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Article dans une revue

Macroscopic Limit of a One-Dimensional Model for Aging Fluids

David Benoit 1, 2 Claude Le Bris 1, 2 Tony Lelièvre 1, 2
1 MATHERIALS - MATHematics for MatERIALS
ENPC - École des Ponts ParisTech, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique, Inria Paris-Rocquencourt
Abstract : We study a one-dimensional equation arising in the multiscale modeling of some non-Newtonian fluids. At a given shear rate, the equation provides the instantaneous mesoscopic response of the fluid, allowing to compute the corresponding stress. In a simple setting, we study the well-posedness of the equation and next the long-time behavior of its solution. In the limit of a response of the fluid much faster than the time variations of the ambient shear rate, we derive some equivalent macroscopic differential equations that relate the shear rate and the stress. Our analytical conclusions are confronted to some numerical experiments. The latter quantitatively confirm our derivations.
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https://hal-enpc.archives-ouvertes.fr/hal-00873577
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Soumis le : mercredi 16 octobre 2013 - 08:45:59
Dernière modification le : vendredi 29 novembre 2019 - 12:42:01

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David Benoit, Claude Le Bris, Tony Lelièvre. Macroscopic Limit of a One-Dimensional Model for Aging Fluids. Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2014, 12 (3), pp.1335 - 1378. ⟨10.1137/13094133X⟩. ⟨hal-00873577⟩

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