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| HAL: hal-00628651, version 2 |
| arXiv: 1110.0799 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2011-10-04) | v2 (2012-08-09) |
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| A new model for shallow viscoelastic fluids |
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| François Bouchut 1Sébastien Boyaval 2, 3 |
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| (2012-07-31) |
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| We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order epsilon, the aspect ratio of the thin layer of fluid), but the relaxation time is kept finite. Additionally to the classical layer depth and velocity in shallow models, our system describes also the evolution of two scalar stresses. It has an intrinsic energy equation. The mathematical properties of the model are established, an important feature being the non-convexity of the physically relevant energy with respect to conservative variables, but the convexity with respect to the physically relevant pseudo-conservative variables. Numerical illustrations are given, based on a suitable well-balanced finite-volume discretization involving an approximate Riemann solver. |
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| 1: | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout |
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| 2: | Laboratoire d'Hydraulique Saint-Venant / Saint-Venant Laboratory for Hydraulics (Saint-Venant) |
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Université Paris-Est Créteil Val-de-Marne (UPEC) – Ecole des Ponts ParisTech – EDF – CETMEF |
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| 3: | MICMAC (INRIA Paris - Rocquencourt) |
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Ecole des Ponts ParisTech – INRIA |
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| Subject | : | Mathematics/Numerical Analysis Physics/Mechanics/Mechanics of the fluids Engineering Sciences/Mechanics/Fluids mechanics Mathematics/Analysis of PDEs |
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| Viscoelastic fluids – Maxwell model – Oldroyd model – Saint Venant equations – shallow-water model – pseudo-conservative hyperbolic system of equations – well-balanced finite-volume scheme |
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| hal-00628651, version 2 | |
| http://hal-enpc.archives-ouvertes.fr/hal-00628651 | |
| oai:hal-enpc.archives-ouvertes.fr:hal-00628651 | |
| From: Sébastien Boyaval | |
| Submitted on: Wednesday, 8 August 2012 23:16:57 | |
| Updated on: Thursday, 9 August 2012 09:02:19 | |
