Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit

SeMA Journal

Volumn 55, Issue 1, 2011, Pages 59-108

  Fernández, Miguel A ^a  

^a INRIA ROCQUENCOURT   (France)

Author keywords

Couple Problem; Coupling Scheme; Discontinuous Galerkin; Explicit Coupling; GMRES Iteration

Indexed keywords

EID: 84859426110     PISSN: 22543902     EISSN: 22817875     Source Type: Journal    
DOI: 10.1007/BF03322593     Document Type: Article

References (121)

1. G. Allaire. Conception optimale de structures, volume 58 of Mathématiques & Applications. Springer, 2007.
2. D.N. Arnold. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal., 19(4):742–760, 1982. DOI: 10.1137/0719052
3. D.N. Arnold, F. Brezzi, B. Cockburn, and D. Marini. Discontinuous Galerkin methods for elliptic problems. In Discontinuous Galerkin methods (Newport, RI, 1999), volume 11 of Lect. Notes Comput. Sci. Eng., pages 89–101. Springer, 2000.
4. M. Astorino. Interaction fluide-structure dans le système cardiovasculaire. Analyse numérique et simulation. PhD thesis, Université Paris VI, France, 2010.
5. M. Astorino, F. Chouly, and M. A. Fernández. Robin based semi-implicit coupling in fluid-structure interaction: Stability analysis and numerics. SIAM J. Sci. Comput., 31(6):4041–4065, 2009. DOI: 10.1137/090749694
6. M. Astorino, J.-F. Gerbeau, O. Pantz, and K.-F. Traoré. Fluid-structure interaction and multi-body contact: application to aortic valves. Comput. Methods Appl. Mech. Engrg., 198(45–46):3603–3612, 2009. DOI: 10.1016/j.cma.2008.09.012
7. M. Astorino and C. Grandmont. Convergence analysis of a projection semi-implicit coupling scheme for fluid-structure interaction problems. Numer. Math., 116:721–767, 2010. DOI: 10.1007/s00211-010-0311-x
8. S. Badia and R. Codina. On some fluid-structure iterative algorithms using pressure segregation methods. Application to aeroelasticity. Internat. J. Numer. Methods Engrg., 72(1):46–71, 2007. DOI: 10.1002/nme.1998
9. S. Badia, F. Nobile, and C. Vergara. Fluid-structure partitioned procedures based on Robin transmission conditions. J. Comp. Phys., 227:7027–7051, 2008. DOI: 10.1016/j.jcp.2008.04.006
10. S. Badia, F. Nobile, and C. Vergara. Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg., 198(33–36):2768–2784, 2009. DOI: 10.1016/j.cma.2009.04.004
11. S. Badia, A. Quaini, and A. Quarteroni. Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect. Comput. Methods Appl. Mech. Engrg., 197(49–50):4216–4232, 2008. DOI: 10.1016/j.cma.2008.04.018
12. S. Badia, A. Quaini, and A. Quarteroni. Splitting methods based on algebraic factorization for fluid-structure interaction. SIAM J. Sci. Comput., 30(4):1778–1805, 2008. DOI: 10.1137/070680497
13. G.A. Baker. Finite element methods for elliptic equations using nonconforming elements. Math. Comp., 31(137):45–59, 1977. DOI: 10.1090/S0025-5718-1977-0431742-5
14. K.J. Bathe and H. Zhang. Finite element developments for general fluid flows with structural interactions. Int. J. Num. Meth. Engng., 2004.
15. Y. Bazilevs, V.M. Calo, T.J.R. Hughes, and Y. Zhang. Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput. Mech., 43(1):3–37, 2008. DOI: 10.1007/s00466-008-0315-x
16. R. Becker, P. Hansbo, and R. Stenberg. A finite element method for domain decomposition with non-matching grids. M2AN Math. Model. Numer. Anal., 37(2):209–225, 2003. DOI: 10.1051/m2an:2003023
17. C. Bernardi, Y. Maday, and A. T. Patera. Domain decomposition by the mortar element method. In Asymptotic and numerical methods for partial differential equations with critical parameters (Beaune, 1992), volume 384 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pages 269–286. Kluwer Acad. Publ., Dordrecht, 1993.
