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FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta

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Abstract

We present a fluid–structure interaction (FSI) analysis of the blood flow and geometrical characteristics in the thoracic aorta. The FSI is handled with the sequentially-coupled arterial FSI technique. The fluid mechanics equations are solved with the ST-VMS method, which is the variational multiscale version of the deforming-spatial-domain/stabilized space–time (DSD/SST) method. We focus on the relationship between the centerline geometry of the aorta and the flow field, which influences the wall shear stress distribution. The centerlines of the aorta models we use in our analysis are extracted from the CT scans, and we assume a constant diameter. Torsion-free model geometries are generated by projecting the original centerline to its averaged plane of curvature. The flow fields for the original and projected geometries are compared to examine the influence of the torsion.

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References

  1. Isselbacher E (2005) Thoracic and abdominal aortic aneurysms. Circulation 111:816–828

    Article  Google Scholar 

  2. Elefteriades J (2002) Natural history of thoracic aortic aneurysms: indications for surgery, and surgical versus nonsurgical risks. Ann Thorac Surg 74:S1877–1880

    Article  Google Scholar 

  3. Davies R, Goldstein L, Coady STMA, Rizzo J, Kopf G, Elefteriades J (2002) Yearly rupture or dissection rates for thoracic aortic aneurysms: simple prediction based on size. Ann Thorac Surg 73:17–28

    Article  Google Scholar 

  4. Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique. Int J Numer Methods Fluids 57:601–629. doi:10.1002/fld.1633

    Article  MATH  MathSciNet  Google Scholar 

  5. Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198:3524–3533. doi:10.1016/j.cma.2008.05.024

    Article  MATH  MathSciNet  Google Scholar 

  6. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46:17–29. doi:10.1007/s00466-009-0423-2

    Article  MATH  MathSciNet  Google Scholar 

  7. Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Comput Mech 48:247–267. doi:10.1007/s00466-011-0571-z

    Article  MATH  MathSciNet  Google Scholar 

  8. Takizawa K, Tezduyar TE (2012) Space–time fluid–structure interaction methods. Math Models Methods Appl Sci 22:1230001. doi:10.1142/S0218202512300013

    Article  MathSciNet  Google Scholar 

  9. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, New York

    Book  Google Scholar 

  10. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44. doi:10.1016/S0065-2156(08)70153-4

    Article  MATH  MathSciNet  Google Scholar 

  11. Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94:339–351. doi:10.1016/0045-7825(92)90059-S

    Article  MATH  MathSciNet  Google Scholar 

  12. Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94:353–371. doi:10.1016/0045-7825(92)90060-W

    Article  MATH  MathSciNet  Google Scholar 

  13. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575. doi:10.1002/fld.505

    Article  MATH  MathSciNet  Google Scholar 

  14. Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900. doi:10.1002/fld.1430

    Article  MATH  MathSciNet  Google Scholar 

  15. Hughes TJR (1995) Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods. Comput Methods Appl Mech Eng 127:387–401

    Google Scholar 

  16. Hughes TJR, Oberai AA, Mazzei L (2001) Large Eddy simulation of turbulent channel flows by the variational multiscale method. Phys Fluids 13:1784–1799

    Article  Google Scholar 

  17. Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197:173–201

    Article  MATH  MathSciNet  Google Scholar 

  18. Bazilevs Y, Akkerman I (2010) Large Eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229:3402–3414

    Article  MATH  MathSciNet  Google Scholar 

  19. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32:199–259

    Google Scholar 

  20. Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity–pressure elements. Comput Methods Appl Mech Eng 95:221–242. doi:10.1016/0045-7825(92)90141-6

    Article  MATH  Google Scholar 

  21. Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods. Comput Mech 43:39–49. doi:10.1007/s00466-008-0261-7

    Article  MATH  Google Scholar 

  22. Tezduyar TE, Sathe S, Schwaab M, Pausewang J, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43:133–142. doi:10.1007/s00466-008-0260-8

