no. 3-4
Numerical Analysis/Mathematical Problems in Mechanics
A fully decoupled scheme for the interaction of a thin-walled structure with an incompressible fluid
[Un schéma totalement découplé pour lʼinteraction dʼune structure mince avec un fluide incompressible]

Présenté par : the Editorial Board

Fernández, Miguel Ángel1, 2 ; Landajuela, Mikel1, 2
1 Inria, REO team, Rocquencourt, BP 105, 78153 Le Chesnay cedex, France
2 Université Pierre-et-Marie-Curie (Paris-6), REO team, laboratoire Jacques-Louis-Lions, UMR 7598, 4, place Jussieu, 75252 Paris cedex 05, France
Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 161-164.

Dans cette note, nous proposons un type de schéma totalement découplé (vitesse–pression–déplacement) pour le couplage dʼun fluide incompressible avec une structure mince. Le découplage en temps est obtenu en combinant un schéma à pas fractionnaire sur lʼensemble du système avec un traitement spécifique Robin–Neumann des conditions dʼinterface. Les deux variantes considérées sont inconditionnellement stables. Des expériences numériques montrent que, pour lʼune dʼelles, on obtient un taux de convergence optimal.

In this note we propose a class of fully decoupled schemes (velocity–pressure–displacement splitting) for the coupling of an incompressible fluid with a thin-walled structure. The time splitting is achieved by combining an overall fractional-step time-marching of the system with a specific Robin–Neumann treatment of the interface coupling. The two variants considered yield unconditional stability. Numerical experiments in a benchmark show that, for one of them, the splitting does not compromises the optimal convergence rate.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.015
Fernández, Miguel Ángel 1, 2 ; Landajuela, Mikel 1, 2

1 Inria, REO team, Rocquencourt, BP 105, 78153 Le Chesnay cedex, France
2 Université Pierre-et-Marie-Curie (Paris-6), REO team, laboratoire Jacques-Louis-Lions, UMR 7598, 4, place Jussieu, 75252 Paris cedex 05, France 
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Fernández, Miguel Ángel; Landajuela, Mikel. A fully decoupled scheme for the interaction of a thin-walled structure with an incompressible fluid. Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 161-164. doi : 10.1016/j.crma.2013.02.015. http://www.numdam.org/articles/10.1016/j.crma.2013.02.015/

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☆ This work has been supported by the French National Research Agency (ANR) through the EXIFSI project (ANR-12-JS01-0004).