18. C. Bertoglio, D. Chapelle, M.A. Fernández, J.-F. Gerbeau, and P. Moireau. Filtering-based data assimilation in vascular fluid-structure interaction through displacement measurements at the interface. In IV European Congress on Computational Mechanics (ECCM IV): Solids, Structures and Coupled Problems in Engineering, 2010.
19. P. N. Brown and Y. Saad. Convergence theory of nonlinear Newton-Krylov algorithms. SIAM J. Optim., 4(2):297–330, 1994. DOI: 10.1137/0804017
20. E. Burman and M.A. Fernández. Robin-based explicit coupling schemes in incompressible fluid-structure interaction. In preparation.
21. E. Burman and M.A. Fernández. Stabilized explicit coupling for fluid-structure interaction using Nitsche’s method. C. R. Math. Acad. Sci. Paris, 345(8):467–472, 2007. DOI: 10.1016/j.crma.2007.09.010
22. E. Burman and M.A. Fernández. Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility. Comput. Methods Appl.Mech. Engrg., 198(5–8):766–784, 2009. DOI: 10.1016/j.cma.2008.10.012
23. E. Burman and P. Hansbo. A unified stabilized method for Stokes’ and Darcy’s equations. J. Comput. Appl. Math., 198:35–51, 2007. DOI: 10.1016/j.cam.2005.11.022
24. E. Burman and P. Zunino. A domain decomposition method based on interior penalties for advection-diffusion-reaction problems. Siam Jour. Num. Anal., 44:1612–1638, 2006. DOI: 10.1137/050634736
25. P. Causin, J.-F. Gerbeau, and F. Nobile. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput. Methods Appl. Mech. Engrg., 194 (42–44):4506–4527, 2005. DOI: 10.1016/j.cma.2004.12.005
26. D. Chapelle and K.J. Bathe. The Finite Element Analysis of Shells —Fundamentals. Springer, 2003.
27. D. Chapelle, P. Moireau, and P. Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete Contin. Dyn. Syst., 23(1–2):65–84, 2009.
28. Y. Cheng, H. Oertel, and T. Schenkel. Fluid-structure coupled CFD simulation of the left ventricular flow during filling phase. Ann. Biomed. Eng., 33(5):567–576, 2005. DOI: 10.1007/s10439-005-4388-9
29. A.J. Chorin. On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comp., 23:341–353, 1969. DOI: 10.1090/S0025-5718-1969-0242393-5
30. P.G. Ciarlet. Mathematical elasticity. Vol. I, volume 20 of Studies in Mathematics and its Applications. North-Holland, 1988.
31. J. Degroote, S. Annerel, and J. Vierendeels. Stability analysis of Gauss-Seidel iterations in a partitioned simulation of fluid-structure interaction. Comp. & Struct., 88(5–6):263–271, 2010. DOI: 10.1016/j.compstruc.2009.09.003
32. J. Degroote, K.-J. Bathe, and J. Vierendeels. Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction. Comp.& Struct., 87(11–12):793–801, 2009. DOI: 10.1016/j.compstruc.2008.11.013
33. J. Degroote, A. Swillens, P. Bruggeman, R. Haelterman, P. Segers, and J. Vierendeels. Simulation of fluid-structure interaction with the interface artificial compressibility method. Int. J. Numer. Meth. Biomed. Engng., 26(3–4):276–289, 2010. DOI: 10.1002/cnm.1276
34. P. Degroote, J. Bruggeman, R. Haelterman, and J. Vierendeels. Stability of a coupling technique for partitioned solvers in FSI applications. Comp. & Struct., 86(23–24):2224–2234, 2008. DOI: 10.1016/j.compstruc.2008.05.005
35. S. Deparis. Numerical Analysis of Axisymmetric Flows and Methods for Fluid-Structure Interaction Arising in Blood Flow Simulation. PhD thesis, EPFL, Switzerland, 2004.
