Comptes Rendus
Modified fixed point algorithm in fluid–structure interaction
Comptes Rendus. Mécanique, Volume 331 (2003) no. 8, pp. 525-530.

In this work, we address the numerical solution of some non-linear problems arising in the time discretization of fluid–structure interaction problems with fully implicit schemes. At each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. We propose a modified fixed-point algorithm which combines the Block-Gauss–Seidel iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard method.

Dans cette Note on s'intéresse à la résolution numérique des problèmes non-linéaires issus de la discrétisation en temps, avec des schémas implicites, de problèmes d'interaction fluide–structure. A chaque pas de temps, on doit résoudre un système couplé fortement non-linéaire, car le domaine fluide dépend de l'inconnue associée au déplacement de la structure. Nous proposons un algorithme de point fixe modifié qui combine des itérations Block-Gauss–Seidel avec une formulation de type transpiration. Des expériences numériques mettent en évidence le gain en temps de calcul par rapport à la méthode standard.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00119-0
Keywords: Computational fluid mechanics, Fluid–structure interaction, Block-Gauss–Seidel iterations, Transpiration, Highly coupled non-linear problems, Weak and strong coupling algorithms, Partitioned procedures
Mot clés : Mécanique des fluides numérique, Interaction fluide–structure, Itérations de Gauss–Seidel, Transpiration, Problémes couplès hautements non-linéaires, Algorithmes de couplage faible et fort, Méthode à partion

Simone Deparis 1; Miguel Ángel Fernández 1; Luca Formaggia 2; Fabio Nobile 3

1 École polytechnique fédérale de Lausanne, IACS, 1015 Lausanne, Switzerland
2 Politecnico di Milano, MOX, Piazza L. da Vinci 32, 20133 Milano, Italy
3 CES, The University of Texas at Austin, Austin, TX 78712, USA
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Simone Deparis; Miguel Ángel Fernández; Luca Formaggia; Fabio Nobile. Modified fixed point algorithm in fluid–structure interaction. Comptes Rendus. Mécanique, Volume 331 (2003) no. 8, pp. 525-530. doi : 10.1016/S1631-0721(03)00119-0. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00119-0/

[1] Z. Belhachmi, C. Bernardi, S. Deparis, Weighted Clément operator and application to the finite element discretisation of the axisymmetric Stokes problem, In preparation

[2] R. Codina; M. Cervera Block iterative algorithms for non-linear coupled problems, Advanced Computational Methods in Structural Mechanics, CIMNE, Barcelona, 1996

[3] S. Deparis, M.A. Fernández, L. Formaggia, Acceleration of a fixed point algorithm for fluid–structure interaction using transpiration conditions, Accepted for printing in M2AN

[4] T. Fanion; M.A. Fernández; P. Le Tallec Deriving adequate formulations for fluide structure interaction problems: from ALE to transpiration, Rév. Européenne Élém. Finis, Volume 9 (2000) no. 6–7, pp. 681-708

[5] M.A. Fernández, Modèles simplifiés d'interaction fluide–structure, PhD thesis, University of Paris IX, France, 2001

[6] P. Le Tallec; J. Mouro Fluid structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., Volume 190 (2001) no. 24–25, pp. 3039-3067

[7] G. Medic, Étude mathématique des modèles aux tensions de Reynolds et simulation numérique d'écoulements turbulents sur parois fixes et mobiles, PhD thesis, University of Paris VI, France, 1999

[8] F. Nobile, Numerical approximation of fluid–structure interaction problems with application to haemodynamics, PhD thesis n. 2458, École Polytechnique Fédérale de Lausanne, Switzerland, 2001

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