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Archives of Computational Methods in Engineering

, Volume 21, Issue 4, pp 359–398 | Cite as

Aerodynamic and FSI Analysis of Wind Turbines with the ALE-VMS and ST-VMS Methods

  • Yuri Bazilevs
  • Kenji Takizawa
  • Tayfun E. Tezduyar
  • Ming-Chen Hsu
  • Nikolay Kostov
  • Spenser McIntyre
Article

Abstract

We provide an overview of the aerodynamic and FSI analysis of wind turbines the first three authors’ teams carried out in recent years with the ALE-VMS and ST-VMS methods. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian–Eulerian (ALE) method. The VMS components are from the residual-based VMS (RBVMS) method. The ST-VMS method is the VMS version of the deforming-spatial-domain/stabilized space–time (DSD/SST) method. The techniques complementing these core methods include weak enforcement of the essential boundary conditions, NURBS-based isogeometric analysis, using NURBS basis functions in temporal representation of the rotor motion, mesh motion and also in remeshing, rotation representation with constant angular velocity, Kirchhoff–Love shell modeling of the rotor-blade structure, and full FSI coupling. The analysis cases include the aerodynamics of standalone wind-turbine rotors, wind-turbine rotor and tower, and the FSI that accounts for the deformation of the rotor blades. The specific wind turbines considered are NREL 5MW, NREL Phase VI and Micon 65/13M, all at full scale, and our analysis for NREL Phase VI and Micon 65/13M includes comparison with the experimental data.

Notes

Acknowledgments

We wish to thank the Texas Advanced Computing Center (TACC) and the San Diego Supercomputing Center (SDSC) for providing HPC resources that have contributed to the research results reported in this paper. The first author acknowledges the support of the NSF CAREER Award, the NSF Award CBET-1306869, and the Air Force Office of Scientific Research Award FA9550-12-1-0005. The ST-VMS part of the work was supported by ARO grants W911NF-09-1-0346 and W911NF-12-1-0162 (third author) and Rice–Waseda Research Agreement (second author).