    Article  MATH  Google Scholar 

  23. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space–time finite element computation of complex fluid–structure interactions. Int J Numer Methods Fluids 64:1201–1218. doi:10.1002/fld.2221

    Article  MATH  Google Scholar 

  24. Takizawa K, Moorman C, Wright S, Spielman T, Tezduyar TE (2011) Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes. Int J Numer Methods Fluids 65:271–285. doi:10.1002/fld.2348

    Article  MATH  Google Scholar 

  25. Takizawa K, Wright S, Moorman C, Tezduyar TE (2011) Fluid–structure interaction modeling of parachute clusters. Int J Numer Methods Fluids 65:286–307. doi:10.1002/fld.2359

    Article  MATH  Google Scholar 

  26. Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech 48:333–344. doi:10.1007/s00466-011-0589-2

    Article  MATH  Google Scholar 

  27. Takizawa K, Spielman T, Tezduyar TE (2011) Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech 48:345–364. doi:10.1007/s00466-011-0590-9

    Article  MATH  Google Scholar 

  28. Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647–657. doi:10.1007/s00466-011-0614-5

    Article  MATH  Google Scholar 

  29. Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid–structure interactions. Arch Comput Methods Eng 19:125–169. doi:10.1007/s11831-012-9070-4

    Article  MathSciNet  Google Scholar 

  30. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space–time and ALE–VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Methods Eng 19:171–225. doi:10.1007/s11831-012-9071-3

    Article  MathSciNet  Google Scholar 

  31. Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2012) Space–time techniques for computational aerodynamics modeling of flapping wings of an actual locust. Comput Mech 50:743–760. doi:10.1007/s00466-012-0759-x

    Article  MATH  Google Scholar 

  32. Takizawa K, Kostov N, Puntel A, Henicke B, Tezduyar TE (2012) Space–time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle. Comput Mech 50:761–778. doi:10.1007/s00466-012-0758-y

    Article  MATH  Google Scholar 

  33. Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2012) Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. Comput Mech 50:675–686. doi:10.1007/s00466-012-0760-4

    Article  MATH  MathSciNet  Google Scholar 

  34. Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar TE (2012) Fluid–structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854. doi:10.1007/s00466-012-0761-3

    Article  MATH  Google Scholar 

  35. Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338. doi:10.1142/S0218202513400058

    Article  MATH  MathSciNet  Google Scholar 

  36. Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013) Space–time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223–248. doi:10.1142/s0218202513400022

    Article  MATH  MathSciNet  Google Scholar 

  37. Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014) Space–time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1–15. doi:10.1007/s00466-013-0888-x

    Article  MATH  Google Scholar 

  38. Takizawa K, Tezduyar TE, Boben J, Kostov N, Boswell C, Buscher A (2013) Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity. Comput Mech 52:1351–1464. doi:10.1007/s00466-013-0880-5

    Article  MATH  Google Scholar 

  39. Takizawa K, Tezduyar TE (2014) Space–time computation techniques with continuous representation in time (ST-C). Comput Mech 53:91–99. doi:10.1007/s00466-013-0895-y

    Article  MATH  MathSciNet  Google Scholar 

  40. Takizawa K, Takagi H, Tezduyar TE, Torii R (2013) Estimation of element-based zero-stress state for arterial FSI computations. Comput Mech. doi:10.1007/s00466-013-0919-7

  41. Takizawa K, Tezduyar TE, Buscher A, Asada S (2013) Space–time interface-tracking with topology change (ST–TC). Comput Mech. doi:10.1007/s00466-013-0935-7

  42. Takizawa K, Tezduyar TE, Kostov N (2014) Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech. doi:10.1007/s00466-014-0980-x

  43. Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349

    Article  MATH  MathSciNet  Google Scholar 

  44. Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190:3009–3019

    Article  MATH  Google Scholar 

  45. van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid–structure interaction problem. SIAM J Sci Comput 27:599–621

