A fully decoupled scheme for the interaction of a thin-walled structure with an incompressible fluid

Miguel Ángel Fernández; Mikel Landajuela

doi:10.1016/j.crma.2013.02.015

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

Miguel Ángel Fernández ^1,² ; Mikel Landajuela ^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

Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 161-164.

Résumé
Abstract

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 : 2013-02-05
Accepté le : 2013-02-28
Publié le : 2013-02-01

DOI : 10.1016/j.crma.2013.02.015

Affiliations des auteurs :

Miguel Ángel Fernández ^{1, 2} ; Mikel Landajuela ^{1, 2}

@article{CRMATH_2013__351_3-4_161_0,
     author = {Miguel \'Angel Fern\'andez and Mikel Landajuela},
     title = {A fully decoupled scheme for the interaction of a thin-walled structure with an incompressible fluid},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {161--164},
     publisher = {Elsevier},
     volume = {351},
     number = {3-4},
     year = {2013},
     doi = {10.1016/j.crma.2013.02.015},
     language = {en},
}

TY  - JOUR
AU  - Miguel Ángel Fernández
AU  - Mikel Landajuela
TI  - A fully decoupled scheme for the interaction of a thin-walled structure with an incompressible fluid
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 161
EP  - 164
VL  - 351
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2013.02.015
LA  - en
ID  - CRMATH_2013__351_3-4_161_0
ER  -

%0 Journal Article
%A Miguel Ángel Fernández
%A Mikel Landajuela
%T A fully decoupled scheme for the interaction of a thin-walled structure with an incompressible fluid
%J Comptes Rendus. Mathématique
%D 2013
%P 161-164
%V 351
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2013.02.015
%G en
%F CRMATH_2013__351_3-4_161_0

Miguel Ángel Fernández; Mikel Landajuela. A fully decoupled scheme for the interaction of a thin-walled structure with an incompressible fluid. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 161-164. doi : 10.1016/j.crma.2013.02.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.015/

Bibliographie
Cité par

[1] S. Badia; A. Quaini; A. Quarteroni Splitting methods based on algebraic factorization for fluid–structure interaction, SIAM J. Sci. Comput., Volume 30 (2008) no. 4, pp. 1778-1805

[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] M.A. Fernández Incremental displacement-correction schemes for incompressible fluid–structure interaction: stability and convergence analysis, Numer. Math., Volume 123 (2013) no. 1, pp. 21-65

[4] 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. Methods Engrg., Volume 69 (2007) no. 4, pp. 794-821

[5] M.A. Fernández, M. Landajuela, Fractional-step time-marching schemes for the coupling of incompressible fluids with thin-walled structures, in preparation.

[6] M.A. Fernández, J. Mullaert, M. Vidrascu, Explicit Robin–Neumann schemes for the coupling of incompressible fluids with thin-walled structures, Research Report RR-8224, Inria, February 2013.

[7] 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

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

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

[10] 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

Cité par Sources :

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

Commentaires - Politique