Comptes Rendus
Numerical Analysis
A projection algorithm for fluid–structure interaction problems with strong added-mass effect
[Un algorithme de projection pour des problèmes d'interaction fluide–structure avec fort effet de masse ajoutée]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 4, pp. 279-284.

Dans cette Note nous introduisons un schéma semi-implicite pour des problèmes d'interaction fluide–structure avec un fort effet de masse-ajoutée. La méthode est basée sur un certain découplage de la masse ajoutée, des effets visqueux et des non linéarités géometriques et convectives. Ce découplage peut être obtenu par une méthode de projection type Chorin–Temam. Nous énonçons un résultat de stabilité dans un cadre linéaire, et nous présentons quelques simulations numériques. Le principal intérêt de l'algorithme proposé est son efficacité par rapport aux approches implicites.

This Note aims at introducing a semi-implicit coupling scheme for fluid–structure interaction problems with a strong added-mass effect. Our main idea relies on the splitting of added-mass, viscous effects and geometrical/convective non-linearities, through a Chorin–Temam projection scheme within the fluid. We state some theoretical stability results, in the linear case, and provide some numerical experiments. The main interest of the proposed scheme is its efficiency compared to the implicit approach.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.12.017

Miguel A. Fernández 1 ; Jean-Frédéric Gerbeau 1 ; Céline Grandmont 1

1 INRIA, REO team, Rocquencourt, B.P. 105, 78153 Le Chesnay cedex, France
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Miguel A. Fernández; Jean-Frédéric Gerbeau; Céline Grandmont. A projection algorithm for fluid–structure interaction problems with strong added-mass effect. Comptes Rendus. Mathématique, Volume 342 (2006) no. 4, pp. 279-284. doi : 10.1016/j.crma.2005.12.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.017/

[1] P. Causin; J.-F. Gerbeau; F. Nobile Added-mass effect in the design of partitioned algorithms for fluid–structure problems, Comput. Methods Appl. Mech. Engrg., Volume 194 (2005) no. 42–44, pp. 4506-4527

[2] S. Deparis, M. Discacciati, G. Fourestey, A. Quarteroni, Heterogeneous domain decomposition methods for fluid–structure interaction problems, Technical report, EPFL-IACS report 08.2005, 2005

[3] C. Farhat, K. van der Zee, Ph. Geuzaine, Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear aeroelasticity, Comput. Methods Appl. Mech. Engrg., in press

[4] M.A. Fernández, J.-F. Gerbeau, C. Grandmont, A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid, Technical Report 5700, INRIA, 2005, Int. J. Numer. Methods Engrg., submitted for publication

[5] M.A. Fernández; M. Moubachir A Newton method using exact Jacobians for solving fluid–structure coupling, Comput. & Structures, Volume 83 (2005), pp. 127-142

[6] J.-F. Gerbeau; M. Vidrascu A quasi-Newton algorithm based on a reduced model for fluid–structure interactions problems in blood flows, Math. Model. Numer. Anal., Volume 37 (2003) no. 4, pp. 631-648

[7] C. Grandmont; V. Guimet; Y. Maday Numerical analysis of some decoupling techniques for the approximation of the unsteady fluid structure interaction, Math. Models Methods Appl. Sci., Volume 11 (2001) no. 8, pp. 1349-1377

[8] J.-L. Guermond, P. Minev, J. Shen, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., submitted for publication

[9] P. Le Tallec; J. Mouro Fluid structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., Volume 190 (2001), pp. 3039-3067

[10] H.G. Matthies; J. Steindorf Partitioned strong coupling algorithms for fluid–structure interaction, Comput. & Structures, Volume 81 (2003), pp. 805-812

[11] D.P. Mok, W.A. Wall, E. Ramm, Partitioned analysis approach for the transient, coupled response of viscous fluids and flexible structures, in: W. Wunderlich (Ed.), Proceedings of the European Conference on Computational Mechanics, ECCM'99, TU Munich, 1999

[12] F. Nobile, Numerical approximation of fluid–structure interaction problems with application to haemodynamics, PhD thesis, EPFL, Switzerland, 2001

Cité par Sources :

This work has been carried out during a one-year délégation of C. Grandmont at INRIA, and partially supported by the European Community through the Research Training Network “Mathematical Modelling of the Cardiovascular System (HaeMOdel)”, contract HPRN-CT-2002-00270.

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