36. S. Deparis, M. Discacciati, G. Fourestey, and A. Quarteroni. Fluid-structure algorithms based on Steklov-Poincaré operators. Comput. Methods Appl. Mech. Engrg., 195(41–43):5797–5812, 2006. DOI: 10.1016/j.cma.2005.09.029
37. S. Deparis, M.A. Fernández, and L. Formaggia. Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions. M2AN Math. Model. Numer. Anal., 37(4):601–616, 2003. DOI: 10.1051/m2an:2003050
38. W. Dettmer and D. Perić. A computational framework for fluid-rigid body interaction: finite element formulation and applications. Comput. Methods Appl. Mech. Engrg., 195(13–16):1633–1666, 2006. DOI: 10.1016/j.cma.2005.05.033
39. N. Diniz dos Santos, J.-F. Gerbeau, and J.-F. Bourgat. A partitioned fluid-structure algorithm for elastic thin valves with contact. Comput. Methods Appl. Mech. Engrg., 197(19–20):1750–1761, 2008. DOI: 10.1016/j.cma.2007.03.019
40. J. Donéa, S. Giuliani, and J. P. Halleux. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comp. Meth. Appl. Mech. Engng., pages 689–723, 1982.
41. C. Farhat, M. Lesoinne, and P. Le Tallec. 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. DOI: 10.1016/S0045-7825(97)00216-8
42. C. Farhat, K. van der Zee, and Ph. Geuzaine. Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear aeroelasticity. Comput. Methods Appl. Mech. Engrg., 195(17–18):1973–2001, 2006. DOI: 10.1016/j.cma.2004.11.031
43. C.A. Felippa, K.C. Park, and C. Farhat. Partitioned analysis of coupled mechanical systems. Comput. Methods Appl. Mech. Engrg., 190(24–25):3247–3270, 2001. DOI: 10.1016/S0045-7825(00)00391-1
44. M.A. Fernández. Incremental displacement-correction schemes for the explicit coupling of a thin structure with an incompressible fluid. C. R. Acad. Sci. Paris Sér. I Math., 2011. In press. DOI: 10.1016/j.crma.2011.03.001. DOI: 10.1016/j.crma.2011.03.001
45. M.A. Fernández, L. Formaggia, J.-F. Gerbeau, and A. Quarteroni. The derivation of the equations for fluids and structures. In Cardiovascular mathematics, volume 1 of MS&A. Model. Simul. Appl., pages 77–121. Springer, 2009.
46. M.A. Fernández and J.-F. Gerbeau. Algorithms for fluid-structure interaction problems. In Cardiovascular mathematics, volume 1 of MS&A. Model. Simul. Appl., pages 307–346. Springer, 2009.
47. M.A. Fernández, J.-F. Gerbeau, and C. Grandmont. A projection algorithm for fluid-structure interaction problems with strong added-mass effect. C. R. Math. Acad. Sci. Paris, 342(4):279–284, 2006. DOI: 10.1016/j.crma.2005.12.017
48. M.A. Fernández, J.F. Gerbeau, and C. Grandmont. A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. Int. J. Num. Meth. Engrg., 69(4):794–821, 2007. DOI: 10.1002/nme.1792
49. M.A. Fernández and M. Moubachir. A Newton method using exact Jacobians for solving fluid-structure coupling. Comp. & Struct., 83:127–142, 2005. DOI: 10.1016/j.compstruc.2004.04.021
50. M.A. Fernández and J. Mullaert. Displacement-velocity correction schemes for incompressible fluid-structure interaction. Submitted to C. R. Acad. Sci. Paris Sér. I Math., http://hal.inria.fr/inria-00583126/en/.
