inria-00204620, version 2
Free-energy-dissipative schemes for the Oldroyd-B model
Sébastien Boyaval
a, 1, 2Tony Lelièvre
a, 1, 2Claude Mangoubi a, 1, 2, 3
N° RR-6413 (2008)
Résumé : In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman, which have been reported to be numerically more stable than discretizations of the usual formulation in some benchmark problems. Our analysis gives some tracks to understand these numerical observations.
- a – Ecole Nationale des Ponts et Chaussées
- 1 : MICMAC (INRIA Paris - Rocquencourt)
- Ecole des Ponts ParisTech – INRIA
- 2 : Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
- INRIA – Ecole des Ponts ParisTech
- 3 : Einstein Institute of Mathematics
- The Hebrew University of Jerusalem
- Domaine : Mathématiques/Analyse numérique
- Mots-clés : Viscoelastic Fluids – Weissenberg Number – Stability – Entropy – Finite Elements Methods – Discontinuous Galerkin Method – Characteristic Method
- Référence interne : RR-6413
- Versions disponibles : v1 (15-01-2008) v2 (15-01-2008)
- inria-00204620, version 2
- http://hal.inria.fr/inria-00204620
- oai:hal.inria.fr:inria-00204620
- Contributeur : Rapport De Recherche Inria
- Soumis le : Mardi 15 Janvier 2008, 13:58:05
- Dernière modification le : Mardi 15 Janvier 2008, 13:59:05
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