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Archives of Computational Methods in Engineering

, Volume 21, Issue 4, pp 481–508 | Cite as

Engineering Analysis and Design with ALE-VMS and Space–Time Methods

  • Kenji Takizawa
  • Yuri Bazilevs
  • Tayfun E. Tezduyar
  • Ming-Chen Hsu
  • Ole Øiseth
  • Kjell M. Mathisen
  • Nikolay Kostov
  • Spenser McIntyre
Article

Abstract

Flow problems with moving boundaries and interfaces include fluid–structure interaction (FSI) and a number of other classes of problems, have an important place in engineering analysis and design, and offer some formidable computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian–Eulerian method (ALE-VMS). Since their inception, these two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid–object and fluid–particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid–object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the FSI modeling were increased with the special ALE-VMS and ST FSI techniques targeting each of those classes of problems. This article provides an overview of the core ALE-VMS and ST FSI techniques, their recent versions, and the special ALE-VMS and ST FSI techniques. It also provides examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.

Keywords

Bridge Deck Oscillatory Shear Index Trim Angle NURBS Basis Function Parachute Canopy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported in part by NASA JSC grant NNX13AD87G. Method development and evaluation components of the work on aerodynamics of flapping wings and wind-turbine aerodynamics were supported in part by ARO Grant W911NF-12-1-0162 (TT) and Rice–Waseda research agreement (KT). The development and application of FOI techniques for bridge aerodynamics was supported by the program for preferred research areas at the Faculty of Engineering Science and Technology, the Norwegian University of Science and Technology. The research work on free-surface FOI was supported by the ARO Grant W911NF-11-1-0083 (YB). We wish to thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin, the San Diego Supercomputer Center (SDSC) at the University of California, San Diego, and the Norwegian Metacenter for Computational Science (Notur) for providing some of the HPC resources used. We thank Professor Fabrizio Gabbiani and Dr. Raymond Chan (Baylor College of Medicine) for providing us the digital data extracted from the wind-tunnel videos of the locust.