51. C.A. Figueroa, I.E. Vignon-Clementel, K.E. Jansen, T.J.R. Hughes, and C.A. Taylor. A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput. Methods Appl. Mech. Engrg., 195(41–43):5685–5706, 2006. DOI: 10.1016/j.cma.2005.11.011
52. L. Formaggia, J.-F. Gerbeau, F. Nobile, and A. Quarteroni. On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels. Comp. Meth. Appl. Mech. Engrg., 191(6–7):561–582, 2001. DOI: 10.1016/S0045-7825(01)00302-4
53. L. Formaggia, K. Perktold, and A. Quarteroni. Basic mathematical models and motivations. In Cardiovascular mathematics, volume 1 of MS&A. Model. Simul. Appl., pages 47–75. Springer, 2009.
54. C. Förster, W.A. Wall, and E. Ramm. Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput. Methods Appl. Mech. Engrg., 196(7):1278–1293, 2007. DOI: 10.1016/j.cma.2006.09.002
55. G. Fourestey and S. Piperno. A second-order time-accurate ALE Lagrange-Galerkin method applied to wind engineering and control of bridge profiles. Comput. Methods Appl. Mech. Engrg., 193(39–41):4117–4137, 2004. DOI: 10.1016/j.cma.2003.12.060
56. Y.C. Fung. Biomechanics, Mechanical properties of living tissues. Springer, 1993.
57. M.J. Gander and L. Halpern. Optimized Schwarz waveform relaxation methods for advection reaction diffusion problems. SIAM J. Numer. Anal., 45(2):666–697, 2007. DOI: 10.1137/050642137
58. M.W. Gee, U. Küttler, and W. Wall. Truly monolithic algebraic multigrid for fluid-structure interaction. Int. J. Numer. Meth. Engng., 2010. To appear.
59. J.-F. Gerbeau and M. Vidrascu. A quasi-Newton algorithm based on a reduced model for fluid-structure interactions problems in blood flows. Math. Model. Num. Anal., 37(4):631–648, 2003. DOI: 10.1051/m2an:2003049
60. J.-F. Gerbeau, M. Vidrascu, and P. Frey. Fluid-structure interaction in blood flows on geometries based on medical imaging. Comp. & Struct., 83(2–3):155–165, 2005. DOI: 10.1016/j.compstruc.2004.03.083
61. C. Grandmont and Y. Maday. Nonconforming grids for the simulation of fluid-structure interaction. In Domain decomposition methods, 10 (Boulder, CO, 1997), volume 218 of Contemp. Math., pages 262–270. Amer. Math. Soc., Providence, RI, 1998.
62. J.-L. Guermond. Some implementation of projection methods for Navier-Stokes equations. M2AN Math. Model. Numer. Anal., 30:637–667, 1996.
63. J. L. Guermond, P. Minev, and J. Shen. An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Engrg., 195(44–47):6011–6045, 2006. DOI: 10.1016/j.cma.2005.10.010
64. G. Guidoboni, R. Glowinski, N. Cavallini, and S. Canic. Stable loosely-coupled-type algorithm for fluid-structure interaction in blood flow. J. Comp. Phys., 228(18):6916–6937, 2009. DOI: 10.1016/j.jcp.2009.06.007
65. G. Guidoboni, R. Glowinski, N. Cavallini, S. Canic, and S. Lapin. A kinematically coupled time-splitting scheme for fluid-structure interaction in blood flow. Appl. Math. Lett., 22(5):684–688, 2009. DOI: 10.1016/j.aml.2008.05.006
66. M.E. Gurtin. An introduction to continuum mechanics, volume 158 of Mathematics in Science and Engineering. Academic Press Inc., 1981.
