zbMATH — the first resource for mathematics

Added-mass effect in the design of partitioned algorithms for fluid–structure problems. (English) Zbl 1101.74027
This is a mathematical contribution to explain the numerical instabilities encountered under certain combinations of physical parameters in the simulation of fluid-structure interaction when using loosely coupled time-advancing schemes. The authors also show, in the case of strongly coupled scheme, how the same combination of parameter leads to problems that demand a greater computational effort to be solved. The authors develop such a study to find some applications to blood flows in arteries. To carry out the mathematical analysis, they consider a simplified model representing the interaction between a potential flow and a linearly elastic tube. Despite its simplicity, this model reproduces propagation phenomena and takes into account the added mass effect of the fluid on the structure.

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Z05 Physiological flows
92C10 Biomechanics
Full Text: DOI
[1] Bjorstad, P.E.; Widlund, O.B., Iterative methods for the solution of elliptic problems on regions partitioned in subdomains, SIAM J. numer. anal., 31, 23, 1097-1120, (1986) · Zbl 0615.65113
[2] Brenner, S., The condition number of the Schur complement in domain decomposition, Numer. math., 83, 2, 187-203, (1999) · Zbl 0936.65141
[3] H. Brezis, Analyse fonctionnelle, Théorie et applications, Masson, 1983. · Zbl 0511.46001
[4] Farhat, C.; Lesoinne, M.; Le Tallec, P., Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation optimal discretization and application to aeroelasticity, Comput. methods appl. mech. engrg., 157, 95-114, (1998) · Zbl 0951.74015
[5] C. Farhat, K. van der Zee, Ph. Geuzaine. Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear aeroelasticity, Comput. Methods Appl. Mech. Engrg., in press. · Zbl 1178.76259
[6] Formaggia, L.; Gerbeau, J.-F.; Nobile, F.; Quarteroni, A., On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels, Comput. methods appl. mech. engrg., 191, 6-7, 561-582, (2001) · Zbl 1007.74035
[7] Gerbeau, J.F.; Vidrascu, M., A quasi-Newton algorithm based on a reduced model for fluid-structure interactions problems in blood flows, Math. model. numer. anal., 37, 4, 631-648, (2003) · Zbl 1070.74047
[8] Holmes, M.H., A spectral problem in hydroelasticity, J. differ. equat., 32, 3, 388-397, (1979) · Zbl 0404.35078
[9] Le Tallec, P., Introduction à la dynamique des structures, Ellipses, (2000) · Zbl 1050.76049
[10] Le Tallec, P.; Mouro, J., Fluid structure interaction with large structural displacements, Comput. methods appl. mech. engrg., 190, 3039-3067, (2001) · Zbl 1001.74040
[11] Matthies, H.G.; Steindorf, J., Partitioned but strongly coupled iteration schemes for nonlinear fluid-structure interaction, Comput. struct., 80, 27-30, 1991-1999, (2002) · Zbl 1312.74009
[12] Nichols, W.; O’Rourke, M.F., Mcdonald’s blood flow in arteries. theoretical, experimental, and clinical principles, (1997), Oxford University Press
[13] Mok, D.P.; Wall, W.A.; Ramm, E., Accelerated iterative substructuring schemes for instationary fluid-structure interaction, (), 1325-1328
[14] H. Morand, R. Ohayon, Interactions fluides-structures, vol. 23 of Recherches en Mathématiques Appliquées, Masson, Paris, 1992. · Zbl 0754.73071
[15] Morand, H.; Ohayon, R., Fluid-structure interaction: applied numerical methods, (1995), John Wiley and Sons
[16] J. Mouro, Interactions fluide structure en grands déplacements, Résolution numérique et application aux composants hydrauliques automobiles, Ph.D. thesis, Ecole Polytechnique, France, 1996.
[17] F. Nobile, Numerical approximation of fluid-structure interaction problems with application to haemodynamics, Ph.D. thesis, EPFL, Switzerland, 2001.
[18] Piperno, S.; Farhat, C.; Larrouturou, B., Partitioned procedures for the transient solution of coupled aeroelastic problems. part I: model problem, theory and two-dimensional application, Comput. methods appl. mech. engrg., 124, 79-112, (1995) · Zbl 1067.74521
[19] A. Quarteroni, A. Valli, Domain decomposition methods for partial differential equations, Numerical Mathematics and Scientific Computation, The Clarendon Press, Oxford University Press, 1999, Oxford Science Publications. · Zbl 0931.65118
[20] Rugonyi, S.; Bathe, K.J., On finite element analysis of fluid flows coupled with structural interaction, CMES—comput. model engrg. sci., 2, 2, 195-212, (2001)
[21] Stein, K.; Benney, R.; Kalro, V.; Tezduyar, T.E.; Leonard, J.; Accorsi, M., Parachute fluid-structure interactions: 3-D computation, Comput. methods appl. mech. engrg., 190, 3-4, 373-386, (2000) · Zbl 0973.76055
[22] Zhang, H.; Zhang, X.; Ji, S.; Guo, Y.; Ledezma, G.; Elabbasi, N.; deCougny, H., Recent development of fluid-structure interaction capabilities in the adina system, Comput. struct., 81, 8-11, 1071-1085, (2003)
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.