zbMATH — the first resource for mathematics

Fluid-structure interaction with large structural displacements. (English) Zbl 1001.74040
Calculations of viscous flows inside deformable structures can meet with difficulties when imposing kinematic compatibility conditions at the fluid-structure interface and updating the geometry of domain. Here the authors propose how to overcome these problems by considering fluid and structure as a common continuous medium in a fixed reference configuration. Then the resulting problem is split into a fluid and a structural part through an additive decomposition of the space of kinematically admissible test functions. The approach treats the structure in a fully Lagrangian way, and an associated arbitrary Lagrangian-Eulerian formulation is applied to the fluid. The method has been implemented into an industrial CFD code, and some results on the simulation of industrial hydraulic shock absorbers are presented at the end of the paper.

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
Full Text: DOI
[1] J.T. Batina, Unsteady Euler airfoil solutions using unstructured dynamic meshes, in: AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, 1989
[2] Carrive-Bedouani, M.; LeTallec, P.; Mouro, J., Approximations par eléments finis d’un modèle de coques minces géométriquement exact, Revue européenne des eléments finis, 4, 5-6, 633-662, (1995) · Zbl 0924.73267
[3] M.A. Crisfield, Nonlinear Finite Element Analysis of Solids and Structures, Wiley, Chichester, New York, Brisbane, Toronto, Singapore, 1990 · Zbl 0855.73001
[4] R. Dautray, J.L. Lions, Analyse Matheématique et Calcul Numérique pour les Science et les Techniques, Collection du Commissariat á I’ Energie Atomique, Masson, Paris, 1984
[5] G. Dhatt, An efficient triangular shell element, AIAA J. 8 (11) (1970); vol. 1, 36 p
[6] C. Farhat, B. Koobus, M. Lesoinne, A high fidelity and high performance computational methodology for the solution of viscous aeroelastic response problems, in: Proceedings of the First AFOSR Conference on Dynamic Motion CFD, Rutgers, 3-5 June, pp. 159-187
[7] C. Farhat, M. Lesoinne, P. LeTallec, Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation. Optimal discretisation and application to aeroelasticity, Comput. Methods Appl. Mech. Engrg. 157 (1-2) (1998) 95-114 · Zbl 0951.74015
[8] Lesoinne, M.; Farhat, C., Geometric conservation laws for flow problems with moving boundaries and deformable meshes and their impact on aeroelastic computations, Comput. methods appl. mech. engrg., 134, 71-90, (1996) · Zbl 0896.76044
[9] W. Brandstatter, FIRE, User’s manual, Ed. by AVL-GmbH, 1994
[10] Le Tallec, P., Numerical methods for nonlinear three-dimensional elasticity, Handbook of numerical analysis, 3, (1994) · Zbl 0875.73234
[11] P. LeTallec, Domain decomposition methods in computational mechanics. Comput. Mech. Adv. 1-2 (1994) 121-220
[12] P. Le Tallec, F. Mallinger, Adaptive multimodel domain decomposition in fluid mechanics, in: Proceedings of the Eigth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Beijing, May 1995, Wiley, New York
[13] P. LeTallec, S. Mani, Analyse Numérique d’un modèle de coques minces de Koiter discrétisé en base cartésienne, M2AN, 1997, to appear
[14] A. Marrocco, Simulations numériques dans la fabrication des circuits à semiconducteurs (Process Modelling), Rapport de Recherche INRIA 305, 1984
[15] J. Mouro, Interactions fluide structure en grands déplacements. Résolution numérique et application aux composants hydrauliques automobiles, Thèse de l’Ecole Polytechnique, 1996
[16] N’konga, B.; Guillard, H., Godunov type method on non-structured meshes for three dimensional moving boundary problems, Comput. methods appl. mech. engrg., 113, 183-204, (1994) · Zbl 0846.76060
[17] S. Piperno, Simulation numérique de phénomènes d’interaction fluide structure, Thèse de l’Ecole Nationale des Ponts et Chaussées 30 juin 1995
[18] Marini, L.D.; Quarteroni, A., A relaxation procedure for domain decomposition methods using finite elements, Numer. math., 55, 575-598, (1989) · Zbl 0661.65111
[19] A. Quarteroni, Domain Decomposition Method for the Numerical Solution of Partial Differential Equations, Technical report UMSI90/246, Supercomputer Institute, University of Minnesota, 1990
[20] A. Quarteroni, G. SacchiLandriani, A. Valli, Coupling of Viscous and Inviscid Stokes Equations via a Domain Decomposition Method for Finite Elements, Technical report UTM89-287, Dipartimento di Mathematica, Universita degli Studi di Trento, 1989
[21] Riks, E., An incremental approach to the solution of snapping and buckling problems, Int. J. solids struct., 15, 529-551, (1979) · Zbl 0408.73040
[22] A.B. Sabir, A.C. Lock, The application of finite elements to the large deflexion geometrically nonlinear behaviour of cylindrical shells, in: C.A. Brebbia, H. Tottenham (Eds.), Variational Methods in Engineering, Southampton University Press, 1973, pp. 7/66-7/75 · Zbl 0308.73042
[23] J.C. Simo, D.D. Fox, M.S. Rifai, On a stress resultant geometrically exact shell model part I formulation and optimal parametrization, Comput. Methods Appl. Mech. Engrg. 72 (1989) 267-304 · Zbl 0692.73062
[24] J.C. Simo, D.D. Fox, M.S. Rifai, On a stress resultant geometrically exact shell model part III: Computational aspects of the nonlinear theory, Comput. Methods Appl. Mech. Engrg. 79 (1990) 21-70 · Zbl 0746.73015
[25] Stein, E.; Ohnimus, S., Dimensional adaptivity in linear elasticity with hierarchical test space for h- and p-refinement processes, Eng. comput., 12, 107-119, (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.