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Computational engineering analysis with the new-generation space–time methods

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Abstract

This is an overview of the new directions we have taken the space–time (ST) methods in bringing solution and analysis to different classes of computationally challenging engineering problems. The classes of problems we have focused on include bio-inspired flapping-wing aerodynamics, wind-turbine aerodynamics, and cardiovascular fluid mechanics. The new directions for the ST methods include the variational multiscale version of the Deforming-Spatial-Domain/Stabilized ST method, using NURBS basis functions in temporal representation of the unknown variables and motion of the solid surfaces and fluid meshes, ST techniques with continuous representation in time, and ST interface-tracking with topology change. We describe the new directions and present examples of the challenging problems solved.

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References

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

    MathSciNet  MATH  Google Scholar 

  2. 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

    MATH  Google Scholar 

  3. 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

    MathSciNet  MATH  Google Scholar 

  4. 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

    MathSciNet  MATH  Google Scholar 

  5. 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

    MATH  Google Scholar 

  6. Lohner R, Cebral JR, Yang C, Baum JD, Mestreau EL, Soto O (2006) “Extending the range of applicability of the loose coupling approach for FSI simulations”, in H.-J. Bungartz and M. Schafer, editors, Fluid-structure interaction, volume 53 of Lecture notes in computational science and engineering, 82–100, Springer, Dordrecht

  7. Bletzinger K-U, Wuchner R, Kupzok A (2006) “Algorithmic treatment of shells and free form-membranes in FSI”, in H.-J. Bungartz and M. Schafer, editors, Fluid-structure interaction, volume 53 of Lecture notes in computational science and engineering, 336–355, Springer, Dordrecht

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

    MathSciNet  MATH  Google Scholar 

  9. 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

    MATH  Google Scholar 

  10. 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 198:3534–3550

    MathSciNet  MATH  Google Scholar 

  11. 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

    MathSciNet  MATH  Google Scholar 

  12. Calderer R, Masud A (2010) A multiscale stabilized ALE formulation for incompressible flows with moving boundaries. Comput Mech 46:185–197

    MathSciNet  MATH  Google Scholar 

  13. 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

    MathSciNet  MATH  Google Scholar 

  14. 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

    Google Scholar 

  15. 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

    MATH  Google Scholar 

  16. 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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  19. 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

    MathSciNet  MATH  Google Scholar 

  20. 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

    Google Scholar 

  21. 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

    Google Scholar 

  22. 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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  24. 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

    MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  26. 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

    MathSciNet  MATH  Google Scholar 

  27. 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

    MathSciNet  MATH  Google Scholar 

  28. 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

    Google Scholar 

  29. 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

    Google Scholar 

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

  31. 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

  32. 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

    Google Scholar 

  33. 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

    Google Scholar 

  34. 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

    MathSciNet  MATH  Google Scholar 

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

  36. 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

    MathSciNet  MATH  Google Scholar 

  37. 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

    MathSciNet  MATH  Google Scholar 

  38. 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

    MathSciNet  MATH  Google Scholar 

  39. 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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  43. 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

    MATH  Google Scholar 

  44. 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

    Google Scholar 

  45. 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

    MATH  Google Scholar 

  46. 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

    MATH  Google Scholar 

  47. 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

    MATH  Google Scholar 

  48. 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

    MATH  Google Scholar 

  49. 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

    MATH  Google Scholar 

  50. 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

    MATH  Google Scholar 

  51. 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

    MATH  Google Scholar 

  52. 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

    MATH  Google Scholar 

  53. 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

    MathSciNet  Google Scholar 

  54. 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

    MATH  Google Scholar 

  55. 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

    MathSciNet  MATH  Google Scholar 

  56. 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 52:1351–1364. doi:10.1007/s00466-013-0880-5

    MATH  Google Scholar 

  57. 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

    MATH  Google Scholar 

  58. 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

    MATH  Google Scholar 

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

  60. 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

    MATH  Google Scholar 

  61. 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

    MATH  Google Scholar 

  62. Cruchaga MA, Celentano DJ, Tezduyar TE (2007) A numerical model based on the Mixed Interface-Tracking/Interface-Capturing Technique (MITICT) for flows with fluid-solid and fluid-fluid interfaces. Int J Numer Methods Fluids 54:1021–1030. doi:10.1002/fld.1498

