Numerical Analysis
Adaptive models for polymeric fluid flow simulation
Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 473-476.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.02.013
Ern, Alexandre 1; Lelièvre, Tony 1

1 CERMICS, École nationale des ponts et chaussées, ParisTech, 6 & 8, avenue Blaise Pascal, 77455 Marne-la-Vallée cedex 2, France
@article{CRMATH_2007__344_7_473_0,
     author = {Ern, Alexandre and Leli\`evre, Tony},
     title = {Adaptive models for polymeric fluid flow simulation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {473--476},
     publisher = {Elsevier},
     volume = {344},
     number = {7},
     year = {2007},
     doi = {10.1016/j.crma.2007.02.013},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2007.02.013/}
}
TY  - JOUR
AU  - Ern, Alexandre
AU  - Lelièvre, Tony
TI  - Adaptive models for polymeric fluid flow simulation
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 473
EP  - 476
VL  - 344
IS  - 7
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2007.02.013/
DO  - 10.1016/j.crma.2007.02.013
LA  - en
ID  - CRMATH_2007__344_7_473_0
ER  - 
%0 Journal Article
%A Ern, Alexandre
%A Lelièvre, Tony
%T Adaptive models for polymeric fluid flow simulation
%J Comptes Rendus. Mathématique
%D 2007
%P 473-476
%V 344
%N 7
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.02.013/
%R 10.1016/j.crma.2007.02.013
%G en
%F CRMATH_2007__344_7_473_0
Ern, Alexandre; Lelièvre, Tony. 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. http://www.numdam.org/articles/10.1016/j.crma.2007.02.013/

[1] Bonvin, J.; Picasso, M. Variance reduction methods for CONNFFESSIT-like simulations, J. Non-Newtonian Fluid Mech., Volume 84 (1999), pp. 191-215

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

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

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

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

Cited by Sources: