The present article deals with the simulation of fluid structure interaction problems in large deformation, and discusses two aspects of their numerical solution: (i) the derivation of energy conserving time integration schemes in presence of fluid structure coupling, moving grids, and nonlinear kinematic constraints such as incompressibility and contact, (ii) the introduction of adequate preconditioners efficiently chaining local fluid and structure solvers. Solutions are proposed, analyzed and tested using nonlinear energy correcting terms, and added mass based Dirichlet Neumann preconditioners. Numerical applications include nonlinear impact problems in elastodynamics and blood flows predictions within flexible arteries.
Du fait des fortes nonlinéarités du problème posé, la simulation de phénomènes d'interaction fluide structure en grands déplacements et vitesses modérées conduit à plusieurs difficultés numériques : respect numérique des mécanismes de conservation d'énergie dans le traitement des grilles mobiles, des forces de raideur, de la synchronisation des forces de contact et d'interface d'une part, construction de préconditionneurs adaptés permettant l'utilisation efficace d'algorithmes de couplage résolvant de manière successive et découplée les parties fluide et structure, d'autre part.
Mots-clés : Mécanique des fluides numérique, Élastodynamique nonlinéaire, Intégration en temps, Conservation de l'énergie, Interaction fluide structure, Masse ajoutée, Préconditionneur
Patrick Le Tallec 1; Jean-Frédéric Gerbeau 2; Patrice Hauret 3; Marina Vidrascu 2
@article{CRMECA_2005__333_12_910_0,
author = {Patrick Le Tallec and Jean-Fr\'ed\'eric Gerbeau and Patrice Hauret and Marina Vidrascu},
title = {Fluid structure interaction problems in large deformation},
journal = {Comptes Rendus. M\'ecanique},
pages = {910--922},
publisher = {Elsevier},
volume = {333},
number = {12},
year = {2005},
doi = {10.1016/j.crme.2005.10.009},
language = {en},
}
TY - JOUR AU - Patrick Le Tallec AU - Jean-Frédéric Gerbeau AU - Patrice Hauret AU - Marina Vidrascu TI - Fluid structure interaction problems in large deformation JO - Comptes Rendus. Mécanique PY - 2005 SP - 910 EP - 922 VL - 333 IS - 12 PB - Elsevier DO - 10.1016/j.crme.2005.10.009 LA - en ID - CRMECA_2005__333_12_910_0 ER -
%0 Journal Article %A Patrick Le Tallec %A Jean-Frédéric Gerbeau %A Patrice Hauret %A Marina Vidrascu %T Fluid structure interaction problems in large deformation %J Comptes Rendus. Mécanique %D 2005 %P 910-922 %V 333 %N 12 %I Elsevier %R 10.1016/j.crme.2005.10.009 %G en %F CRMECA_2005__333_12_910_0
Patrick Le Tallec; Jean-Frédéric Gerbeau; Patrice Hauret; Marina Vidrascu. Fluid structure interaction problems in large deformation. Comptes Rendus. Mécanique, Fluid-solid interactions: modeling, simulation, bio-mechanical applications, Volume 333 (2005) no. 12, pp. 910-922. doi : 10.1016/j.crme.2005.10.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.10.009/
[1] Exact energy and momentum conserving algorithms for general models in nonlinear elasticity, Comput Methods Appl. Mech. Engrg., Volume 190 ( December 2000 ) no. 13–14, pp. 1763-1783
[2] Truncation error and energy conservation for fluid structure interactions, Comput. Methods Appl. Mech. Engrg., Volume 192 (2003) no. 43, pp. 4769-4804
[3] P. Le Tallec, S. Mani, Conservation laws for fluid structure interactions, in: T. Kvamsdal (Ed.), International Symposium on Computational Methods for Fluid Structure Interactions, Trondheim, 1999, pp. 61–78
[4] Mathematical Analysis and Numerical Methods for Science and Technology, Springer-Verlag, Berlin, 1990
[5] Fluides et Solides, Editions de l'Ecole Polytechnique, Palaiseau, 2001
[6] The discrete energy-momentum method. Conserving algorithms for non linear elastodynamics, Z. Angew. Math. Phys., Volume 43 (1992), pp. 757-792
[7] Energy conservation in fluid–structure interactions (P. Neittanmaki; Y. Kuznetsov; O. Pironneau, eds.), Numerical Methods for Scientific Computing, Variational Problems and Applications, CIMNE, Barcelona, 2003, pp. 94-107
[8] P. Hauret, Méthodes numériques pour la dynamique des structures nonlinéaires incompressibles à deux échelles, PhD thesis, Ecole Polytechnique, 2004
[9] Domain Decomposition Methods for Partial Differential Equations, Oxford Univ. Press, 1999
[10] Fluid structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., Volume 190 (2001) no. 24–25, pp. 3039-3068
[11] A quasi-newton algorithm based on a reduced model for fluid–structure interaction problems in blood flows, M2AN, Volume 37 (2003), pp. 663-680
[12] Finite Element Procedures in Engineering Analysis, Prentice-Hall, 1982
[13] Nonlinear Finite Element Analysis of Solids and Structures, vol. 2, Advanced Topics, Wiley, 1997
[14] Design of energy conserving algorithms for frictionless dynamic contact problems, Int. J. Numer. Methods Engrg., Volume 40 (1997), pp. 863-886
[15] Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems, Comput. Methods Appl. Mech. Engrg., Volume 158 (1998), pp. 269-300
[16] Improved implicit integrators for transient impact problems; geometric admissibility within the conserving framework, Int. J. Numer. Methods Engrg., Volume 53 ( January 2002 ) no. 2, pp. 245-274
[17] Iterative Methods for Sparse Linear Systems, PWS, 1996
Cited by Sources:
Comments - Policy