Mathematical Problems in Mechanics
Influence of interfacial pressure on the hyperbolicity of the two-fluid model
Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 407-412.

The two-fluid model, widely used in the modeling of two phase flows, generally fails to be hyperbolic in its basic formulation. However, it is well known that interfacial forces, bringing new differential terms to the system can make the model hyperbolic. This Note details the effects interfacial pressure has on the hyperbolicity of the two-fluid model, in the general case of two compressible phases. We characterise the location and topology of the non-hyperbolic regions and propose a closure law for the interfacial pressure to make the system hyperbolic.

Les équations de base du modèle bifluide, couramment utilisées dans la modélisation des écoulements diphasiques ne sont en général pas hyperboliques. Cependant, les forces interfaciales apportant de nouveaux termes différentiels peuvent modifier ce résultat. Cette Note se propose de détailler l'effet du défaut de pression interfaciale sur l'hyperbolicité du modèle, dans le cas général de deux phases compressibles. Nous mettons en évidence la localisation et la topologie des régions non hyperboliques, et nous proposons une relation de fermeture de la pression interfaciale rendant le système hyperbolique.

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DOI: 10.1016/j.crma.2007.02.006
Ndjinga, Michaël 1, 2

1 Commissariat à l'énergie atomique, centre de Saclay, CEA/DEN/DM2S/SFME, 91191 Gif-sur-Yvette cedex, France
2 Laboratoire de mathématiques appliquées aux systèmes, École centrale Paris, 92295 Châtenay-Malabry cedex, France
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Ndjinga, Michaël. Influence of interfacial pressure on the hyperbolicity of the two-fluid model. Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 407-412. doi : 10.1016/j.crma.2007.02.006. http://www.numdam.org/articles/10.1016/j.crma.2007.02.006/

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