References

  1. 1.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Comput Mech 48:247–267. doi: 10.1007/s00466-011-0571-z zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Takizawa K, Tezduyar TE (2012) Space–time fluid–structure interaction methods. Math Models Methods Appl Sci 22:1230001. doi: 10.1142/S0218202512300013 MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, LondonCrossRefGoogle Scholar
  9. 9.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190:3009–3019zbMATHCrossRefGoogle Scholar
  11. 11.
    van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid–structure interaction problem. SIAM J Sci Comput 27:599–621zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    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 38:403–416zbMATHCrossRefGoogle Scholar
  14. 14.
    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: Bungartz H-J, Schafer M (eds) Fluid–structure Interaction, volume 53 of Lecture Notes in Computational Science and Engineering. Springer, Berlin, pp 82–100Google Scholar
  15. 15.
    Bletzinger K-U, Wuchner R, Kupzok A (2006) Algorithmic treatment of shells and free form-membranes in FSI. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction, volume 53 of Lecture Notes in Computational Science and Engineering. Springer, Berlin, pp 336–355Google Scholar
  16. 16.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43:81–90zbMATHCrossRefGoogle Scholar
  18. 18.
    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 198:3534–3550zbMATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    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 45:77–89zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Calderer R, Masud A (2010) A multiscale stabilized ALE formulation for incompressible flows with moving boundaries. Comput Mech 46:185–197zbMATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    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 46:3–16zbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    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 9:481–498CrossRefGoogle Scholar
  23. 23.
    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 zbMATHCrossRefGoogle Scholar
  24. 24.
    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 65:236–253zbMATHCrossRefGoogle Scholar
  25. 25.
    Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230:4137–4152zbMATHMathSciNetCrossRefGoogle Scholar
  26. 26.
    Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations. Finite Elem Anal Des 47:593–599MathSciNetCrossRefGoogle Scholar
  27. 27.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    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 CrossRefGoogle Scholar
  29. 29.
    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 79:010905CrossRefGoogle Scholar
  30. 30.
    Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: validation and role of weakly enforced boundary conditions. Comput Mech 50:499–511zbMATHMathSciNetCrossRefGoogle Scholar
  31. 31.
    Hsu M-C, Bazilevs Y (2012) Fluid–structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833zbMATHMathSciNetCrossRefGoogle Scholar
  32. 32.
    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 50:719–727zbMATHCrossRefGoogle Scholar
  33. 33.
    Minami S, Kawai H, Yoshimura S (2012) Parallel BDD-based monolithic approach for acoustic fluid–structure interaction. Comput Mech 50:707–718zbMATHMathSciNetCrossRefGoogle Scholar
  34. 34.
    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 50:729–741zbMATHMathSciNetCrossRefGoogle Scholar
  35. 35.
    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 50:779–788zbMATHMathSciNetCrossRefGoogle Scholar
  36. 36.
    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 50:789–804zbMATHMathSciNetCrossRefGoogle Scholar
  37. 37.
    Larese A, Rossi R, Onate E, Idelsohn SR (2012) A coupled PFEM–Eulerian approach for the solution of porous FSI problems. Comput Mech 50:805–819zbMATHMathSciNetCrossRefGoogle Scholar
  38. 38.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  39. 39.
    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 23:249–272zbMATHMathSciNetCrossRefGoogle Scholar
  40. 40.
    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 23:273–305zbMATHMathSciNetCrossRefGoogle Scholar
  41. 41.
    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 23:339–367zbMATHMathSciNetCrossRefGoogle Scholar
  42. 42.
    Hsu M-C, Akkerman I, Bazilevs Y (2014) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy 17:461–481. doi: 10.1002/we.1599
  43. 43.
    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 CrossRefGoogle Scholar
  44. 44.
    Tezduyar T, Aliabadi S, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18:397–412. doi: 10.1007/BF00350249 zbMATHCrossRefGoogle Scholar
  45. 45.
    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 zbMATHCrossRefGoogle Scholar
  46. 46.
    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 zbMATHCrossRefGoogle Scholar
  47. 47.
    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 CrossRefGoogle Scholar
  48. 48.
    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 zbMATHCrossRefGoogle Scholar
  49. 49.
    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 zbMATHCrossRefGoogle Scholar
  50. 50.
    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 CrossRefGoogle Scholar
  51. 51.
    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 zbMATHCrossRefGoogle Scholar
  52. 52.
    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 zbMATHCrossRefGoogle Scholar
  53. 53.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    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 zbMATHCrossRefGoogle Scholar
  55. 55.
    Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu MC, 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 zbMATHCrossRefGoogle Scholar
