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An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems. (English) Zbl 1137.74439
Summary: This paper is concerned with the fully coupled (`monolithic’) solution of large-displacement fluid-structure interaction problems by Newton’s method. We show that block-triangular approximations of the Jacobian matrix, obtained by neglecting selected fluid--structure interaction blocks, provide good preconditioners for the solution of the linear systems with GMRES. We present an efficient approximate implementation of the preconditioners, based on a Schur complement approximation for the Navier-Stokes block and the use of multigrid approximations for the solution of the computationally most expensive operations. The performance of the the preconditioners is examined in representative steady and unsteady simulations which show that the GMRES iteration counts only display a mild dependence on the Reynolds number and the mesh size. The final part of the paper demonstrates the importance of consistent stabilisation for the accurate simulation of fluid-structure interaction problems.

MSC:
74S05Finite element methods in solid mechanics
74F10Fluid-solid interactions
76D05Navier-Stokes equations (fluid dynamics)
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[1] Farhat, C.; Lesoinne, M.: Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput. methods appl. Mech. engrg. 182, 499-515 (2000) · Zbl 0991.74069
[2] Stein, K.; Benney, R.; Tezduyar, T.; Potvin, J.: Fluid--structure interactions of a cross parachute: numerical simulation. Comput. methods appl. Mech. engrg. 191, 673-687 (2001) · Zbl 0999.76085
[3] Casadei, F.; Halleux, J. P.; Sala, A.; Chille, F.: Transient fluid--structure interaction algorithms for large industrial applications. Comput. methods appl. Mech. engrg. 190, 3081-3110 (2001) · Zbl 0998.74069
[4] Charvet, T.; Hauville, F.; Huberson, S.: Numerical simulation of the flow over sails in real sailing conditions. J. wind engrg. Indust. aerodynam. 63, 111-129 (1996)
[5] Heil, M.; Jensen, O. E.: Flows in deformable tubes and channels----theoretical models and biological applications. Flow in collapsible tubes and past other highly compliant boundaries, 15-50 (2003) · Zbl 1077.76075
[6] Hart, J. D.; Peters, G. W. M.; Schreurs, P. J. G.; Baaijens, F. P. T.: A three-dimensional computational analysis of fluid--structure interaction in the aortic valve. J. biomech. 36, 103-112 (2003)
[7] Ohayon, R.; Felippa, C.: Special issue: advances in computational methods for fluid--structure interaction and coupled problems. Comput. methods appl. Mech. engrg. 190, No. 24--25 (2001)
[8] Heil, M.: Stokes flow in an elastic tube----a large-displacement fluid--structure interaction problem. Int. J. Numer. methods fluids 28, 243-265 (1998) · Zbl 0916.73054
[9] Mok, D. P.; Wall, W. A.: Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures. Trends in computational structural mechanics (2001)
[10] Felippa, C. A.; Park, K. C.; Farhat, C.: Partitioned analysis of coupled mechanical systems. Comput. methods appl. Mech. engrg. 190, 3247-3270 (2001) · Zbl 0985.76075
[11] Heil, M.: Finite Reynolds number effects in the propagation of an air finger into a liquid-filled flexible-walled channel. J. fluid mech. 424, 21-44 (2000) · Zbl 0997.76086
[12] Heil, M.; White, J. P.: Airway closure: surface-tension-driven non-axisymmetric instabilities of liquid-lined elastic rings. J. fluid mech. 462, 79-109 (2002) · Zbl 1156.74320
[13] Hazel, A. L.; Heil, M.: Three-dimensional airway reopening: the steady propagation of a semi-infinite bubble into a buckled elastic tube. J. fluid mech. 478, 47-70 (2003) · Zbl 1037.76059
[14] Jensen, O. E.; Heil, M.: High-frequency self-excited oscillations in a collapsible-channel flow. J. fluid mech. 481, 235-268 (2003) · Zbl 1049.76015
[15] Hazel, A. L.; Heil, M.: Steady finite Reynolds number flow in three-dimensional collapsible tubes. J. fluid mech. 486, 79-103 (2003) · Zbl 1070.76011
[16] Wempner, G. A.: Mechanics of solids with applications to thin bodies. (1981) · Zbl 0498.73006
[17] Bogner, F. K.; Fox, R. L.; Schmit, L. A.: A cylindrical shell discrete element. Aiaa j. 5, 645-750 (1967) · Zbl 0146.21707
[18] Heil, M.; Pedley, T. J.: Large axisymmetric deformations of cylindrical shells conveying viscous flow. J. fluids struct. 9, 237-256 (1995)
[19] Keller, H. E.: Numerical solution of bifurcation and non-linear eigenvalue problems. Applications of bifurcation theory, 359-383 (1977)
[20] Kistler, S. F.; Scriven, L. E.: Coating flows. Computational analysis of polymer processing (1983)
[21] Taylor, C.; Hood, P.: A numerical solution of the Navier--Stokes equations using the finite element technique. Comput. fluids 1, 73-100 (1973) · Zbl 0328.76020
[22] Hughes, T. J. R.: Finite element methods for convection dominated flows. 34 of AMD (1979) · Zbl 0418.00017
[23] Tezduyar, T. E.; Ganjoo, D. K.: Petrov--Galerkin formulations with weighting functions dependent on spatial and temporal discretizations: applications to transient convection--diffusion problems. Comput. methods appl. Mech. engrg. 59, 49-71 (1986) · Zbl 0604.76077
[24] Tezduyar, T. E.: Stabilized finite element formulations for incompressible flow computations. Adv. appl. Mech. 28, 1-44 (1992) · Zbl 0747.76069
[25] Tezduyar, T. E.; Osawa, Y.: Finite element stabilisation parameters computed from element matrices and vectors. Comput. methods appl. Mech. engrg. 190, 411-430 (2000) · Zbl 0973.76057
[26] Fischer, B.; Ramage, A.; Silvester, D. J.; Wathen, A. J.: On parameter choice and iterative convergence for stabilised discretisations of advection--diffusion problems. Comput. methods appl. Mech. engrg. 179, 185-202 (1999) · Zbl 0977.76043
[27] Ramage, A.: A multigrid preconditioner for stabilised discretisations of advection--diffusion problems. J. comput. Appl. math. 101, 187-203 (1999) · Zbl 0939.65135
[28] Hughes, T. J. R.; Brooks, A.: A multi-dimensional upwind scheme with no crosswind diffusion. Finite element methods for convection dominated flows 34 of AMD, 19-35 (1979)
[29] Pedley, T. J.; Stephanoff, K. D.: Flow along a channel with a time-dependent indentation in one wall: the generation of vorticity waves. J. fluid mech. 160, 337-367 (1985)
[30] HSL 2000, A collection of Fortran codes for large scale scientific computation. Available from <http://www.numerical.rl.ac.uk>
[31] Ghattas, O.; Li, X.: A variational finite-element method for stationary nonlinear fluid--solid interaction. J. comput. Phys. 121, 347-356 (1995) · Zbl 0924.76057
[32] Kelley, C. T.: Iterative methods for linear and nonlinear equations. (1995) · Zbl 0832.65046
[33] Turek, S.: Efficient solvers for incompressible flow problems----an algorithmic and computational approach. (1999) · Zbl 0930.76002
[34] Elman, H. C.: Preconditioning the steady-state Navier--Stokes equations with low viscosity. SIAM J. Sci. comput. 29, 1299-1316 (1999) · Zbl 0935.76057
[35] H.C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements and Fast Iterative Solvers, Oxford University Press, Oxford, to appear in 2004 · Zbl 1083.76001
[36] Demmel, J. W.; Eisenstat, S. C.; Gilbert, J. R.; Li, X. S.; Liu, J. W. H.R.: A supernodal approach to sparse partial pivoting. SIAM J. Matrix anal. Appl. 20, 720-755 (1999) · Zbl 0931.65022
[37] Briggs, W. L.; Henson, V. E.; Mccormick, S. F.: A multigrid tutorial. (2000) · Zbl 0958.65128
[38] D.J. Silvester, personal communication, 2002
[39] Dembo, R. S.; Eisenstat, S. C.; Steilhaug, T.: Inexact Newton methods. SIAM J. Numer. anal. 19, 400-408 (1982) · Zbl 0478.65030
[40] Gresho, P. M.; Lee, R. L.: Don’t suppress the wiggles----they’re telling you something. Comput. fluids 9, 223-253 (1981) · Zbl 0436.76065
[41] V. Frayss, L. Giraud, S.G.J. Langou, A set of GMRES routines for real and complex arithmetics on high performance computers, CERFACS Technical Report TR/PA/03/3, Public domain software available on <www.cerfacs/algor/Softs>, 2002 · Zbl 1070.65527