Comptes Rendus
no. 9
Mathematical problems in mechanics
A hybrid collocated/staggered version of the Fast Vector Penalty-Projection method for dilatable fluids
[Une version hybride colocalisée/décalée de la méthode Fast Vector Penalty-Projection pour les fluides dilatables]

Présenté par : Olivier Pironneau

Michel Belliard1
1 Commissariat à l'énergie atomique et aux énergies alternatives (CEA), DEN/DANS/DM2S/STMF/LMEC, CEA Cadarache, bât. 238, 13108 Saint-Paul-lez-Durance, France
Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 761-766.

On propose une version hybride de la méthode Fast-VPP en écoulement dilatable : variables colocalisées et projection décalée. On précise les conditions nécessaires à son application efficace. Des résultats numériques illustrent le gain en effort de calcul pour l'obtention de régimes stationnaires.

We propose a hybrid version of the Fast VPP method for dilatable fluids: collocated variables/staggered projection. The necessary conditions for its effective application are outlined. Numerical results illustrate the significant computation-cost reduction to reach stationary regimes.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.05.004
Michel Belliard 1

1 Commissariat à l'énergie atomique et aux énergies alternatives (CEA), DEN/DANS/DM2S/STMF/LMEC, CEA Cadarache, bât. 238, 13108 Saint-Paul-lez-Durance, France 
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     title = {A hybrid collocated/staggered version of the {Fast} {Vector} {Penalty-Projection} method for dilatable fluids},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {761--766},
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Michel Belliard. A hybrid collocated/staggered version of the Fast Vector Penalty-Projection method for dilatable fluids. Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 761-766. doi : 10.1016/j.crma.2014.05.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.05.004/

[1] P. Angot; J.-P. Caltagirone; P. Fabrie Vector Penalty-Projection methods for the solution of unsteady incompressible flows, Aussois, France, Wiley (8–13 June 2008), pp. 169-176

[2] P. Angot; J.-P. Caltagirone; P. Fabrie A spectacular Vector Penalty-Projection method for Darcy and Navier–Stokes problems, Prague, Czech Republic (1–23 July 2011)

[3] A.J. Chorin A numerical method for solving incompressible viscous flow problems, J. Comput. Phys., Volume 2 (1967), pp. 12-26

[4] A.J. Chorin Numerical solution of the Navier–Stokes equations, Math. Comp., Volume 22 (1968), pp. 745-762

[5] S. Faure; J. Laminie; R. Temam Colocated finite volume schemes for fluid flows, Commun. Comput. Phys., Volume 4 (2008) no. 1, pp. 1-25

[6] M. Fortin; R. Glowinski Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, Studies in Mathematics and Its Applications, vol. 15, North-Holland, Amsterdam, 1983

[7] R. Temam Sur l'approximation de la solution des équations de Navier–Stokes par la méthode des pas fractionnaires, Arch. Ration. Mech. Anal., Volume 32 (1969), pp. 135-153

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