67. P. Hansbo. Nitsche’s method for interface problems in computational mechanics. GAMM-Mitt., 28(2):183–206, 2005.
68. P. Hansbo and J. Hermansson. Nitsche’s method for coupling non-matching meshes in fluid-structure vibration problems. Computational Mechanics, 32(1–2):134–139, 2003. DOI: 10.1007/s00466-003-0467-7
69. P. Hansbo, J. Hermansson, and T. Svedberg. Nitsche’s method combined with space-time finite elements for ALE fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg., 193:4195–4206, 2004. DOI: 10.1016/j.cma.2003.09.029
70. M. Heil. An efficient solver for the fully coupled solution of large-displacement fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg., 193(1–2):1–23, 2004. DOI: 10.1016/j.cma.2003.09.006
71. M. Heil, A.L. Hazel, and J. Boyle. Solvers for large-displacement fluid-structure interaction problems: Segregated vs. monolithic approaches. Comp. Mech., 43:91–101, 2008. DOI: 10.1007/s00466-008-0270-6
72. B. Hübner, E. Walhorn, and D. Dinkle. A monolithic approach to fluid-structure interaction using space-time finite elements. Comp. Meth. Appl. Mech. Engng., 193:2087–2104, 2004. DOI: 10.1016/j.cma.2004.01.024
73. E. Järvinen, P. Rȧback, M. Lyly, and J.-P. Salenius. A method for partitioned fluid-structure interaction computation of flow in arteries. Medical Engineering & Physics, 30(7):917–923, 2008. DOI: 10.1016/j.medengphy.2007.12.008
74. M.M. Joosten, W.G. Dettmer, and D. Perić. Analysis of the block Gauss-Seidel solution procedure for a strongly coupled model problem with reference to fluid-structure interaction. Internat. J. Numer. Methods Engrg., 78(7):757–778, 2009. DOI: 10.1002/nme.2503
75. M. Juntunen and R. Stenberg. Nitsche’s method for general boundary conditions. Math. Comp., 78(267):1353–1374, 2009. DOI: 10.1090/S0025-5718-08-02183-2
76. S.A. Kock, J.V. Nygaard, N. Eldrup, E.-T. Fründ, A. Klaerke, W.P. Paaske, E. Falk, and W. Yong Kim. Mechanical stresses in carotid plaques using mri-based fluid-structure interaction models. J. Biomech., 41(8):1651–1658, 2008. DOI: 10.1016/j.jbiomech.2008.03.019
77. U. Küttler, M.W. Gee, C. Förster, A. Comerford, and W.A. Wall. Coupling strategies for biomedical fluid-structure interaction problems. Int. J. Numer. Meth. Biomed. Engng., 26(3–4):305–321, 2009.
78. U. Küttler and W.A. Wall. Fixed-point fluid-structure interaction solvers with dynamic relaxation. Comp. Mech., 43(1):61–72, 2008. DOI: 10.1007/s00466-008-0255-5
79. U. Küttler and W.A. Wall. Vector extrapolation for strong coupling fluid-structure interaction solvers. J. App. Mech., 76(2):021205, 2009. DOI: 10.1115/1.3057468
80. L. Lanoye, J. Vierendeels, P. Segers, and P. Verdonck. Vascular fluid-structure-interaction using Fluent and Abaqus software. J. Biomech., 39 (Supplement 1):S440–S440, 2006. DOI: 10.1016/S0021-9290(06)84797-4
81. W. Layton, H. K. Lee, and J. Peterson. A defect-correction method for the incompressible Navier-Stokes equations. Appl. Math. Comput., 129(1):1–19, 2002. DOI: 10.1016/S0096-3003(01)00026-1
82. P. Le Tallec. Numerical methods for nonlinear three-dimensional elasticity. In Handbook of numerical analysis, Vol. III, pages 465–622. North-Holland, 1994. DOI: 10.1016/S1570-8659(05)80018-3
83. P. Le Tallec and P. Hauret. Energy conservation in fluid structure interactions. In Numerical methods for scientific computing. Variational problems and applications, pages 94–107. Internat. Center Numer. Methods Eng. (CIMNE), Barcelona, 2003.
