Numerical Analysis
Numerical simulation of a lid-driven cavity viscoelastic flow at high Weissenberg numbers
Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 283-286.

In this Note we present a finite element method for simulating the Stokes flow of an Oldroyd-B fluid in a lid-driven cavity, which is a stringent test problem at high Weissenberg numbers. The key considerations are: (i) the preservation of the positive definiteness of the conformation tensor at the discrete level; (ii) the use of a coarser mesh when discretizing the conformation tensor to lower the number of high frequency modes; and (iii) additional diffusion to smooth the high frequency modes. The methodologies with the above three features are found to be stable at high Weissenberg numbers.

Dans cette Note nous présentons une méthode d'éléments finis pour la simulation de l'écoulement d'un fluide viscoélastique de type Oldroyd-B dans une cavité entraînée par une vitesse imposée sur l'une de ses parois. Ce problème est un test modèle pour des nombres de Weissenberg élevés. Les caractéristiques principales de notre méthode sont : (i) la conservation du caractère défini positif du tenseur de conformation au niveau discret ; (ii) l'utilisation d'une maille grossière pour la discrétisation du tenseur de conformation afin de réduire le nombre de modes à haute fréquence ; et (iii) l'introduction d'une diffusion additionnelle pour lisser les modes à haute fréquence. La prise en compte de ces trois mécanismes permet d'obtenir des méthodes stables pour des nombres de Weissenberg élevés.

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Published online:
DOI: 10.1016/j.crma.2006.12.014
Pan, Tsorng-Whay 1; Hao, Jian 1

1 University of Houston, Department of Mathematics, Houston, TX 77204-3476, USA
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Pan, Tsorng-Whay; Hao, Jian. Numerical simulation of a lid-driven cavity viscoelastic flow at high Weissenberg numbers. Comptes Rendus. Mathématique, Volume 344 (2007) no. 4, pp. 283-286. doi : 10.1016/j.crma.2006.12.014. http://www.numdam.org/articles/10.1016/j.crma.2006.12.014/

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