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Consistent section-averaged shallow water equations with bottom friction

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Victor Michel-Dansac (Toulouse)

In this work, we present a general framework to construct section-averaged models when the flow is constrained - e.g. by topography - to be almost one-dimensional (1D). These models are consistent with the two-dimensional (2D) shallow water equations. After rewriting the 2D shallow water equations in a suitable set of coordinates allowing to take care of a meandering configuration, we consider the quasi-1D regime of the 2D shallow water equations. Then, we expand the water elevation and velocity field in the spirit of the diffusive wave equations, and we establish a set of 1D equations made of a mass, momentum and energy equations which are close to the ones usually used in hydraulic engineering. Out of these configurations, there is an O(1) deviation of our model from the classical ones. Finally, we present the main mathematical properties of our model and carry out numerical simulation as validation of our approach with comparison to the full two-dimensional shallow water equations. This is joint work with Pascal Noble (IMT & INSA Toulouse) and Jean-Paul Vila (IMT & INSA Toulouse).