  56. 56.
    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 zbMATHCrossRefGoogle Scholar
  57. 57.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  58. 58.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  59. 59.
    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 zbMATHCrossRefGoogle Scholar
  60. 60.
    Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23:130–143. doi: 10.1007/s004660050393 zbMATHCrossRefGoogle Scholar
  61. 61.
    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 zbMATHCrossRefGoogle Scholar
  62. 62.
    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 zbMATHCrossRefGoogle Scholar
  63. 63.
    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 zbMATHCrossRefGoogle Scholar
  64. 64.
    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 zbMATHCrossRefGoogle Scholar
  65. 65.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  66. 66.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  67. 67.
    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 zbMATHCrossRefGoogle Scholar
  68. 68.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  69. 69.
    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
  70. 70.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduya TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36:160–168. doi: 10.1016/j.compfluid.2005.07.014 zbMATHCrossRefGoogle Scholar
  71. 71.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  72. 72.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  73. 73.
    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 zbMATHCrossRefGoogle Scholar
  74. 74.
    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 zbMATHCrossRefGoogle Scholar
  75. 75.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  76. 76.
    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 zbMATHCrossRefGoogle Scholar
  77. 77.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  78. 78.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  79. 79.
    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 CrossRefGoogle Scholar
  80. 80.
    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 zbMATHCrossRefGoogle Scholar
  81. 81.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  82. 82.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  83. 83.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  84. 84.
    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 zbMATHCrossRefGoogle Scholar
  85. 85.
    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 zbMATHCrossRefGoogle Scholar
  86. 86.
    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 zbMATHCrossRefGoogle Scholar
  87. 87.
    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 zbMATHCrossRefGoogle Scholar
  88. 88.
    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 zbMATHCrossRefGoogle Scholar
  89. 89.
    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 zbMATHCrossRefGoogle Scholar
  90. 90.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  91. 91.
    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 zbMATHCrossRefGoogle Scholar
  92. 92.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  93. 93.
    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 zbMATHCrossRefGoogle Scholar
  94. 94.
    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 zbMATHCrossRefGoogle Scholar
  95. 95.
    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 CrossRefGoogle Scholar
  96. 96.
    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 CrossRefGoogle Scholar
  97. 97.
    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 MathSciNetCrossRefGoogle Scholar
  98. 98.
    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 MathSciNetCrossRefGoogle Scholar
  99. 99.
    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 zbMATHCrossRefGoogle Scholar
  100. 100.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  101. 101.
    Takizawa K, Tezduyar TE (2012) Bringing them down safely. Mech Eng 134:34–37Google Scholar
  102. 102.
    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
  103. 103.
    Takizawa K, Tezduyar TE, Buscher A, Asada S (2013) Space–time interface-tracking with topology change (ST-TC). Comput Mech. published online. doi: 10.1007/s00466-013-0935-7
  104. 104.
    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 32:199–259zbMATHMathSciNetCrossRefGoogle Scholar
  105. 105.
    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
  106. 106.
    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 127:387–401zbMATHCrossRefGoogle Scholar
  107. 107.
    Hughes TJR, Oberai AA, Mazzei L (2001) Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys Fluids 13:1784–1799CrossRefGoogle Scholar
  108. 108.
    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 197:173–201zbMATHMathSciNetCrossRefGoogle Scholar
  109. 109.
    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 229:3402–3414zbMATHMathSciNetCrossRefGoogle Scholar
  110. 110.
    Akkerman I, Bazilevs Y, Calo VM, Hughes TJR, Hulshoff S (2008) The role of continuity in residual-based variational multiscale modeling of turbulence. Comput Mech 41:371–378zbMATHMathSciNetCrossRefGoogle Scholar
  111. 111.
    Bazilevs Y, Hsu M-C, Kiendl J, Benson DJ (2012) A computational procedure for pre-bending of wind turbine blades. Int J Numer Methods Eng 89:323–336zbMATHCrossRefGoogle Scholar
  112. 112.
    Korobenko A, Hsu M-C, Akkerman I, Bazilevs Y (2013) Aerodynamic simulation of vertical-axis wind turbines. J Appl Mech. 81:021011. doi: 10.1115/1.4024415
  113. 113.
    Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36:12–26zbMATHMathSciNetCrossRefGoogle Scholar
  114. 114.
    Bazilevs Y, Michler C, Calo VM, Hughes TJR (2010) Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. Comput Methods Appl Mech Eng 199:780–790zbMATHMathSciNetCrossRefGoogle Scholar
