Comptes Rendus
no. 1-2
Numerical Analysis
An added-mass free semi-implicit coupling scheme for fluid–structure interaction
[Couplage semi-implicite en interaction fluide–structure insensible aux effets de masse-ajoutée]

Présenté par : Olivier Pironneau

Matteo Astorino1 ; Franz Chouly1 ; Miguel A. Fernández1
1 INRIA, REO team, Rocquencourt, BP 105, 78153 Le Chesnay cedex, France
Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 99-104.

Dans cette Note, nous proposons un schéma de couplage semi-implicite pour la simulation numérique de phénomènes d'interaction fluide–structure dans lesquels le fluide est incompressible. Le schéma est stable indépendamment des effets de masse-ajoutée et permet l'utilisation de schémas conservatifs pour la structure. L'efficacité du schéma provient du traitement explicite des effets visqueux et des non-linéarités dues à la convection et à la géométrie, grâce à un schéma de projection de Chorin–Temam pour le fluide. D'autre part, la stabilité du schéma s'appuie sur le traitement implicite des efforts de pression et sur le couplage visqueux faible, effectué avec la méthode de Nitsche.

In this Note we propose a semi-implicit coupling scheme for the numerical simulation of fluid–structure interaction systems involving a viscous incompressible fluid. The scheme is stable irrespectively of the so-called added-mass effect and allows for conservative time-stepping within the structure. The efficiency of the scheme is based on the explicit splitting of the viscous effects and geometrical/convective non-linearities, through the use of the Chorin–Temam projection scheme within the fluid. Stability relies on the implicit treatment of the pressure stresses and on the Nitsche's treatment of the viscous coupling.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.11.003
Matteo Astorino 1 ; Franz Chouly 1 ; Miguel A. Fernández 1

1 INRIA, REO team, Rocquencourt, BP 105, 78153 Le Chesnay cedex, France 
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     journal = {Comptes Rendus. Math\'ematique},
     pages = {99--104},
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     volume = {347},
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     year = {2009},
     doi = {10.1016/j.crma.2008.11.003},
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Matteo Astorino; Franz Chouly; Miguel A. Fernández. An added-mass free semi-implicit coupling scheme for fluid–structure interaction. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 99-104. doi : 10.1016/j.crma.2008.11.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.003/

[1] M. Astorino, F. Chouly, M.A. Fernández, An added-mass free semi-implicit coupling scheme in fluid–structure interaction: numerical analysis and applications, in preparation

[2] R. Becker; P. Hansbo; R. Stenberg A finite element method for domain decomposition with non-matching grids, M2AN Math. Model. Numer. Anal., Volume 37 (2003) no. 2, pp. 209-225

[3] E. Burman; M.A. Fernández Stabilized explicit coupling for fluid–structure interaction using Nitsche's method, C. R. Math. Acad. Sci. Paris, Volume 345 (2007) no. 8, pp. 467-472

[4] E. Burman, M.A. Fernández, Stabilization of explicit coupling in fluid–structure interaction involving fluid incompressibility, INRIA Research Report RR-6445, 2008, Comput. Methods Appl. Mech. Engrg., , | DOI

[5] 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

[6] M.A. Fernández; J.F. Gerbeau; C. Grandmont A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid, Int. J. Numer. Meth. Engrg., Volume 69 (2007) no. 4, pp. 794-821

[7] (L. Formaggia; A. Quarteroni; A. Veneziani, eds.), Cardiovascular Mathematics, vol. 1, Springer-Verlag, 2009 (Chapter 9: Algorithms for fluid–structure interaction problems. Modeling, Simulation and Applications)

[8] F. Hecht, O. Pironneau, A. Le Hyaric, K. Ohtsuka, FreeFem++ v. 2.11. User's Manual, University of Paris 6

[9] A. Quaini; A. Quarteroni A semi-implicit approach for fluid–structure interaction based on an algebraic fractional step method, Math. Models Methods Appl. Sci., Volume 17 (2007) no. 6, pp. 957-983

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