    Article  MATH  MathSciNet  Google Scholar 

  46. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322

    Article  MATH  MathSciNet  Google Scholar 

  47. Khurram RA, Masud A (2006) A multiscale/stabilized formulation of the incompressible Navier–Stokes equations for moving boundary flows and fluid–structure interaction. Comput Mech 38:403–416

    Article  MATH  Google Scholar 

  48. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    Article  MATH  MathSciNet  Google Scholar 

  49. Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43:81–90

    Article  MATH  Google Scholar 

  50. Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik (2000) left ventricular assist device. Comput Methods Appl Mech Eng 198(2009):3534–3550

    Article  MATH  MathSciNet  Google Scholar 

  51. Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009) Computational fluid–structure interaction: methods and application to a total cavopulmonary connection. Comput Mech 45:77–89

    Article  MATH  MathSciNet  Google Scholar 

  52. Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen J (2010) A fully-coupled fluid–structure interaction simulation of cerebral aneurysms. Comput Mech 46:3–16

    Article  MATH  MathSciNet  Google Scholar 

  53. Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Kvamsdal T, Hentschel S, Isaksen J (2010) Computational fluid–structure interaction: methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9:481–498

    Article  Google Scholar 

  54. Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65:207–235. doi:10.1002/fld.2400

    Article  MATH  Google Scholar 

  55. Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid–structure interaction modeling with composite blades. Int J Numer Methods Fluids 65:236–253

    Article  MATH  Google Scholar 

  56. Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152

    Article  MATH  MathSciNet  Google Scholar 

  57. Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations. Finite Elem Anal Des 47:593–599

    Article  MathSciNet  Google Scholar 

  58. Nagaoka S, Nakabayashi Y, Yagawa G, Kim YJ (2011) Accurate fluid–structure interaction computations using elements without mid-side nodes. Comput Mech 48:269–276. doi:10.1007/s00466-011-0620-7

    Article  MATH  MathSciNet  Google Scholar 

  59. Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE–VMS and ST–VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid–structure interaction. Math Models Methods Appl Sci 22:1230002. doi:10.1142/S0218202512300025

    Article  Google Scholar 

  60. Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2012) Free-surface flow and fluid–object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech 79:010905

    Article  Google Scholar 

  61. Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE–VMS: validation and role of weakly enforced boundary conditions. Comput Mech 50:499–511

    Article  MATH  MathSciNet  Google Scholar 

  62. Hsu M-C, Bazilevs Y (2012) Fluid–structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833

    Article  MATH  MathSciNet  Google Scholar 

  63. Akkerman I, Dunaway J, Kvandal J, Spinks J, Bazilevs Y (2012) Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE–VMS. Comput Mech 50:719–727

    Article  MATH  Google Scholar 

  64. Minami S, Kawai H, Yoshimura S (2012) Parallel BDD-based monolithic approach for acoustic fluid–structure interaction. Comput Mech 50:707–718

    Article  MATH  MathSciNet  Google Scholar 

  65. Miras T, Schotte J-S, Ohayon R (2012) Energy approach for static and linearized dynamic studies of elastic structures containing incompressible liquids with capillarity: a theoretical formulation. Comput Mech 50:729–741

    Article  MATH  MathSciNet  Google Scholar 

  66. van Opstal TM, van Brummelen EH, de Borst R, Lewis MR (2012) A finite-element/boundary-element method for large-displacement fluid–structure interaction. Comput Mech 50:779–788

    Article  MATH  MathSciNet  Google Scholar 

  67. Yao JY, Liu GR, Narmoneva DA, Hinton RB, Zhang Z-Q (2012) Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves. Comput Mech 50:789–804

    Article  MATH  MathSciNet  Google Scholar 

  68. Larese A, Rossi R, Onate E, Idelsohn SR (2012) A coupled PFEM–Eulerian approach for the solution of porous FSI problems. Comput Mech 50:805–819

    Article  MATH  MathSciNet  Google Scholar 

  69. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid–structure interaction. Math Models Methods Appl Sci 23:215–221. doi:10.1142/S0218202513400010

