Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid

Miguel A. Fernández

doi:10.1016/j.crma.2011.03.001

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]

Présenté par : the Editorial Board

Miguel A. Fernández ¹

¹ INRIA, CRI Paris-Rocquencourt, Rocquencourt BP 105, 78153 Le Chesnay cedex, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 473-477.

Résumé
Abstract

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.

Reçu le : 2010-12-02
Accepté le : 2011-03-01
Publié le : 2011-03-16

DOI : 10.1016/j.crma.2011.03.001

Affiliations des auteurs :

Miguel A. Fernández ¹

¹ INRIA, CRI Paris-Rocquencourt, Rocquencourt BP 105, 78153 Le Chesnay cedex, France

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Miguel A. Fernández. Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 473-477. doi : 10.1016/j.crma.2011.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.001/

Bibliographie
Cité par

[1] E. Burman; M.A. 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

[2] 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

[3] D. Chapelle; K.J. Bathe 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 (L. Formaggia; A. Quarteroni; A. Veneziani, eds.), Modeling, Simulation and Applications, vol. 1, Springer, 2009

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

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

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Miguel A. Fernández Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit, SeMA Journal, Volume 55 (2011) no. 1, p. 59 | DOI:10.1007/bf03322593

Cité par 19 documents. Sources : Crossref, zbMATH

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