Adaptive models for polymeric fluid flow simulation

Alexandre Ern; Tony Lelièvre

doi:10.1016/j.crma.2007.02.013

Numerical Analysis

Adaptive models for polymeric fluid flow simulation

Presented by: Philippe G. Ciarlet

Alexandre Ern ¹; Tony Lelièvre ¹

¹ CERMICS, École nationale des ponts et chaussées, ParisTech, 6 & 8, avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France

Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 473-476.

Abstract
Résumé

We propose a new adaptive algorithm for multiscale simulations of non-Newtonian fluids. Using a posteriori error indicators, the method can switch dynamically at each timestep between a rough (macroscopic) and a detailed (microscopic) model in each cell of the mesh. The validity of the approach is tested on a plane shear flow for the FENE model of polymeric fluids.

Nous proposons un nouvel algorithme adaptatif pour la simulation multi-échelles de fluides non-newtoniens. Le principe est d'utiliser soit un modèle simple (macroscopique) soit un modèle plus détaillé (microscopique) dans chaque maille, le choix étant effectué de manière dynamique à chaque pas de temps sur la base d'indicateurs d'erreur a posteriori. Des tests sur un écoulement cisaillé pour le modèle FENE de fluides polymériques démontrent l'intérêt de l'approche.

Received: 2007-01-24
Accepted: 2007-02-05
Published online: 2007-03-26

DOI: 10.1016/j.crma.2007.02.013

Author's affiliations:

Alexandre Ern ¹; Tony Lelièvre ¹

¹ CERMICS, École nationale des ponts et chaussées, ParisTech, 6 & 8, avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France

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     author = {Alexandre Ern and Tony Leli\`evre},
     title = {Adaptive models for polymeric fluid flow simulation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {473--476},
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     volume = {344},
     number = {7},
     year = {2007},
     doi = {10.1016/j.crma.2007.02.013},
     language = {en},
}

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Alexandre Ern; Tony Lelièvre. Adaptive models for polymeric fluid flow simulation. Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 473-476. doi : 10.1016/j.crma.2007.02.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.02.013/

References
Cited by

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[2] M. Braack; A. Ern A posteriori control of modeling errors and discretization errors, Multiscale Model. Simul., Volume 1 (2003) no. 2, pp. 221-238

[3] M. Doi; S.F. Edwards The Theory of Polymer Dynamics, International Series of Monographs on Physics, Oxford University Press, 1988

[4] R. Keunings On the Peterlin approximation for finitely extensible dumbbells, J. Non-Newtonian Fluid Mech., Volume 68 (1997), pp. 85-100

[5] M. Laso; H.C. Öttinger Calculation of viscoelastic flow using molecular models: The CONNFFESSIT approach, J. Non-Newtonian Fluid Mech., Volume 47 (1993), pp. 1-20

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