References

  1. 1.
    Jonkman JM, Buhl ML (2005) FAST user’s guide. Technical report NREL/EL-500-38230, National Renewable Energy Laboratory, Golden, COGoogle Scholar
  2. 2.
    Jonkman J, Butterfield S, Musial W, Scott G (2009) Definition of a 5-MW reference wind turbine for offshore system development. Technical report NREL/TP-500-38060, National Renewable Energy Laboratory, Golden, COGoogle Scholar
  3. 3.
    Sørensen NN, Michelsen JA, Schreck S (2002) Navier–Stokes predictions of the NREL phase VI rotor in the NASA Ames 80 ft \(\times \) 120 ft wind tunnel. Wind Energy 5:151–169Google Scholar
  4. 4.
    Pape AL, Lecanu J (2004) 3D Navier–Stokes computations of a stall-regulated wind turbine. Wind Energy 7:309–324Google Scholar
  5. 5.
    Zahle F, Sørensen NN, Johansen J (2009) Wind turbine rotor-tower interaction using an incompressible overset grid method. Wind Energy 12:594–619Google Scholar
  6. 6.
    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 zbMATHGoogle Scholar
  7. 7.
    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 zbMATHGoogle Scholar
  8. 8.
    Li Y, Carrica PM, Paik K-J, Xing T (2012) Dynamic overset CFD simulations of wind turbine aerodynamics. Renew Energy 37:285–298Google Scholar
  9. 9.
    Guttierez E, Primi S, Taucer F, Caperan P, Tirelli D, Mieres J, Calvo I, Rodriguez J, Vallano F, Galiotis G, Mouzakis D (2003) A wind turbine tower design based on fibre-reinforced composites. Technical report, Joint Research Centre—Ispra, European Laboratory for Structural Assessment (ELSA), Institute For Protection and Security of the Citizen (IPSC), European CommissionGoogle Scholar
  10. 10.
    Kong C, Bang J, Sugiyama Y (2005) Structural investigation of composite wind turbine blade considering various load cases and fatigue life. Energy 30:2101–2114Google Scholar
  11. 11.
    Hansen MOL, Sørensen JN, Voutsinas S, Sørensen N, Madsen HA (2006) State of the art in wind turbine aerodynamics and aeroelasticity. Prog Aerosp Sci 42:285–330Google Scholar
  12. 12.
    Jensen FM, Falzon BG, Ankersen J, Stang H (2006) Structural testing and numerical simulation of a 34 m composite wind turbine blade. Compos Struct 76:52–61Google Scholar
  13. 13.
    Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199:2403–2416zbMATHGoogle Scholar
  14. 14.
    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 89:323–336zbMATHGoogle Scholar
  15. 15.
    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 65:236–253zbMATHGoogle Scholar
  16. 16.
    Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195zbMATHMathSciNetGoogle Scholar
  17. 17.
    Cottrell JA, Reali A, Bazilevs Y, Hughes TJR (2006) Isogeometric analysis of structural vibrations. Comput Methods Appl Mech Eng 195:5257–5297zbMATHMathSciNetGoogle Scholar
  18. 18.
    Bazilevs Y, da Veiga LB, Cottrell JA, Hughes TJR, Sangalli G (2006) Isogeometric analysis: approximation, stability and error estimates for \(h\)-refined meshes. Math Models Methods Appl Sci 16:1031–1090zbMATHMathSciNetGoogle Scholar
  19. 19.
    Cottrell JA, Hughes TJR, Reali A (2007) Studies of refinement and continuity in isogeometric structural analysis. Comput Methods Appl Mech Eng 196:4160–4183zbMATHMathSciNetGoogle Scholar
  20. 20.
    Wall WA, Frenzel MA, Cyron C (2008) Isogeometric structural shape optimization. Comput Methods Appl Mech Eng 197:2976–2988zbMATHMathSciNetGoogle Scholar
  21. 21.
    Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, ChichesterGoogle Scholar
  22. 22.
    Evans JA, Bazilevs Y, Babuška I, Hughes TJR (2009) n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method. Comput Methods Appl Mech Eng 198:1726–1741zbMATHGoogle Scholar
  23. 23.
    Dörfel MR, Jüttler B, Simeon B (2010) Adaptive isogeometric analysis by local h-refinement with T-splines. Comput Methods Appl Mech Eng 199:264–275zbMATHGoogle Scholar
  24. 24.
    Bazilevs Y, Calo VM, Cottrell JA, Evans JA, Hughes TJR, Lipton S, Scott MA, Sederberg TW (2010) Isogeometric analysis using T-splines. Comput Methods Appl Mech Eng 199:229–263zbMATHMathSciNetGoogle Scholar
  25. 25.
    Auricchio F, Beirão da Veiga L, Lovadina C, Reali A (2010) The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations. Comput Methods Appl Mech Eng 199:314–323zbMATHGoogle Scholar
  26. 26.
    Wang W, Zhang Y (2010) Wavelets-based NURBS simplification and fairing. Comput Methods Appl Mech Eng 199:290–300zbMATHGoogle Scholar
  27. 27.
    Cohen E, Martin T, Kirby RM, Lyche T, Riesenfeld RF (2010) Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis. Comput Methods Appl Mech Eng 199:334–356zbMATHMathSciNetGoogle Scholar
  28. 28.
    Srinivasan V, Radhakrishnan S, Subbarayan G (2010) Coordinated synthesis of hierarchical engineering systems. Comput Methods Appl Mech Eng 199:392–404zbMATHGoogle Scholar
  29. 29.
    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 197:173–201zbMATHMathSciNetGoogle Scholar
  30. 30.
    Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196:4853–4862zbMATHMathSciNetGoogle Scholar
  31. 31.
    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 199:780–790zbMATHMathSciNetGoogle Scholar
  32. 32.
    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 41:371–378zbMATHMathSciNetGoogle Scholar
  33. 33.
    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 zbMATHMathSciNetGoogle Scholar
  34. 34.
    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 229:3402–3414zbMATHMathSciNetGoogle Scholar
  35. 35.
    Elguedj T, Bazilevs Y, Calo VM, Hughes TJR (2008) B-bar and F-bar projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order NURBS elements. Comput Methods Appl Mech Eng 197:2732–2762zbMATHGoogle Scholar
  36. 36.
    Lipton S, Evans JA, Bazilevs Y, Elguedj T, Hughes TJR (2010) Robustness of isogeometric structural discretizations under severe mesh distortion. Comput Methods Appl Mech Eng 199:357–373zbMATHGoogle Scholar
  37. 37.
    Benson DJ, Bazilevs Y, De Luycker E, Hsu M-C, Scott M, Hughes TJR, Belytschko T (2010) A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM. Int J Numer Methods Eng 83:765–785zbMATHGoogle Scholar
  38. 38.
    Benson DJ, Bazilevs Y, Hsu M-C, Hughes TJR (2010) Isogeometric shell analysis: the Reissner–Mindlin shell. Comput Methods Appl Mech Eng 199:276–289zbMATHMathSciNetGoogle Scholar
  39. 39.
    Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff–Love elements. Comput Methods Appl Mech Eng 198:3902–3914zbMATHGoogle Scholar
  40. 40.
    Zhang Y, Bazilevs Y, Goswami S, Bajaj C, Hughes TJR (2007) Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Comput Methods Appl Mech Eng 196:2943–2959zbMATHMathSciNetGoogle Scholar
  41. 41.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310–322zbMATHMathSciNetGoogle Scholar
  42. 42.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid–structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37zbMATHMathSciNetGoogle Scholar
  43. 43.
    Isaksen JG, Bazilevs Y, Kvamsdal T, Zhang Y, Kaspersen JH, Waterloo K, Romner B, Ingebrigtsen T (2008) Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39:3172–3178Google Scholar
  44. 44.
    Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech 43:143–150zbMATHMathSciNetGoogle Scholar
  45. 45.
    Cirak F, Ortiz M, Schröder P (2000) Subdivision surfaces: a new paradigm for thin shell analysis. Int J Numer Methods Eng 47:2039–2072zbMATHGoogle Scholar
  46. 46.
    Cirak F, Ortiz M (2001) Fully \({C}^1\)-conforming subdivision elements for finite deformation thin shell analysis. Int J Numer Methods Eng 51:813–833zbMATHGoogle Scholar
  47. 47.
    Cirak F, Scott MJ, Antonsson EK, Ortiz M, Schröder P (2002) Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision. Comput-Aided Des 34:137–148Google Scholar
  48. 48.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349zbMATHMathSciNetGoogle Scholar
  49. 49.
    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 127:387–401zbMATHGoogle Scholar
  50. 50.
    Hughes TJR, Oberai AA, Mazzei L (2001) Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys Fluids 13:1784–1799Google Scholar
  51. 51.
    Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Comput Mech 48:247–267. doi: 10.1007/s00466-011-0571-z zbMATHMathSciNetGoogle Scholar
  52. 52.
    Takizawa K, Tezduyar TE (2012) Space–time fluid–structure interaction methods. Math Models Methods Appl Sci 22:1230001. doi: 10.1142/S0218202512300013 MathSciNetGoogle Scholar
  53. 53.
    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 zbMATHMathSciNetGoogle Scholar
  54. 54.
    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 zbMATHMathSciNetGoogle Scholar
  55. 55.
    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 zbMATHMathSciNetGoogle Scholar
  56. 56.
    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 zbMATHMathSciNetGoogle Scholar
  57. 57.
    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 zbMATHMathSciNetGoogle Scholar
  58. 58.
    Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, LondonGoogle Scholar
  59. 59.
    Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36:12–26zbMATHMathSciNetGoogle Scholar
  60. 60.
    Nitsche J (1971) Uber ein variationsprinzip zur losung von Dirichlet-problemen bei verwendung von teilraumen, die keinen randbedingungen unterworfen sind. Abh Math Univ Hamburg 36:9–15zbMATHMathSciNetGoogle Scholar
  61. 61.
    Arnold DN, Brezzi F, Cockburn B, Marini LD (2002) Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39:1749–1779zbMATHMathSciNetGoogle Scholar
  62. 62.
    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 32:199–259zbMATHMathSciNetGoogle Scholar
  63. 63.
    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 zbMATHGoogle Scholar
  64. 64.
    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
  65. 65.
    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 zbMATHGoogle Scholar
  66. 66.
    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 zbMATHGoogle Scholar
