2D Versus 1D Models for Shallow Water Equations

Jean-Paul Vila (1) , Florent Chazel (1) , Pascal Noble (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Energy Balance; Asymptotic expansion; Saint Venant equations

Domaines: Mécanique des fluides [physics.class-ph]

Jean-Paul Vila, Florent Chazel, Pascal Noble. 2D Versus 1D Models for Shallow Water Equations. Procedia IUTAM, 2017, 20, pp.167 - 174. ⟨10.1016/j.piutam.2017.03.023⟩. ⟨hal-01870744⟩