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Université d'Orléans |  |
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Université d'Orléans | |
| HAL: hal-00710654, version 1 |
| arXiv: 1206.4986 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2012-06-21) | v2 (2012-08-12) |
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| A limitation of some well-balanced schemes for Shallow Water equations |
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| Olivier Delestre 1Stéphane Cordier 2 |
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| (2012-06-20) |
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| Because of their capability to preserve steady-states, well-balanced schemes for Shallow Water equations are becoming popular. They allow to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid the unstabilities when dealing with dry zones. In this note, we prove that the well-balanced scheme based on hydrostatic reconstruction proposed in 2004 [2] exhibits an abnormal behavior for some combinations of slope, mesh size and water height. |
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| 1: | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| 2: | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| 3: | Unité de recherche Science du Sol (USS) |
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Institut national de la recherche agronomique (INRA) : UR0272 |
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| Subject | : | Mathematics/Numerical Analysis Mathematics/Analysis of PDEs |
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| Shallow water equations – Saint-Venant system – well-balanced scheme – hydrostatic reconstruction – finite volume schemes – exact solution |
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| hal-00710654, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00710654 | |
| oai:hal.archives-ouvertes.fr:hal-00710654 | |
| From: Olivier Delestre | |
| Submitted on: Thursday, 21 June 2012 13:57:05 | |
| Updated on: Thursday, 21 June 2012 21:14:29 | |