84. P. Le Tallec and S. Mani. Numerical analysis of a linearised fluid-structure interaction problem. Numer. Math., 87(2):317–354, 2000. DOI: 10.1007/s002110000183
85. P. Le Tallec and J. Mouro. Fluid structure interaction with large structural displacements. Comput. Meth. Appl. Mech. Engrg., 190:3039–3067, 2001. DOI: 10.1016/S0045-7825(00)00381-9
86. M. Lesoinne and C. Farhat. Higher-order subiteration-free staggered algorithm for nonlinear transient aeroelastic problems. AIAA Journal, 36(9):1754–1757, 1998. DOI: 10.2514/2.7555
87. Z. Li and C. Kleinstreuer. Computational analysis of type II endoleaks in a stented abdominal aortic aneurysm model. J. Biomech., 39(14):2573–2582, 2006. DOI: 10.1016/j.jbiomech.2005.09.002
88. Y. Maday. Analysis of coupled models for fluid-structure interaction of internal flows. In Cardiovascular mathematics, volume 1 of MS&A. Model. Simul. Appl., pages 279–306. Springer, 2009.
89. H.G. Matthies and J. Steindorf. Partitioned but strongly coupled iteration schemes for nonlinear fluid-structure interaction. Comp. & Struct., 80(27–30):1991–1999, 2002. DOI: 10.1016/S0045-7949(02)00259-6
90. D.P. Mok and W.A. Wall. Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures. In W.A. Wall, K.U. Bletzinger, and K. Schweizerhof, editors, Trends in computational structural mechanics, Barcelona, 2001. CIMNE.
91. D.P. Mok, W.A. Wall, and E. Ramm. Partitioned analysis approach for the transient, coupled response of viscous fluids and flexible structures. In W. Wunderlich, editor, Proceedings of the European Conference n Computational Mechanics. ECCM’99, TU Munich, 1999.
92. D.P. Mok, W.A. Wall, and E. Ramm. Accelerated iterative substructuring schemes for instationary fluid-structure interaction. In Bathe. K.J., editor, Computational Fluid and Solid Mechanics, pages 1325–1328. Elsevier, 2001. DOI: 10.1016/B978-008043944-0/50907-0
93. H. Morand and R. Ohayon. Fluid-Structure Interaction: Applied Numerical Methods. John Wiley & Sons, 1995.
94. J. Mouro. Interactions fluide structure en grands déplacements. Résolution numérique et application aux composants hydrauliques automobiles. PhD thesis, Ecole Polytechnique, France, 1996.
95. J. Nitsche. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg, 36:9–15, 1971. DOI: 10.1007/BF02995904
96. F. Nobile. Numerical approximation of fluid-structure interaction problems with application to haemodynamics. PhD thesis, EPFL, Switzerland, 2001.
97. F. Nobile and C. Vergara. An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM J. Sci. Comput., 30(2):731–763, 2008. DOI: 10.1137/060678439
98. T. Nomura and T.J.R. Hughes. An arbitray Lagrangian-Eulerian finite element method for interaction of fluid and rigid body. Comput. Methods Appl. Mech. Eng., 95(1):115–138, 1992. DOI: 10.1016/0045-7825(92)90085-X
99. S. Piperno. Simulation numérique de phénomènes d’interaction fluide-structure. PhD thesis, Ecole Nationale des Ponts et Chaussées, France, 1995.
100. S. Piperno. Explicit/implicit fluid/structure staggered procedures with a structural predictor and fluid subcycling for 2D inviscid aeroelastic simulations. Internat. J. Numer. Methods Fluids, 25(10):1207–1226, 1997. DOI: 10.1002/(SICI)1097-0363(19971130)25:10<1207::AID-FLD616>3.0.CO;2-R
101. S. Piperno and P.E. Bournet. Numerical simulations of wind effects on flexible civil engineering structures. Rev. Eur. Élém. Finis, 8(5–6):659–687, 2001.
102. S. Piperno and C. Farhat. Design of efficient partitioned procedures for the transient solution of aeroelastic problems. In Fluid-structure interaction, Innov. Tech. Ser., pages 23–49. Kogan Page Sci., 2003.
