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| HAL: hal-00355730, version 1 |
| arXiv: 0901.3887 |
| Detailed view |  Export this paper |
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| Modelisation Mathématique et Analyse Numérique (2009) 1-30 |
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| {A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation |
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| Emmanuel Audusse 1Marie-Odile Bristeau 2 |
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| (2009-01-23) |
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| The standard multilayer Saint-Venant system consists in introducing fluid layers that are advected by the interfacial velocities. As a consequence there is no mass exchanges between these layers and each layer is described by its height and its average velocity. Here we introduce another multilayer system with mass exchanges between the neighborhing layers where the unknowns are a total height of water and an average velocity per layer. We derive it from Navier-Stokes system with an hydrostatic pressure and prove energy and hyperbolicity properties of the model. We also give a kinetic interpretation leading to effective numerical schemes with positivity and energy properties. Numerical tests show the versatility of the approach and its ability to compute recirculation cases with wind forcing. |
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| 1: | Laboratoire Analyse, Géométrie et Application (LAGA) |
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CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis |
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| 2: | BANG (INRIA Rocquencourt) |
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INRIA – Laboratoire Jacques-Louis Lions |
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| 3: | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| 4: | MACS (INRIA Rocquencourt) |
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INRIA |
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| Subject | : | Computer Science/Modeling and Simulation Mathematics/Analysis of PDEs Physics/Mechanics/Mechanics of the fluids Engineering Sciences/Mechanics/Fluids mechanics |
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| Navier-Stokes equations – Saint-Venant equations – Free surface – Multilayer system – Kinetic scheme |
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| Attached file list to this document: | ||||||||||
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| hal-00355730, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00355730 | |
| oai:hal.archives-ouvertes.fr:hal-00355730 | |
| From: Jacques Sainte-Marie | |
| Submitted on: Friday, 23 January 2009 18:58:32 | |
| Updated on: Sunday, 25 January 2009 11:18:43 | |