  115. 115.
    Takizawa K, Yabe T, Tsugawa Y, Tezduyar TE, Mizoe H (2007) Computation of free-surface flows and fluid–object interactions with the CIP method based on adaptive meshless Soroban grids. Comput Mech 40:167–183. doi: 10.1007/s00466-006-0093-2 zbMATHCrossRefGoogle Scholar
  116. 116.
    Takizawa K, Tanizawa K, Yabe T, Tezduyar TE (2007) Ship hydrodynamics computations with the CIP method based on adaptive Soroban grids. Int J Numer Methods Fluids 54:1011–1019. doi: 10.1002/fld.1466 zbMATHCrossRefGoogle Scholar
  117. 117.
    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 zbMATHCrossRefGoogle Scholar
  118. 118.
    Cruchaga M, Celentano D, Tezduyar T (2001) A moving Lagrangian interface technique for flow computations over fixed meshes. Comput Methods Appl Mech Eng 191:525–543. doi: 10.1016/S0045-7825(01)00300-0 zbMATHCrossRefGoogle Scholar
  119. 119.
    Sethian J (1999) Level set methods and fast marching methods. Cambridge University Press, CambridgezbMATHGoogle Scholar
  120. 120.
    Kees CE, Akkerman I, Farthing MW, Bazilevs Y (2011) A conservative level set method suitable for variable-order approximations and unstructured meshes. J Comput Phys 230:4536–4558zbMATHMathSciNetCrossRefGoogle Scholar
  121. 121.
    Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods—space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol 246/AMD-Vol 143. ASME, New York, pp 7–24Google Scholar
  122. 122.
    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 zbMATHCrossRefGoogle Scholar
  123. 123.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195zbMATHMathSciNetCrossRefGoogle Scholar
  124. 124.
    Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech 43:143–150zbMATHMathSciNetCrossRefGoogle Scholar
  125. 125.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  126. 126.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, ChichesterzbMATHGoogle Scholar
  127. 127.
    Hughes TJR, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int J Numer Methods Eng 15:1862–1867zbMATHMathSciNetCrossRefGoogle Scholar
  128. 128.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  129. 129.
    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 zbMATHCrossRefGoogle Scholar
  130. 130.
    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
  131. 131.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  132. 132.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  133. 133.
    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 CrossRefGoogle Scholar
  134. 134.
    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 zbMATHCrossRefGoogle Scholar
  135. 135.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  136. 136.
    Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics withimproved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–375zbMATHMathSciNetCrossRefGoogle Scholar
  137. 137.
    Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319zbMATHMathSciNetCrossRefGoogle Scholar
  138. 138.
    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 zbMATHMathSciNetCrossRefGoogle Scholar
  139. 139.
    Cruchaga M, Celentano D, Tezduyar T (2002) Computation of mould filling processes with a moving lagrangian interface technique. Commun Numer Methods Eng 18:483–493. doi: 10.1002/cnm.506 zbMATHCrossRefGoogle Scholar
  140. 140.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2005) Moving-interface computations with the edge–tracked interface locator technique (ETILT). Int J Numer Methods Fluids 47:451–469. doi: 10.1002/fld.825 zbMATHCrossRefGoogle Scholar
  141. 141.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2007) Collapse of a liquid column: numerical simulation and experimental validation. Comput Mech 39:453–476. doi: 10.1007/s00466-006-0043-z zbMATHCrossRefGoogle Scholar
  142. 142.
    Kleefsman KMT, Fekken G, Veldman AEP, Iwanowski B, Buchner B (2005) A volume-of-fluid based simulation method for wave impact problems. J Comput Phys 206:363–393zbMATHMathSciNetCrossRefGoogle Scholar
  143. 143.
    Fridsma G (1968) A systematic study of the rough-water performance of planing boats. Davidson Laboratory Report, p 1275Google Scholar
  144. 144.
    Longo J, Stern F (2005) Uncertainty assessment for towing tank tests with example for surface combatant DTMB model 5415. J Ship Res 49:55–68Google Scholar
  145. 145.
    Garcia J, O\(\tilde{\text{ n }}\)ate E (2003) An unstructured finite element solver for ship hydrodynamics problems. J Appl Mech 70:18–26Google Scholar
  146. 146.
    Longo J, Shao J, Irvine M, Stern F (2007) Phase-averaged PIV for the nominal wake of a surface ship in regular head waves. J Fluids Eng 129:524–541CrossRefGoogle Scholar
  147. 147.
    McCormick ME (2010) Ocean engineering mechanics. With applications. Cambridge University Press, CambridgeGoogle Scholar
  148. 148.
    Svend Ole Hansen APS (2006) The Hardanger bridge: static and dynamic wind tunnel tests with a section model. Technical report, prepared for Norwegian Public Roads AdministrationGoogle Scholar

Copyright information

© CIMNE, Barcelona, Spain 2014

Authors and Affiliations

  • Kenji Takizawa
    • 1
  • Yuri Bazilevs
    • 2
  • Tayfun E. Tezduyar
    • 3
  • Ming-Chen Hsu
    • 4
  • Ole Øiseth
    • 5
  • Kjell M. Mathisen
    • 5
  • Nikolay Kostov
    • 3
  • Spenser McIntyre
    • 3
  1. 1.Department of Modern Mechanical Engineering and Waseda Institute for Advanced StudyWaseda UniversityTokyo Japan
  2. 2.Department of Structural EngineeringUniversity of California, San DiegoLa JollaUSA
  3. 3.Mechanical EngineeringRice University – MS 321HoustonUSA
  4. 4.Department of Mechanical EngineeringIowa State UniversityAmesUSA
  5. 5.Department of Structural EngineeringNorwegian University of Science and TechnologyTrondheimNorway

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