shallow water model which enters in the framework of sectionaveraged 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 section-averaged model is asymptotically consistent with the Euler system in terms of mass, momentum, and energy equation which provides the richness of content for this model. 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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“…The main purpose of the paper is to analyze some of the properties of the system in any dimension and to examine some 1D numerical algorithms. Developing robust and efficient algorithms for the numerical resolution of the Serre-Green-Naghdi system has drawn much attention lately, partially due to the knowledge from theoretical analyses and the surge in computational power (see for instance [6,13,15,[20][21][22]25]).…”

Section: Unknownsmentioning

confidence: 99%

Simulation of complex free surface flows

et al. 2021

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We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike the well-known (nonlinear) Saint-Venant equations, takes into account the effects of the non-hydrostatic pressure term as well as dispersive phenomena. Two numerical schemes are designed, based on a finite volume - finite difference type splitting scheme and iterative correction algorithms. The methods are compared by means of simulations concerning the propagation of solitary wave solutions. The model is also assessed with experimental data concerning the Favre secondary wave experiments [12].

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Generalised Serre–Green–Naghdi equations for open channel and for natural river hydraulics

Cited by 4 publications

References 35 publications

Serre Equations in Channels and Rivers of Arbitrary Cross Section

Serre Equations in Channels and Rivers of Arbitrary Cross Section

A Generalised Serre-Green-Naghdi Equations for Variable Rectangular Open Channel Hydraulics and Its Finite Volume Approximation

Simulation of complex free surface flows

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