# A kinetic interpretation of the section-averaged Saint-Venant system for natural river hydraulics.

Abstract : The classical Saint-Venant system is well suited for the modeling of dam breaks, hydraulic jumps, reservoir emptying, flooding, etc. For many applications, the extension of the Saint-Venant system to the case of non rectangular channels is necessary and this section-averaged Saint-Venant system exhibits additional source terms. The main difficulty of these equations consists in the discretization of these source terms. In this paper we propose a kinetic interpretation for the section averaged Saint-Venant system and we derive an associated numerical scheme. The numerical scheme~-- 2$^{nd}$ order in space and time~-- preserves the positivity of the water height, and is well-balanced. Numerical results including comparisons with analytic and experimental test problems illustrate the accuracy and the robustness of the numerical algorithm
Type de document :
Article dans une revue
International Journal for Numerical Methods in Fluids, Wiley, 2011, 67 (7), pp.914-938. 〈10.1002/fld.2401〉

https://hal.inria.fr/inria-00551487
Contributeur : Jacques Sainte-Marie <>
Soumis le : lundi 3 janvier 2011 - 19:29:25
Dernière modification le : vendredi 25 mai 2018 - 12:02:03

### Citation

N. Goutal, Jacques Sainte-Marie. A kinetic interpretation of the section-averaged Saint-Venant system for natural river hydraulics.. International Journal for Numerical Methods in Fluids, Wiley, 2011, 67 (7), pp.914-938. 〈10.1002/fld.2401〉. 〈inria-00551487〉

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