  67. 67.
    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 zbMATHMathSciNetGoogle Scholar
  68. 68.
    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 MathSciNetGoogle Scholar
  69. 69.
    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 zbMATHMathSciNetGoogle Scholar
  70. 70.
    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 MathSciNetGoogle Scholar
  71. 71.
    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 zbMATHMathSciNetGoogle Scholar
  72. 72.
    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 zbMATHGoogle Scholar
  73. 73.
    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 zbMATHMathSciNetGoogle Scholar
  74. 74.
    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 zbMATHGoogle Scholar
  75. 75.
    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 zbMATHMathSciNetGoogle Scholar
  76. 76.
    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 zbMATHMathSciNetGoogle Scholar
  77. 77.
    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 zbMATHGoogle Scholar
  78. 78.
    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 zbMATHGoogle Scholar
  79. 79.
    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 zbMATHGoogle Scholar
  80. 80.
    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 zbMATHGoogle Scholar
  81. 81.
    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 zbMATHGoogle Scholar
  82. 82.
    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
  83. 83.
    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 zbMATHGoogle Scholar
  84. 84.
    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
  85. 85.
    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 zbMATHGoogle Scholar
  86. 86.
    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 zbMATHGoogle Scholar
  87. 87.
    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 zbMATHMathSciNetGoogle Scholar
  88. 88.
    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
  89. 89.
    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
  90. 90.
    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 zbMATHGoogle Scholar
  91. 91.
    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 zbMATHGoogle Scholar
  92. 92.
    Hsu M-C, Bazilevs Y (2012) Fluid–structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833zbMATHMathSciNetGoogle Scholar
  93. 93.
    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
  94. 94.
    Hand MM, Simms DA, Fingersh LJ, Jager DW, Cotrell JR, Schreck S, Larwood SM (2001) Unsteady aerodynamics experiment phase VI: wind tunnel test configurations and available data campaigns. Technical report NREL/TP-500-29955. National Renewable Energy Laboratory, Golden, COGoogle Scholar
  95. 95.
    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 23:249–272zbMATHMathSciNetGoogle Scholar
  96. 96.
    Johnson C (1987) Numerical solution of partial differential equations by the finite element method. Cambridge University Press, SwedenzbMATHGoogle Scholar
  97. 97.
    Brenner SC, Scott LR (2002) The mathematical theory of finite element methods, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  98. 98.
    Ern A, Guermond JL (2004) Theory and practice of finite elements. Springer, BerlinzbMATHGoogle Scholar
  99. 99.
    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 zbMATHMathSciNetGoogle Scholar
  100. 100.
    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 zbMATHGoogle Scholar
  101. 101.
    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 59:85–99zbMATHMathSciNetGoogle Scholar
  102. 102.
    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 zbMATHGoogle Scholar
  103. 103.
    Hughes TJR, Feijóo GR, Mazzei L, Quincy J-B (1998) The variational multiscale method—a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166:3–24zbMATHGoogle Scholar
  104. 104.
    Hughes TJR, Sangalli G (2007) Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal 45:539– 557zbMATHMathSciNetGoogle Scholar
  105. 105.
    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 zbMATHGoogle Scholar
  106. 106.
    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 zbMATHGoogle Scholar
  107. 107.
    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 38:440–455zbMATHGoogle Scholar
  108. 108.
    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 zbMATHMathSciNetGoogle Scholar
  109. 109.
    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 zbMATHGoogle Scholar
  110. 110.
    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 zbMATHMathSciNetGoogle Scholar
  111. 111.
    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 zbMATHMathSciNetGoogle Scholar
  112. 112.
    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
  113. 113.
    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 zbMATHMathSciNetGoogle Scholar
  114. 114.
    Launder BE, Spalding DB (1974) The numerical computation of turbulent flows. Comput Methods Appl Mech Eng 3:269–289zbMATHGoogle Scholar