    Article  MATH  MathSciNet  Google Scholar 

  70. Korobenko A, Hsu M-C, Akkerman I, Tippmann J, Bazilevs Y (2013) Structural mechanics modeling and FSI simulation of wind turbines. Math Models Methods Appl Sci 23:249–272

    Article  MATH  MathSciNet  Google Scholar 

  71. Yao JY, Liu GR, Qian D, Chen CL, Xu GX (2013) A moving-mesh gradient smoothing method for compressible CFD problems. Math Models Methods Appl Sci 23:273–305

    Article  MATH  MathSciNet  Google Scholar 

  72. Kamran K, Rossi R, Onate E, Idelsohn SR (2013) A compressible Lagrangian framework for modeling the fluid–structure interaction in the underwater implosion of an aluminum cylinder. Math Models Methods Appl Sci 23:339–367

    Article  MATH  MathSciNet  Google Scholar 

  73. Hsu M-C, Akkerman I, Bazilevs Y (2013) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy. doi:10.1002/we.1599

  74. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    Article  MATH  MathSciNet  Google Scholar 

  75. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis. Toward integration of CAD and FEA. Wiley, New York

    Book  Google Scholar 

  76. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26:27–36. doi:10.1109/2.237441

    Article  Google Scholar 

  77. Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119:73–94. doi:10.1016/0045-7825(94)00077-8

    Article  MATH  Google Scholar 

  78. Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130. doi:10.1007/BF02897870

    Article  MATH  Google Scholar 

  79. Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70:58–63. doi:10.1115/1.1530635

    Article  MATH  Google Scholar 

  80. Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193:2019–2032. doi:10.1016/j.cma.2003.12.046

    Article  MATH  Google Scholar 

  81. Mittal S, Tezduyar TE (1992) Notes on the stabilized space–time finite element formulation of unsteady incompressible flows. Comput Phys Commun 73:93–112. doi:10.1016/0010-4655(92)90031-S

    Article  Google Scholar 

  82. Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119:157–177. doi:10.1016/0045-7825(94)00082-4

    Article  MATH  Google Scholar 

  83. Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18:397–412. doi:10.1007/BF00350249

    Article  MATH  Google Scholar 

  84. Wren GP, Ray SE, Aliabadi SK, Tezduyar TE (1997) Simulation of flow problems with moving mechanical components, fluid–structure interactions and two-fluid interfaces. Int J Numer Methods Fluids 24:1433–1448

    Article  MATH  Google Scholar 

  85. Tezduyar TE (1999) CFD methods for three-dimensional computation of complex flow problems. J Wind Eng Ind Aerodyn 81:97–116. doi:10.1016/S0167-6105(99)00011-2

    Article  Google Scholar 

  86. Guler I, Behr M, Tezduyar T (1999) Parallel finite element computation of free-surface flows. Comput Mech 23:117–123. doi:10.1007/s004660050391

    Article  Google Scholar 

  87. Tezduyar TE (2006) Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. Comput Methods Appl Mech Eng 195:2983–3000. doi:10.1016/j.cma.2004.09.018

    Article  MATH  MathSciNet  Google Scholar 

  88. Mittal S, Tezduyar TE (1992) A finite element study of incompressible flows past oscillating cylinders and aerofoils. Int J Numer Methods Fluids 15:1073–1118. doi:10.1002/fld.1650150911

    Article  Google Scholar 

  89. Mittal S, Tezduyar TE (1994) Massively parallel finite element computation of incompressible flows involving fluid–body interactions. Comput Methods Appl Mech Eng 112:253–282. doi:10.1016/0045-7825(94)90029-9

    Article  MATH  MathSciNet  Google Scholar 

  90. Kalro V, Aliabadi S, Garrard W, Tezduyar T, Mittal S, Stein K (1997) Parallel finite element simulation of large ram-air parachutes. Int J Numer Methods Fluids 24:1353–1369

