Numerical Analysis/Mathematical Problems in Mechanics
Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid
[Schémas avec correction de déplacement incrémentale pour le couplage explicite dʼune structure mince et dʼun fluide incompressible]
Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 473-477.

Dans cette Note nous proposons deux schémas avec correction de déplacement incrémentale pour le couplage explicite dʼune structure mince et dʼun fluide incompressible. La stabilité et la précision supérieure de ces schémas (par rapport à la variante originale non-incrémentale) sont analysées théoriquement et puis confirmées numériquement.

In this Note we propose two incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid. The stability and the superior accuracy of these schemes (with respect to the original non-incremental variant) are theoretically analyzed and then numerically confirmed in a benchmark.

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Accepté le :
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DOI : 10.1016/j.crma.2011.03.001
Fernández, Miguel A. 1

1 INRIA, CRI Paris-Rocquencourt, Rocquencourt BP 105, 78153 Le Chesnay cedex, France
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Fernández, Miguel A. Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid. Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 473-477. doi : 10.1016/j.crma.2011.03.001. http://www.numdam.org/articles/10.1016/j.crma.2011.03.001/

[1] Burman, E.; Fernández, M.A. 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

[2] Causin, P.; Gerbeau, J.-F.; Nobile, F. 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

[3] Chapelle, D.; Bathe, K.J. The Finite Element Analysis of Shells – Fundamentals, Springer, 2011

[4] M.A. Fernández, Incremental displacement-correction schemes for incompressible fluid-structure interaction: stability and convergence analysis, in preparation.

[5] Cardiovascular Mathematics. Modeling and Simulation of the Circulatory System (Formaggia, L.; Quarteroni, A.; Veneziani, A., eds.), Modeling, Simulation and Applications, vol. 1, Springer, 2009

[6] Guermond, J.L.; Minev, P.; Shen, J. An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., Volume 195 (2006) no. 44–47, pp. 6011-6045

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

[8] Pironneau, O.; Hecht, F.; Le Hyaric, A.; Morice, J. http://www.freefem.org/ff++ (Freefem++)

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