A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids

Sébastien Boyaval 1, 2
2 MATHERIALS - MATHematics for MatERIALS
CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria de Paris
Abstract : Saint-Venant equations can be generalized to account for a viscoelastic rheology in shallow flows. A Finite-Volume discretization for the 1D Saint-Venant system generalized to Upper-Convected Maxwell (UCM) fluids was proposed in [Bouchut & Boyaval, 2013], which preserved a physically-natural stability property (i.e. free-energy dissipation) of the full system. It invoked a relaxation scheme of Suliciu type for the numerical computation of approximate solution to Riemann problems. Here, the approach is extended to the 1D Saint-Venant system generalized to the finitely-extensible nonlinear elastic fluids of Peterlin (FENE-P). We are currently not able to ensure all stability conditions a priori, but numerical simulations went smoothly in a practically useful range of parameters.
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Chapitre d'ouvrage
Clément Cancès; Pascal Omnes. Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, 200, Springer, pp.163-170, 2017, Print ISBN : 978-3-319-57393-9 / online : 978-3-319-57394-6. 〈10.1007/978-3-319-57394-6_18〉. 〈https://rd.springer.com/chapter/10.1007/978-3-319-57394-6_18〉
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Contributeur : Sébastien Boyaval <>
Soumis le : jeudi 12 janvier 2017 - 21:07:20
Dernière modification le : jeudi 17 mai 2018 - 10:34:02
Document(s) archivé(s) le : vendredi 14 avril 2017 - 16:36:33

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Sébastien Boyaval. A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids. Clément Cancès; Pascal Omnes. Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, 200, Springer, pp.163-170, 2017, Print ISBN : 978-3-319-57393-9 / online : 978-3-319-57394-6. 〈10.1007/978-3-319-57394-6_18〉. 〈https://rd.springer.com/chapter/10.1007/978-3-319-57394-6_18〉. 〈hal-01433712〉

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