    Article  MATH  Google Scholar 

  91. Tezduyar T, Kalro V, Garrard W (1997) Parallel computational methods for 3D simulation of a parafoil with prescribed shape changes. Parallel Comput 23:1349–1363. doi:10.1016/S0167-8191(97)00057-4

    Article  MATH  MathSciNet  Google Scholar 

  92. Tezduyar T, Osawa Y (1999) Methods for parallel computation of complex flow problems. Parallel Comput 25:2039–2066. doi:10.1016/S0167-8191(99)00080-0

    Article  MathSciNet  Google Scholar 

  93. Tezduyar T, Osawa Y (2001) The multi-domain method for computation of the aerodynamics of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191:705–716. doi:10.1016/S0045-7825(01)00310-3

    Article  MATH  Google Scholar 

  94. Ray SE, Tezduyar TE (2000) Fluid–object interactions in interior ballistics. Comput Methods Appl Mech Eng 190:363–372. doi:10.1016/S0045-7825(00)00207-3

    Article  MATH  Google Scholar 

  95. Akin JE, Tezduyar TE, Ungor M (2007) Computation of flow problems with the mixed interface-tracking/interface-capturing technique (MITICT). Comput Fluids 36:2–11. doi:10.1016/j.compfluid.2005.07.008

    Article  MATH  Google Scholar 

  96. Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows—fluid–structure interactions. Int J Numer Methods Fluids 21:933–953. doi:10.1002/fld.1650211011

    Article  MATH  Google Scholar 

  97. Wren GP, Ray SE, Aliabadi SK, Tezduyar TE (1995) Space–time finite element computation of compressible flows between moving components. Int J Numer Methods Fluids 21:981–991. doi:10.1002/fld.1650211015

    Article  MATH  Google Scholar 

  98. Ray SE, Wren GP, Tezduyar TE (1997) Parallel implementations of a finite element formulation for fluid–structure interactions in interior flows. Parallel Comput 23:1279–1292. doi:10.1016/S0167-8191(97)00053-7

    Article  MATH  MathSciNet  Google Scholar 

  99. Takase S, Kashiyama K, Tanaka S, Tezduyar TE (2010) Space–time SUPG formulation of the shallow-water equations. Int J Numer Methods Fluids 64:1379–1394. doi:10.1002/fld.2464

    Article  MATH  MathSciNet  Google Scholar 

  100. Takase S, Kashiyama K, Tanaka S, Tezduyar TE (2011) Space–time SUPG finite element computation of shallow-water flows with moving shorelines. Comput Mech 48(2011):293–306. doi:10.1007/s00466-011-0618-1

    Article  MATH  MathSciNet  Google Scholar 

  101. Johnson AA, Tezduyar TE (1996) Simulation of multiple spheres falling in a liquid-filled tube. Comput Methods Appl Mech Eng 134:351–373. doi:10.1016/0045-7825(95)00988-4

    Article  MATH  MathSciNet  Google Scholar 

  102. Johnson AA, Tezduyar TE (1997) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24:1321–1340

    Article  MATH  Google Scholar 

  103. Johnson AA, Tezduyar TE (1997) 3D simulation of fluid–particle interactions with the number of particles reaching 100. Comput Methods Appl Mech Eng 145:301–321. doi:10.1016/S0045-7825(96)01223-6

    Article  MATH  Google Scholar 

  104. Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23:130–143. doi:10.1007/s004660050393

    Article  MATH  Google Scholar 

  105. Johnson A, Tezduyar T (2001) Methods for 3D computation of fluid–object interactions in spatially-periodic flows. Comput Methods Appl Mech Eng 190:3201–3221. doi:10.1016/S0045-7825(00)00389-3

    Article  MATH  Google Scholar 

  106. Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190:321–332

    Article  MATH  Google Scholar 

  107. Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D computation. Comput Methods Appl Mech Eng 190:373–386. doi:10.1016/S0045-7825(00)00208-5

    Article  MATH  Google Scholar 

  108. Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191:717–726. doi:10.1016/S0045-7825(01)00311-5