    MATH  Google Scholar 

  63. Wick T (2013) Coupling of fully Eulerian and arbitrary Lagrangian–Eulerian methods for fluid-structure interaction computations. Comput Mech 52:1113–1124

    MathSciNet  MATH  Google Scholar 

  64. 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

    Google Scholar 

  65. 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

    MATH  Google Scholar 

  66. 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. doi:10.1002/(SICI)1097-0363(199706)24:12<1433:AID-FLD568>3.3.CO;2-L

  67. 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

    Google Scholar 

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

    Google Scholar 

  69. 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

    MathSciNet  MATH  Google Scholar 

  70. 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

    Google Scholar 

  71. 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

    MathSciNet  MATH  Google Scholar 

  72. Aliabadi SK, Tezduyar TE (1995) Parallel fluid dynamics computations in aerospace applications. Int J Numer Methods Fluids 21:783–805. doi:10.1002/fld.1650211003

    MathSciNet  MATH  Google Scholar 

  73. 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. doi:10.1002/(SICI)1097-0363(199706)24:12<1353:AID-FLD564>3.0.CO;2-6

    MATH  Google Scholar 

  74. 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

    MathSciNet  MATH  Google Scholar 

  75. 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

    MathSciNet  Google Scholar 

  76. 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

    MATH  Google Scholar 

  77. 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

    MATH  Google Scholar 

  78. 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

    MATH  Google Scholar 

  79. Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2012) Space-time computational techniques for the aerodynamics of flapping wings. J Appl Mech 79:010903. doi:10.1115/1.4005073

    Google Scholar 

  80. Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2013) Computer modeling techniques for flapping-wing aerodynamics of a locust. Comput & Fluids 85:125–134. doi:10.1016/j.compfluid.2012.11.008

    MathSciNet  MATH  Google Scholar 

  81. Behr M, Tezduyar T (1999) The Shear-Slip Mesh Update Method. Comput Methods Appl Mech Eng 174:261–274. doi:10.1016/S0045-7825(98)00299-0

    MATH  Google Scholar 

  82. Behr M, Tezduyar T (2001) Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Methods Appl Mech Eng 190:3189–3200. doi:10.1016/S0045-7825(00)00388-1

    MATH  Google Scholar 

  83. 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

    MATH  Google Scholar 

  84. Aliabadi SK, Tezduyar TE (1993) Space-time finite element computation of compressible flows involving moving boundaries and interfaces. Comput Methods Appl Mech Eng 107:209–223. doi:10.1016/0045-7825(93)90176-X

    MATH  Google Scholar 

  85. 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

    MATH  Google Scholar 

  86. 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

    MathSciNet  MATH  Google Scholar 

  87. 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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  89. 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

    MathSciNet  MATH  Google Scholar 

  90. Johnson AA, Tezduyar TE (1997) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24:1321–1340. doi:10.1002/(SICI)1097-0363(199706)24:12<1321::AID-FLD562>3.3.CO;2-C

  91. 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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  93. 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

    MATH  Google Scholar 

  94. 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. doi:10.1016/S0045-7825(00)00204-8

    MATH  Google Scholar 

  95. 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

    MATH  Google Scholar 

  96. 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

    MATH  Google Scholar 

  97. 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

    MATH  Google Scholar 

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

    Google Scholar 

  99. 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

    MATH  Google Scholar 

  100. 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

    Google Scholar 

  101. 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

    MathSciNet  MATH  Google Scholar 

  102. 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

    MathSciNet  MATH  Google Scholar 

  103. 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

    MathSciNet  MATH  Google Scholar 

  104. 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

    MathSciNet  MATH  Google Scholar 

  105. 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

    MATH  Google Scholar 

  106. 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

    MathSciNet  MATH  Google Scholar 

  107. 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

    MathSciNet  MATH  Google Scholar 

  108. 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

    MathSciNet  MATH  Google Scholar 

  109. 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

    MathSciNet  MATH  Google Scholar 

  110. 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

    MathSciNet  MATH  Google Scholar 

  111. 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

    MATH  Google Scholar 

  112. 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

    MATH  Google Scholar 

  113. 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

    MathSciNet  MATH  Google Scholar 

  114. 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

    MathSciNet  MATH  Google Scholar 

  115. Manguoglu M, Sameh AH, Tezduyar TE, Sathe S (2008) A nested iterative scheme for computation of incompressible flows in long domains. Comput Mech 43:73–80. doi:10.1007/s00466-008-0276-0