  115. 115.
    Wilcox DC (1998) Turbulence modeling for CFD. DCW Industries, La Canada, CAGoogle Scholar
  116. 116.
    Kooijman HJT, Lindenburg C, Winkelaar D, van der Hooft EL (2003) DOWEC 6 MW pre-design: aero-elastic modelling of the DOWEC 6 MW pre-design in PHATAS. Technical report DOWEC-F1W2-HJK-01-046/9Google Scholar
  117. 117.
    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 zbMATHGoogle Scholar
  118. 118.
    Takizawa K, Moorman C, Wright S, Tezduyar TE (2010) Computer modeling and analysis of the Orion spacecraft parachutes. In: Bungartz H-J, Mehl M, Schafer M (eds) Fluid–structure interaction II—modelling, simulation, optimization, volume 73 of lecture notes in computational science and engineering, pp 53–81. Springer. ISBN 3642142052Google Scholar
  119. 119.
    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 zbMATHGoogle Scholar
  120. 120.
    Spera DA (1994) Introduction to modern wind turbines. In: Spera DA (eds) Wind turbine technology: fundamental concepts of wind turbine engineering. ASME Press, pp 47–72Google Scholar
  121. 121.
    Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869zbMATHMathSciNetGoogle Scholar
  122. 122.
    Karypis G, Kumar V (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20:359–392MathSciNetGoogle Scholar
  123. 123.
    Bazilevs Y, Hsu M-C, Scott MA (2012) Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41 Google Scholar
  124. 124.
    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 zbMATHMathSciNetGoogle Scholar
  125. 125.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, LondonzbMATHGoogle Scholar
  126. 126.
    Bischoff M, Wall WA, Bletzinger K-U, Ramm E (2004) Models and finite elements for thin-walled structures. In: Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, vol. 2, solids, structures and coupled problems, chapter 3. Wiley, LondonGoogle Scholar
  127. 127.
    Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis, 2nd edn. CRC Press, Boca Raton, FLGoogle Scholar
  128. 128.
    Bletzinger K-U, Kimmich S, Ramm E (1991) Efficient modeling in shape optimal design. Comput Syst Eng 2:483–495Google Scholar
  129. 129.
    Benson DJ, Bazilevs Y, Hsu M-C, Hughes TJR (2011) A large deformation, rotation-free, isogeometric shell. Comput Methods Appl Mech Eng 200:1367–1378zbMATHMathSciNetGoogle Scholar
  130. 130.
    Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. Prentice Hall, Englewood CliffszbMATHGoogle Scholar
  131. 131.
    Melbø H, Kvamsdal T (2003) Goal oriented error estimators for Stokes equations based on variationally consistent postprocessing. Comput Methods Appl Mech Eng 192:613–633Google Scholar
  132. 132.
    van Brummelen EH, Garg VV, Prudhomme S, van der Zee KG (2011) Flux evaluation in primal and dual boundary-coupled problems. J Appl Mech 79:010904Google Scholar
  133. 133.
    Zayas JR, Johnson WD (2008) 3X-100 blade field test. Report of the Sandia National Laboratories, Wind Energy Technology DepartmentGoogle Scholar
  134. 134.
    Sutherland JH, Jones PL, Neal BA (2001) The long-term inflow and structural test program. In: Proceedings of the 2001 ASME wind energy symposium, p 162Google Scholar
  135. 135.
    Berry D, Ashwill T (2007) Design of 9-meter carbon-fiberglass prototype blades: CX-100 and TX-100. Report of the Sandia National LaboratoriesGoogle Scholar
  136. 136.
    White JR, Adams DE, Rumsey MA (2011) Modal analysis of CX-100 rotor blade and Micon 65/13 wind turbine. Structural dynamics and renewable energy, volume 1, conference proceedings of the society for experimental mechanics series, p 10Google Scholar
  137. 137.
    Marinone T, LeBlanc B, Harvie J, Niezrecki C, Avitabile P (2012) Modal testing of a 9 m CX-100 turbine blade. Topics in experimental dynamics substructuring and wind turbine dynamics, volume 2, conference proceedings of the society for experimental mechanics series, p 27Google Scholar
  138. 138.
    Shield RT (1967) Inverse deformation results in finite elasticity. ZAMP 18:381–389Google Scholar
  139. 139.
    Govindjee S, Mihalic PA (1996) Computational methods for inverse finite elastostatics. Comput Methods Appl Mech Eng 136:47–57zbMATHGoogle Scholar
  140. 140.
    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 zbMATHMathSciNetGoogle Scholar

Copyright information

© CIMNE, Barcelona, Spain 2014

Authors and Affiliations

  • Yuri Bazilevs
    • 1
  • Kenji Takizawa
    • 2
  • Tayfun E. Tezduyar
    • 3
  • Ming-Chen Hsu
    • 4
  • Nikolay Kostov
    • 3
  • Spenser McIntyre
    • 3
  1. 1.Structural EngineeringUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of Modern Mechanical Engineering, Waseda Institute for Advanced StudyWaseda UniversityTokyoJapan
  3. 3.Mechanical EngineeringRice University—MS 321HoustonUSA
  4. 4.Department of Mechanical EngineeringIowa State UniversityAmesUSA

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