[hal-01088995] A 2D reconstruction for the transverse coupling of shallow water models

This work is dedicated to the modeling of exchanges between a river and its surrounding floodplains during floods overflowing its bed. Modeling flows in each subdomain, that of the river and that of the floodplain, has been the subject of numerous works for over 50 years and is now well understood. A coupling strategy is considered in order to preserve the advantages of 1D and 2D models in their respective subdomains. In comparison with other transverse coupling strategies already presented in the literature, we introduce a direct method, without overlapping the models or introducing numerical parameters. This strategy is based on the resolution of the Riemann 2D problem at the coupling interface (the bank) and requires the estimation of the transverse velocity close to the interface. We propose a model of transverse velocity using successive resolutions of Riemann problems. Then, we present a numerical resolution of the coupling system, based on a finite volume method for any Riemann solvers. Particular attention was given to the essential properties of the model (conservation of mass, positivity of water depth, and well-balanced scheme). Lastly, the precision and efficiency of the method are illustrated using examples of simulations.



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