    MathSciNet  MATH  Google Scholar 

  116. 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

    MathSciNet  MATH  Google Scholar 

  117. 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

    MATH  Google Scholar 

  118. 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

    MathSciNet  MATH  Google Scholar 

  119. 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

    MathSciNet  MATH  Google Scholar 

  120. Manguoglu M, Sameh AH, Saied F, Tezduyar TE, Sathe S (2009) Preconditioning techniques for nonsymmetric linear systems in the computation of incompressible flows. J Appl Mech 76:021204. doi:10.1115/1.3059576

    Google Scholar 

  121. 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

    MATH  Google Scholar 

  122. 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

    MathSciNet  MATH  Google Scholar 

  123. 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

    MathSciNet  MATH  Google Scholar 

  124. 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

    MathSciNet  MATH  Google Scholar 

  125. Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2010) Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement. Comput Mech 46:83–89. doi:10.1007/s00466-009-0426-z

    MATH  Google Scholar 

  126. 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

    MATH  Google Scholar 

  127. 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

    MATH  Google Scholar 

  128. 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

    MATH  Google Scholar 

  129. 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

    MATH  Google Scholar 

  130. Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2011) Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement. Int J Numer Methods Fluids 65:135–149. doi:10.1002/fld.2415

    MathSciNet  MATH  Google Scholar 

  131. 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

    MATH  Google Scholar 

  132. 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

    MathSciNet  MATH  Google Scholar 

  133. Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2011) A parallel sparse algorithm targeting arterial fluid mechanics computations. Comput Mech 48:377–384. doi:10.1007/s00466-011-0619-0

    MATH  Google Scholar 

  134. 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

    Google Scholar 

  135. 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

    Google Scholar 

  136. 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

    MathSciNet  Google Scholar 

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

    Google Scholar 

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

  139. 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

    MathSciNet  MATH  Google Scholar 

  140. 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

    MATH  Google Scholar 

  141. 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

    MATH  Google Scholar 

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

    Google Scholar 

  143. 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

    MathSciNet  MATH  Google Scholar 

  144. 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

    MathSciNet  MATH  Google Scholar 

  145. 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

    Google Scholar 

  146. 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

    Google Scholar 

  147. Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech 43:143–150

    MathSciNet  MATH  Google Scholar 

  148. 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

    MathSciNet  MATH  Google Scholar 

  149. Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45:217–284. doi:10.1016/0045-7825(84)90157-9

    MathSciNet  MATH  Google Scholar 

  150. Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59:307–325. doi:10.1016/0045-7825(86)90003-4

    MATH  Google Scholar 

  151. Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59:85–99

    MathSciNet  MATH  Google Scholar 

  152. Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190:411–430. doi:10.1016/S0045-7825(00)00211-5

    MATH  Google Scholar 

  153. Tezduyar TE, Ganjoo DK (1986) Petrov–Galerkin formulations with weighting functions dependent upon spatial and temporal discretization: applications to transient convection-diffusion problems. Comput Methods Appl Mech Eng 59:49–71. doi:10.1016/0045-7825(86)90023-X

    MATH  Google Scholar 

  154. Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104:397–422. doi:10.1016/0045-7825(93)90033-T

    MATH  Google Scholar 

  155. Akin JE, Tezduyar T, Ungor M, Mittal S (2003) Stabilization parameters and Smagorinsky turbulence model. J Appl Mech 70:2–9. doi:10.1115/1.1526569

    MATH  Google Scholar 

  156. Akin JE, Tezduyar TE (2004) Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements. Comput Methods Appl Mech Eng 193:1909–1922. doi:10.1016/j.cma.2003.12.050

    MATH  Google Scholar 

  157. Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195:1621–1632. doi:10.1016/j.cma.2005.05.032

    MathSciNet  MATH  Google Scholar 

  158. Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ\(\beta \) shock-capturing. Comput & Fluids 36:147–159. doi: 10.1016/j.compfluid.2005.07.009

    MATH  Google Scholar 

  159. Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ\(\beta \) shock-capturing. Comput Mech 38:469–481. doi: 10.1007/s00466-005-0025-6

