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2D Versus 1D Models for Shallow Water Equations

Abstract : In this paper we present a general framework to construct 1D width averaged models when the flow is constrained-e.g. by topography-to be almost 1D. We start from two dimensional shallow water equations, perform an asymptotic expansion of the fluid elevation and velocity field in the spirit of wave diffusive equations and establish a set of 1D equations made of a mass, momentum and energy equations which are close to the one usually used in hydraulic engineering. We show that in some special cases, like the U-shaped river bed, that our set of equations reduces to the classical 1d shallow water equations. Out of these configurations, there is an O (1) deviation of our model from the classical one.
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https://hal.archives-ouvertes.fr/hal-01870744
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Submitted on : Sunday, September 9, 2018 - 11:26:14 AM
Last modification on : Monday, July 4, 2022 - 10:25:29 AM
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Jean-Paul Vila, Florent Chazel, Pascal Noble. 2D Versus 1D Models for Shallow Water Equations. Procedia IUTAM, Elsevier, 2017, 20, pp.167 - 174. ⟨10.1016/j.piutam.2017.03.023⟩. ⟨hal-01870744⟩

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