Numerical Analysis
Level-Set method and stability condition for curvature-driven flows
Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 703-708.

We consider models for the simulation of curvature-driven incompressible bifluid flows, where the surface tension term is discretized explicitly. From this formulation a numerical stability condition arises for which we present a new theoretical estimation for low and medium Reynolds numbers. We illustrate our analysis with numerical simulations of microfluidic flows using Level-Set method. Finally, we propose a method to reduce computational cost induced by this stability condition for low flow velocities.

Dans cette Note, nous considérons des modèles utilisés pour simuler des écoulements bifluides incompressibles, pilotés par la tension de surface. En particulier, lorsque la discrétisation du terme de tension de surface est explicite, une condition de stabilité contraint le pas de temps et nous en proposons ici une nouvelle estimation théorique, pour des écoulements dont le nombre de Reynolds est faible ou modéré. Notre analyse est étayée par des simulations numériques, basées sur la méthode Level Set et appliquées à des écoulements en microfluidique. Nous proposons, de plus, une méthode pour réduire les coûts de calculs induits par cette condition de stabilité pour des écoulements lents.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.05.001
Galusinski, Cédric 1; Vigneaux, Paul 2

1 MC2 (INRIA Futurs) & ANAM/CPT – Université du sud Toulon Var, avenue de l'université, BP 20132, 83957 La Garde cedex, France
2 MC2 (INRIA Futurs) & MAB – Université Bordeaux 1, 351, cours de la libération, 33405 Talence cedex, France
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Galusinski, Cédric; Vigneaux, Paul. Level-Set method and stability condition for curvature-driven flows. Comptes Rendus. Mathématique, Volume 344 (2007) no. 11, pp. 703-708. doi : 10.1016/j.crma.2007.05.001. http://www.numdam.org/articles/10.1016/j.crma.2007.05.001/

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