103. A. Quaini and A. Quarteroni. A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method. Math. Models Methods Appl. Sci., 17(6):957–983, 2007. DOI: 10.1142/S0218202507002170
104. K. Riemslagh, J. Vierendeels, and E. Dick. An efficient coupling procedure for flexible wall fluid-structure interaction. In ECCOMAS 2000, Barcelona, 2000.
105. S. Rugonyi and K.J. Bathe. On finite element analysis of fluid flows coupled with structural interaction. CMES — Comp. Modeling Eng. Sci., 2(2):195–212, 2001.
106. A.-V. Salsac, S.R. Sparks, J.M. Chomaz, and J.C. Lasheras. Evolution of the wall shear stresses during the progressive enlargement of symmetric abdominal aortic aneurysms. J. Fluid Mech., 550:19–51, 2006. DOI: 10.1017/S002211200600036X
107. M. Schäfer, M. Heck, and S. Yigit. An implicit partitioned method for the numerical simulation of fluid-structure interaction. In Fluid-structure interaction, volume 53 of Lect. Notes Comput. Sci. Eng., pages 171–194. Springer, 2006.
108. J. Sokolowski and J.-P. Zolésio. Introduction to shape optimization, volume 16 of Springer Series in Computational Mathematics. Springer, 1992.
109. H.J. Stetter. The defect correction principle and discretization methods. Numer. Math, 29:425–443, 1978. DOI: 10.1007/BF01432879
110. E. W. Swim and P. Seshaiyer. A nonconforming finite element method for fluid-structure interaction problems. Comput. Methods Appl. Mech. Engrg., 195(17–18):2088–2099, 2006. DOI: 10.1016/j.cma.2005.01.017
111. S. Sy and C.M. Murea. A stable time advancing scheme for solving fluid-structure interaction problem at small structural displacements. Comput. Methods Appl. Mech. Engrg., 198(2):210–222, 2008. DOI: 10.1016/j.cma.2008.07.010
112. R. Temam. Une methode d’approximation de la solution des équations de Navier-Stokes. Bull. Soc. Math. France, 96:115–152, 1968.
113. T.E Tezduyar. Finite element methods for fluid dynamics with moving boundaries and interfaces. Arch. Comput. Methods Engrg., 8:83–130, 2001. DOI: 10.1007/BF02897870
114. T.E. Tezduyar and S. Sathe. Modelling of fluid-structure interactions with the space-time finite elements: solution techniques. Internat. J. Numer. Methods Fluids, 54(6–8):855–900, 2007. DOI: 10.1002/fld.1430
115. M. Thiriet. Biology and Mechanics of Blood Flows. Part II: Mechanics and Medical Aspects. CRM Series in Mathematical Physics. Springer, 2008.
116. J. Vierendeels, Lanoye. L., J. Degroote, and P. Verdonck. Implicit coupling of partitioned fluid-structure interaction problems with reduced order models. Comp. & Struct., 85(11–14):970–976, 2007. DOI: 10.1016/j.compstruc.2006.11.006
117. W.A. Wall, S. Genkinger, and E. Ramm. A strong coupling partitioned approach for fluid-structure interaction with free surfaces. Comput. & Fluids, 36(1):169–183, 2007. DOI: 10.1016/j.compfluid.2005.08.007
118. H. Watanabe, S. Sugiura, H. Kafuku, and T. Hisada. Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. Biophysical Journal, 87(3):2074–2085, 2004. DOI: 10.1529/biophysj.103.035840
119. M.F. Wheeler. An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal., 15(1):152–161, 1978. DOI: 10.1137/0715010
120. L. Wiechert, T. Rabczuk, A. Comerford, R. Metzke, and W.A. Wall. Towards stresses and strains in the respiratory system. In Mathematical and numerical modelling of the human lung, volume 23 of ESAIM Proc., pages 98–113. EDP Sci., 2008.
121. X.L. Yang, Y. Liu, and J.M. Yang. Fluid-structure interaction in a pulmonary arterial bifurcation. J. Biomech., 40(12):2694–2699, 2007. DOI: 10.1016/j.jbiomech.2007.01.008