    Article  MATH  Google Scholar 

  109. Stein K, Benney R, Tezduyar T, Potvin J (2001) Fluid–structure interactions of a cross parachute: numerical simulation. Comput Methods Appl Mech Eng 191:673–687. doi:10.1016/S0045-7825(01)00312-7

    Article  MATH  Google Scholar 

  110. Stein KR, Benney RJ, Tezduyar TE, Leonard JW, Accorsi ML (2001) Fluid–structure interactions of a round parachute: modeling and simulation techniques. J Aircraft 38:800–808. doi:10.2514/2.2864

    Article  Google Scholar 

  111. Stein K, Tezduyar T, Kumar V, Sathe S, Benney R, Thornburg E, Kyle C, Nonoshita T (2003) Aerodynamic interactions between parachute canopies. J Appl Mech 70:50–57. doi:10.1115/1.1530634

    Article  MATH  Google Scholar 

  112. Stein K, Tezduyar T, Benney R (2003) Computational methods for modeling parachute systems. Comput Sci Eng 5:39–46. doi:10.1109/MCISE.2003.1166551

    Article  Google Scholar 

  113. Tezduyar TE, Sathe S (2004) Enhanced-discretization space–time technique (EDSTT). Comput Methods Appl Mech Eng 193:1385–1401. doi:10.1016/j.cma.2003.12.029

    Article  MATH  MathSciNet  Google Scholar 

  114. Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid—structure interactions. Comput Methods Appl Mech Eng 195:2002–2027. doi:10.1016/j.cma.2004.09.014

    Article  MATH  MathSciNet  Google Scholar 

  115. Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195:5743–5753. doi:10.1016/j.cma.2005.08.023

    Article  MATH  MathSciNet  Google Scholar 

  116. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the deforming-spatial-domain/stabilized space–time formulation. Comput Methods Appl Mech Eng 195:1885–1895. doi:10.1016/j.cma.2005.05.050

    Article  MATH  MathSciNet  Google Scholar 

  117. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38:482–490. doi:10.1007/s00466-006-0065-6

    Article  MATH  Google Scholar 

  118. Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36:191–206. doi:10.1016/j.compfluid.2005.02.011

    Article  MATH  MathSciNet  Google Scholar 

  119. Tezduyar TE (2007) Finite elements in fluids: special methods and enhanced solution techniques. Comput Fluids 36:207–223. doi:10.1016/j.compfluid.2005.02.010

    Article  MATH  MathSciNet  Google Scholar 

  120. Tezduyar TE, Sameh A (2006) Parallel finite element computations in fluid mechanics. Comput Methods Appl Mech Eng 195:1872–1884. doi:10.1016/j.cma.2005.05.038

    Article  MATH  MathSciNet  Google Scholar 

  121. Stein K, Tezduyar TE, Sathe S, Benney R, Charles R (2005) Fluid–structure interaction modeling of parachute soft-landing dynamics. Int J Numer Methods Fluids 47:619–631. doi:10.1002/fld.835

    Article  MATH  MathSciNet  Google Scholar 

  122. Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid–structure interactions with the space–time finite elements: arterial fluid mechanics. Int J Numer Methods Fluids 54:901–922. doi:10.1002/fld.1443

    Article  MATH  MathSciNet  Google Scholar 

  123. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36:160–168. doi:10.1016/j.compfluid.2005.07.014

    Article  MATH  Google Scholar 

  124. Sathe S, Benney R, Charles R, Doucette E, Miletti J, Senga M, Stein K, Tezduyar TE (2007) Fluid–structure interaction modeling of complex parachute designs with the space–time finite element techniques. Comput Fluids 36:127–135. doi:10.1016/j.compfluid.2005.07.010

    Article  MATH  Google Scholar 

  125. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm—dependence of the effect on the aneurysm shape. Int J Numer Methods Fluids 54:995–1009. doi:10.1002/fld.1497