    MATH  Google Scholar 

  160. Tezduyar TE, Sathe S (2006) Enhanced-discretization selective stabilization procedure (EDSSP). Comput Mech 38:456–468. doi:10.1007/s00466-006-0056-7

    MATH  Google Scholar 

  161. Catabriga L, Coutinho ALGA, Tezduyar TE (2005) Compressible flow SUPG parameters computed from element matrices. Commun Numer Methods Eng 21:465–476. doi:10.1002/cnm.759

    Google Scholar 

  162. Catabriga L, Coutinho ALGA, Tezduyar TE (2006) Compressible flow SUPG parameters computed from degree-of-freedom submatrices. Comput Mech 38:334–343. doi:10.1007/s00466-006-0033-1

    Google Scholar 

  163. Onate E, Valls A, Garcia J (2006) FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynolds numbers. Comput Mech 38:440–455

    MATH  Google Scholar 

  164. Corsini A, Rispoli F, Santoriello A, Tezduyar TE (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38:356–364. doi:10.1007/s00466-006-0045-x

    MathSciNet  MATH  Google Scholar 

  165. Rispoli F, Corsini A, Tezduyar TE (2007) Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD). Comput & Fluids 36:121–126. doi:10.1016/j.compfluid.2005.07.004

    MATH  Google Scholar 

  166. Tezduyar TE, Ramakrishnan S, Sathe S (2008) Stabilized formulations for incompressible flows with thermal coupling. Int J Numer Methods Fluids 57:1189–1209. doi:10.1002/fld.1743

    MathSciNet  MATH  Google Scholar 

  167. Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZ\(\beta \) shock-capturing. Int J Numer Methods Fluids 54:695–706. doi: 10.1002/fld.1447

    MathSciNet  MATH  Google Scholar 

  168. Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2007) YZ\(\beta \) discontinuity-capturing for advection-dominated processes with application to arterial drug delivery. Int J Numer Methods Fluids 54:593–608. doi: 10.1002/fld.1484

    MathSciNet  MATH  Google Scholar 

  169. Corsini A, Menichini C, Rispoli F, Santoriello A, Tezduyar TE (2009) A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms. J Appl Mech 76:021211. doi:10.1115/1.3062967

    Google Scholar 

  170. Rispoli F, Saavedra R, Menichini F, Tezduyar TE (2009) Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZ\(\beta \) shock-capturing. J Appl Mech 76:021209. doi: 10.1115/1.3057496

    Google Scholar 

  171. Hughes TJR, Scovazzi G, Tezduyar TE (2010) Stabilized methods for compressible flows. J Sci Comput 43:343–368. doi:10.1007/s10915-008-9233-5

    Google Scholar 

  172. Corsini A, Iossa C, Rispoli F, Tezduyar TE (2010) A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors. Comput Mech 46:159–167. doi:10.1007/s00466-009-0441-0

    MathSciNet  MATH  Google Scholar 

  173. Hsu M-C, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199:828–840. doi:10.1016/j.cma.2009.06.019

    MathSciNet  MATH  Google Scholar 

  174. Corsini A, Rispoli F, Tezduyar TE (2011) Stabilized finite element computation of NOx emission in aero-engine combustors. Int J Numer Methods Fluids 65:254–270. doi:10.1002/fld.2451

    MathSciNet  MATH  Google Scholar 

  175. Corsini A, Rispoli F, Tezduyar TE (2012) Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique. J Appl Mech 79:010910. doi:10.1115/1.4005060

    Google Scholar 

  176. Corsini A, Rispoli F, Sheard AG, Tezduyar TE (2012) Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations. Comput Mech 50:695–705. doi:10.1007/s00466-012-0789-4

    MathSciNet  MATH  Google Scholar 

  177. Kler PA, Dalcin LD, Paz RR, Tezduyar TE (2013) SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems. Comput Mech 51:171–185. doi:10.1007/s00466-012-0712-z

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work was supported in part by Rice–Waseda Research Agreement.

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  1. Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Kenji Takizawa

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Takizawa, K. Computational engineering analysis with the new-generation space–time methods. Comput Mech 54, 193–211 (2014). https://doi.org/10.1007/s00466-014-0999-z

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