Comptes Rendus
no. 17-18
Numerical Analysis/Mathematical Problems in Mechanics
Displacement-velocity correction schemes for incompressible fluid–structure interaction
[Schémas de correction de déplacement-vitesse en interaction fluide–une structure incompressible]

Présenté par : Olivier Pironneau

Miguel A. Fernández1 ; Jimmy Mullaert1
1 INRIA, Rocquencourt BP 105, 78153 Le Chesnay cedex, France
Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 1011-1015.

Nous proposons une nouvelle classe de schémas de couplage explicite pour lʼinteraction entre un fluide incompressible et une structure élastique dans le cas où la structure nʼest pas nécessairement mince. On énonce un résultat de stabilité général pour ces nouveaux schémas et on analyse numériquement leur précision.

We propose a new class of time-marching schemes for the explicit coupling of an incompressible fluid and an elastic solid (not necessarily thin). We state a general energy-based stability result and illustrate the accuracy of the different variants in a numerical benchmark.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.08.004
Miguel A. Fernández 1 ; Jimmy Mullaert 1

1 INRIA, Rocquencourt BP 105, 78153 Le Chesnay cedex, France 
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     author = {Miguel A. Fern\'andez and Jimmy Mullaert},
     title = {Displacement-velocity correction schemes for incompressible fluid{\textendash}structure interaction},
     journal = {Comptes Rendus. Math\'ematique},
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     language = {en},
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Miguel A. Fernández; Jimmy Mullaert. Displacement-velocity correction schemes for incompressible fluid–structure interaction. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 1011-1015. doi : 10.1016/j.crma.2011.08.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.004/

[1] S. Badia; F. Nobile; C. Vergara Fluid–structure partitioned procedures based on Robin transmission conditions, J. Comp. Phys., Volume 227 (2008), pp. 7027-7051

[2] E. Burman; M. Fernández Galerkin finite element methods with symmetric pressure stabilization for the transient Stokes equations: stability and convergence analysis, SIAM J. Numer. Anal., Volume 47 (2008/09) no. 1, pp. 409-439

[3] E. Burman; M. Fernández Stabilization of explicit coupling in fluid–structure interaction involving fluid incompressibility, Comput. Methods Appl. Mech. Engrg., Volume 198 (2009) no. 5–8, pp. 766-784

[4] M. Fernández Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid, C. R. Acad. Sci. Paris, Ser. I, Volume 349 (2011) no. 7–8, pp. 473-477

[5] M. Fernández; J.-F. Gerbeau Algorithms for fluid–structure interaction problems, Cardiovascular Mathematics, MS&A. Model. Simul. Appl., vol. 1, Springer, 2009, pp. 307-346

[6] M. Fernández, J. Mullaert, Displacement-velocity correction schemes for incompressible fluid–structure interaction: Stability analysis and numerics, in preparation.

[7] G. Guidoboni; R. Glowinski; N. Cavallini; S. Canic Stable loosely-coupled-type algorithm for fluid–structure interaction in blood flow, J. Comp. Phys., Volume 228 (2009) no. 18, pp. 6916-6937

[8] T. Hughes The Finite Element Method, Prentice Hall, 1987

[9] O. Pironneau; F. Hecht; A. Le Hyaric; J. Morice Freefem++ www.freefem.org/ff++

[10] V. Thomée Galerkin Finite Element Methods for Parabolic Problems, Springer, 2006

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