    Article  MATH  MathSciNet  Google Scholar 

  126. Sathe S, Tezduyar TE (2008) Modeling of fluid–structure interactions with the space–time finite elements: contact problems. Comput Mech 43:51–60. doi:10.1007/s00466-008-0299-6

    Article  MATH  MathSciNet  Google Scholar 

  127. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43:151–159. doi:10.1007/s00466-008-0325-8

    Article  MATH  Google Scholar 

  128. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Fluid–structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes. Comput Methods Appl Mech Eng 198:3613–3621. doi:10.1016/j.cma.2008.08.020

    Article  MATH  MathSciNet  Google Scholar 

  129. Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010) Space–time finite element computation of arterial fluid–structure interactions with patient-specific data. Int J Numer Methods Biomed Eng 26:101–116. doi:10.1002/cnm.1241

    Article  MATH  Google Scholar 

  130. Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions. Comput Mech 46:31–41. doi:10.1007/s00466-009-0425-0

    Article  MATH  MathSciNet  Google Scholar 

  131. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms. Int J Numer Methods Biomed Eng 26:336–347. doi:10.1002/cnm.1289

    Article  MATH  MathSciNet  Google Scholar 

  132. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Role of 0D peripheral vasculature model in fluid–structure interaction modeling of aneurysms. Comput Mech 46:43–52. doi:10.1007/s00466-009-0439-7

    Article  MATH  Google Scholar 

  133. Takizawa K, Moorman C, Wright S, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2011) Patient-specific arterial fluid–structure interaction modeling of cerebral aneurysms. Int J Numer Methods Fluids 65:308–323. doi:10.1002/fld.2360

    Article  MATH  Google Scholar 

  134. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2011) Influencing factors in image-based fluid–structure interaction computation of cerebral aneurysms. Int J Numer Methods Fluids 65:324–340. doi:10.1002/fld.2448

    Article  MATH  Google Scholar 

  135. Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space–time fluid–structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27:1665–1710. doi:10.1002/cnm.1433

    Article  MATH  MathSciNet  Google Scholar 

  136. Takizawa K, Spielman T, Moorman C, Tezduyar TE (2012) Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design. J Appl Mech 79:010907. doi:10.1115/1.4005070

    Article  Google Scholar 

  137. Takizawa K, Brummer T, Tezduyar TE, Chen PR (2012) A comparative study based on patient-specific fluid–structure interaction modeling of cerebral aneurysms. J Appl Mech 79:010908. doi:10.1115/1.4005071

    Article  Google Scholar 

  138. Takizawa K, Tezduyar TE (2012) Bringing them down safely. Mech Eng 134:34–37

    Google Scholar 

  139. Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, Borst RD, Hughes TJR (eds) Encyclopedia of computational mechanics, vol 3. Wiley, New York

    Google Scholar 

  140. Rubin G, Paik D, Johnson P, Napel S (1998) Measurement of the aorta and its branches with helical CT. Radiology 206:823–829

    Article  Google Scholar 

  141. Antiga L, Piccinelli M, Botti L, Ene-Iordache B, Remuzzi A, Steinman DA (2008) An image-based modeling framework for patient-specific computational hemodynamics. Med Biol Eng Comput 46:1097–1112

    Article  Google Scholar 

  142. Geuzaine C, Remacle J-F (2009) Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79:1309–1331

    Article  MATH  MathSciNet  Google Scholar 

  143. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulation. Jpn Soc Mech Eng J A 70:1224–1231 in Japanese

    Article  Google Scholar 

  144. Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073. doi:10.1007/s00466-012-0790-y

    Google Scholar 

  145. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics withimproved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–375

    Article  MATH  MathSciNet  Google Scholar 

  146. Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the JST-CREST Mathematics program. The authors would like to thank Dr. Ryo Torii at University College London for providing observed data of pressure history in the aorta.

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Correspondence to Hiroshi Suito.

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Suito, H., Takizawa, K., Huynh, V.Q.H. et al. FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta. Comput Mech 54, 1035–1045 (2014). https://doi.org/10.1007/s00466-014-1017-1

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