An hybrid finite volume-finite element method for variable density incompressible flows

Authors:
Caterina Calgaro;Emmanuel Creusé;Thierry Goudon
Affiliations:
Laboratoire Paul Painlevé, UMR 8524, CNRS - Université Sciences et Technologies de Lille, Cité Scientifique, F-59655 Villeneuve d'Ascq cedex, France and Equipe-Projet SIMPAF, Centre ...;Laboratoire Mathématiques et Applications de Valenciennes, FR CNRS 2956, Université de Valenciennes et du Hainaut-Cambrésis, Le Mont Houy, F-59313 Valenciennes cedex 09, France and ...;Equipe-Projet SIMPAF, Centre de Recherche INRIA Futurs, Parc Scientifique de la Haute Borne, Avenue Halley, B.P. 70478, F-59658 Villeneuve d'Ascq cedex, France and Laboratoire Paul Painlevé, ...
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh-Taylor instability evolution is carefully investigated.