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Stabilized space–time computation of wind-turbine rotor aerodynamics

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Abstract

We show how we use the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) formulation for accurate 3D computation of the aerodynamics of a wind-turbine rotor. As the test case, we use the NREL 5MW offshore baseline wind-turbine rotor. This class of computational problems are rather challenging, because they involve large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. We compute the problem with both the original version of the DSD/SST formulation and a recently introduced version with an advanced turbulence model. The DSD/SST formulation with the advanced turbulence model is a space–time version of the residual-based variational multiscale method. We compare our results to those reported recently, which were obtained with the residual-based variational multiscale Arbitrary Lagrangian–Eulerian method using NURBS for spatial discretization and which we take as the reference solution. While the original DSD/SST formulation yields torque values not far from the reference solution, the DSD/SST formulation with the variational multiscale turbulence model yields torque values very close to the reference solution.

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References

  1. 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

    Article  MATH  Google Scholar 

  2. 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 MethodsFluids 65: 236–253

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  6. 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

    Article  MATH  Google Scholar 

  7. 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

    Article  MathSciNet  MATH  Google Scholar 

  8. Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows—Fluid–structure interactions. Int J Numer Methods Fluids 21: 933–953

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  12. Behr M, Tezduyar T (1999) The Shear-Slip Mesh Update Method. Comput Methods Appl Mech Eng 174: 261–274

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  14. 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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  16. 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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  18. 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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  20. 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

    Article  MATH  Google Scholar 

  21. Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence ofwall elasticity on image-based blood flowsimulation. Jpn Soc Mech Eng J Ser A 70:1224–1231 (in Japanese)

    Google Scholar 

  22. Tezduyar TE, Sathe S, Keedy R, Stein K (2004) Space–time techniques for finite element computation of flows with moving boundaries and interfaces. In: Gallegos S, Herrera I, Botello S, Zarate F, Ayala G (eds) Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Science. CD-ROM, Monterrey

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

    Article  MathSciNet  MATH  Google Scholar 

  24. 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

    Article  MathSciNet  MATH  Google Scholar 

  25. 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

    Article  MathSciNet  MATH  Google Scholar 

  26. 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

    Article  MathSciNet  MATH  Google Scholar 

  27. 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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  30. 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

    Article  MathSciNet  MATH  Google Scholar 

  31. 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

    Article  MATH  Google Scholar 

  32. Sawada T, Hisada T (2007) Fuid–structure interaction analysis of the two dimensional flag-in-wind problem by an interface tracking ALE finite element method. Comput Fluids 36: 136–146

    Article  MATH  Google Scholar 

  33. 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

    Article  MathSciNet  MATH  Google Scholar 

  34. 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

    Article  MathSciNet  MATH  Google Scholar 

  35. 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

    Article  MathSciNet  MATH  Google Scholar 

  36. 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

    Article  MATH  Google Scholar 

  37. 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

    Article  MathSciNet  MATH  Google Scholar 

  38. 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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  40. 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: 3172–3178

    Article  Google Scholar 

  41. Kuttler U, Wall WA (2008) Fixed-point fluid–structure interaction solvers with dynamic relaxation. Comput Mech 43: 61–72

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  44. Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled Arterial Fluid–Structure Interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198: 3524–3533

    Article  MathSciNet  MATH  Google Scholar 

  45. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  47. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  49. 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

    Article  MATH  Google Scholar 

  50. Tezduyar TE, Takizawa K, Christopher J (2009) Multiscale Sequentially-Coupled Arterial Fluid–Structure Interaction (SCAFSI) technique”. In: Hartmann S, Meister A, Schaefer M, Turek S (eds) International workshop on fluid–structure interaction—theory, numerics and applications. Kassel University Press, Germany, pp 231–252

  51. Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46: 17–29

    Article  MathSciNet  MATH  Google Scholar 

  52. 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

    Article  MathSciNet  MATH  Google Scholar 

  53. 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

    Article  MathSciNet  MATH  Google Scholar 

  54. 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

    Article  MATH  Google Scholar 

  55. 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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  57. 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

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  59. 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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  61. 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

    Article  MathSciNet  MATH  Google Scholar 

  62. 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. doi:10.1002/cnm.1433

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

  64. Tezduyar T, Aliabadi S, Behr M (1998) Enhanced-Discretization Interface-Capturing Technique (EDICT) for computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 155: 235–248

    Article  MATH  Google Scholar 

  65. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575

    Article  MathSciNet  MATH  Google Scholar 

  66. Tezduyar T, Aliabadi S, Behr M (1997) Enhanced-Discretization Interface-Capturing Technique. In: Matsumoto Y, Prosperetti A (eds) ISAC ’97 High Performance Computing on Multiphase Flows. Japan Society of Mechanical Engineers, Japan, pp 1–6

  67. Benek JA, Buning PG, Steger JL (1985) A 3-D chimera grid embedding technique. Paper 85-1523, AIAA, New York

  68. 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

    Article  MATH  Google Scholar 

  69. 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

    Article  MATH  Google Scholar 

  70. Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44

    Article  MathSciNet  MATH  Google Scholar 

  71. 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

    Article  MathSciNet  MATH  Google Scholar 

  72. 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

    Article  MathSciNet  MATH  Google Scholar 

  73. 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

    Article  MathSciNet  MATH  Google Scholar 

  74. 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

    Article  MATH  Google Scholar 

  75. 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

    Article  MathSciNet  MATH  Google Scholar 

  76. Hughes TJR, Hulbert GM (1988) Space–time finite element methods for elastodynamics: formulations and error estimates. Comput Methods Appl Mech Eng 66: 339–363

    Article  MathSciNet  MATH  Google Scholar 

  77. Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59: 307–325

    Article  MATH  Google Scholar 

  78. Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  80. Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, Borst RD, Hughes TJR (eds) Encyclopedia of Computational Mechanics: fluids, vol 3, Chap 17. John Wiley and Sons, New York

  81. 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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  83. 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

    Article  MathSciNet  MATH  Google Scholar 

  84. Catabriga L, Coutinho ALGA, Tezduyar TE (2006) Compressible flow SUPG parameters computed from degree-of-freedom submatrices. Comput Mech 38: 334–343

    Article  MATH  Google Scholar 

  85. Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206

    Article  MathSciNet  MATH  Google Scholar 

  86. 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

    Article  MATH  Google Scholar 

  87. Catabriga L, de Souza DAF, Coutinho ALGA, Tezduyar TE (2009) Three-dimensional edge-based SUPG computation of inviscid compressible flows with YZβ shock-capturing. J Appl Mech 76: 021208

    Article  Google Scholar 

  88. 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

    Article  MathSciNet  MATH  Google Scholar 

  89. 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

    Article  MathSciNet  MATH  Google Scholar 

  90. 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

    Article  MathSciNet  MATH  Google Scholar 

  91. Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43: 133–142

    Article  MATH  Google Scholar 

  92. 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

    Article  MATH  Google Scholar 

  93. 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

    Article  MATH  Google Scholar 

  94. Hughes TJR, Mazzei L, Jansen KE (2000) Large-eddy simulation and the variational multiscale method. Comput Vis Sci 3: 47–59

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  96. 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: 539–557

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  99. 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

  100. Kooijman HJT, Lindenburg C, Winkelaar D, van der Hooft E (2003) DOWEC 6 MW pre-design: aero-elastic modelling of the DOWEC 6 MW pre-design in PHATAS. Technical Report DOWEC-F1W2-HJK-01-046/9

  101. Jonkman JM, Jr MLB (2005) FAST user’s guide. Technical Report NREL/EL-500-38230, National Renewable Energy Laboratory, Golden

  102. Spera DA (1994) Introduction to modern wind turbines. In: Spera DA (ed) Wind turbine technology: fundamental concepts of wind Turbine engineering. ASME Press, New York, pp 47–72

    Google Scholar 

  103. 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, Lecture Notes in Computational Science and Engineering, vol 73. Springer, Berlin, pp 53–81

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

    Article  MathSciNet  MATH  Google Scholar 

  105. Karypis G, Kumar V (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20: 359–392

    Article  MathSciNet  Google Scholar 

  106. Spalart PR (2000) Strategies for turbulence modelling and simulations. Int J Heat Fluid Flow 21: 252–263

    Article  Google Scholar 

  107. 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: 780–790

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  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

  2. Mechanical Engineering, Rice University, MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Bradley Henicke & Tayfun E. Tezduyar

  3. Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

    Ming-Chen Hsu & Yuri Bazilevs

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  1. Kenji Takizawa
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  2. Bradley Henicke
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  3. Tayfun E. Tezduyar
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  4. Ming-Chen Hsu
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  5. Yuri Bazilevs
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Correspondence to Tayfun E. Tezduyar.

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Takizawa, K., Henicke, B., Tezduyar, T.E. et al. Stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech 48, 333–344 (2011). https://doi.org/10.1007/s00466-011-0589-2

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