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Wind turbine wake computation with the ST-VMS method, isogeometric discretization and multidomain method: I. Computational framework

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Abstract

In this first part of a two-part article, we present a framework for wind turbine wake computation. The framework is made of the Space–Time Variational Multiscale (ST-VMS) method, ST isogeometric discretization, and the Multidomain Method (MDM). The ST context provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables increased accuracy in the flow solution. With the MDM, a long wake can be computed over a sequence of subdomains, instead of a single, long domain, thus somewhat reducing the computational cost. Furthermore, with the MDM, the computation over a downstream subdomain can start several turbine rotations after the computation over the upstream subdomain starts, thus reducing the computational cost even more. All these good features of the framework, in combination, enable accurate representation of the turbine long-wake vortex patterns in a computationally efficient way. In the computations we present, the velocity data on the inflow plane comes from a previous wind turbine computation, extracted by projection from a plane located 10 m downstream of the turbine, which has a diameter of 126 m. The results show the effectiveness of the framework in wind turbine long-wake computation.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Takizawa K, Tezduyar TE, Kuraishi T (2015) Multiscale ST methods for thermo-fluid analysis of a ground vehicle and its tires. Math Models Methods Appl Sci 25:2227–2255. https://doi.org/10.1142/S0218202515400072

    Article  MathSciNet  MATH  Google Scholar 

  3. Takizawa K, Tezduyar TE, Otoguro Y, Terahara T, Kuraishi T, Hattori H (2017) Turbocharger flow computations with the space-time isogeometric analysis (ST-IGA). Comput Fluids 142:15–20. https://doi.org/10.1016/j.compfluid.2016.02.021

    Article  MathSciNet  MATH  Google Scholar 

  4. Osawa Y, Kalro V, Tezduyar T (1999) Multi-domain parallel computation of wake flows. Comput Methods Appl Mech Eng 174:371–391. https://doi.org/10.1016/S0045-7825(98)00305-3

    Article  MATH  Google Scholar 

  5. Korobenko A, Yan J, Gohari SMI, Sarkar S, Bazilevs Y (2017) FSI simulation of two back-to-back wind turbines in atmospheric boundary layer flow. Comput Fluids 158:167–175. https://doi.org/10.1016/j.compfluid.2017.05.010

    Article  MathSciNet  MATH  Google Scholar 

  6. 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 

  7. Bazilevs Y, Takizawa K, Tezduyar TE (February 2013) Computational fluid-structure interaction: methods and applications. Wiley, ISBN 978-0470978771

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Hughes TJR, Brooks AN (1979) A multi-dimensional upwind scheme with no crosswind diffusion. In: Hughes TJR (ed) Finite element methods for convection dominated flows, AMD, vol 34. ASME, New York, pp 19–35

    Google Scholar 

  10. 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 

  11. Tezduyar TE, Hughes TJR (1982) Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. In: NASA Technical Report NASA-CR-204772. NASA, http://www.researchgate.net/publication/24313718/

  12. Tezduyar TE, Hughes TJR (1983) Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: Proceedings of AIAA 21st aerospace sciences meeting, AIAA Paper 83-0125, Reno, Nevada, https://doi.org/10.2514/6.1983-125

  13. 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. https://doi.org/10.1016/0045-7825(84)90157-9

    Article  MathSciNet  MATH  Google Scholar 

  14. 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  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  19. Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Models Methods Appl Sci 22(supp02):1230001. https://doi.org/10.1142/S0218202512300013

    Article  MathSciNet  MATH  Google Scholar 

  20. 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 

  21. 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. https://doi.org/10.1016/S0045-7825(00)00204-8

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  23. Hsu M-C, Akkerman I, Bazilevs Y (2011) High-performance computing of wind turbine aerodynamics using isogeometric analysis. Comput Fluids 49:93–100

    Article  MathSciNet  MATH  Google Scholar 

  24. 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

    Article  MathSciNet  MATH  Google Scholar 

  25. 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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  27. Bazilevs Y, Korobenko A, Deng X, Yan J (2015) Novel structural modeling and mesh moving techniques for advanced FSI simulation of wind turbines. Int J Numer Methods Eng 102:766–783. https://doi.org/10.1002/nme.4738

    Article  MATH  Google Scholar 

  28. Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2018) Recent advances in ALE-VMS and ST-VMS computational aerodynamic and FSI analysis of wind turbines. In: Tezduyar TE (eds),Frontiers in computational fluid–structure interaction and flow simulation: research from lead investigators under forty—2018, modeling and simulation in science, engineering and technology. Springer, pp 253–336, ISBN 978-3-319-96468-3, https://doi.org/10.1007/978-3-319-96469-0_7

  29. Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Otoguro Y, Mochizuki H, Wu MCH (2020) Wind turbine and turbomachinery computational analysis with the ALE and space-time variational multiscale methods and isogeometric discretization. J Adv Eng Comput 4:1–32. https://doi.org/10.25073/jaec.202041.278

    Article  MATH  Google Scholar 

  30. Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Otoguro Y, Mochizuki H, Wu MCH (2020) ALE and space–time variational multiscale isogeometric analysis of wind turbines and turbomachinery. In: Grama A, Sameh A (eds.), Parallel algorithms in computational science and engineering, modeling and simulation in science, engineering and technology. Springer, pp 195–233, ISBN 978-3-030-43735-0. https://doi.org/10.1007/978-3-030-43736-7_7

  31. Ravensbergen M, Bayram AM, Korobenko A (2020) The actuator line method for wind turbine modelling applied in a variational multiscale framework. Comput Fluids 201:104465. https://doi.org/10.1016/j.compfluid.2020.104465

    Article  MathSciNet  MATH  Google Scholar 

  32. Korobenko A, Hsu M-C, Akkerman I, Bazilevs Y (2013) Aerodynamic simulation of vertical-axis wind turbines. J Appl Mech 81:021011. https://doi.org/10.1115/1.4024415

    Article  Google Scholar 

  33. Bazilevs Y, Korobenko A, Deng X, Yan J, Kinzel M, Dabiri JO (2014) FSI modeling of vertical-axis wind turbines. J Appl Mech 81:081006. https://doi.org/10.1115/1.4027466

    Article  Google Scholar 

  34. Bayram AM, Bear C, Bear M, Korobenko A (2020) Performance analysis of two vertical-axis hydrokinetic turbines using variational multiscale method. Comput Fluids 200:104432. https://doi.org/10.1016/j.compfluid.2020.104432

    Article  MathSciNet  MATH  Google Scholar 

  35. Yan J, Korobenko A, Deng X, Bazilevs Y (2016) Computational free-surface fluid-structure interaction with application to floating offshore wind turbines. Comput Fluids 141:155–174. https://doi.org/10.1016/j.compfluid.2016.03.008

    Article  MathSciNet  MATH  Google Scholar 

  36. Bazilevs Y, Korobenko A, Yan J, Pal A, Gohari SMI, Sarkar S (2015) ALE-VMS formulation for stratified turbulent incompressible flows with applications. Math Models Methods Appl Sci 25:2349–2375. https://doi.org/10.1142/S0218202515400114

    Article  MathSciNet  MATH  Google Scholar 

  37. Takizawa K, Bazilevs Y, Tezduyar TE, Korobenko A (2020) Computational flow analysis in aerospace, energy and transportation technologies with the variational multiscale methods. J Adv Eng Comput 4:83–117. https://doi.org/10.25073/jaec.202042.279

    Article  MATH  Google Scholar 

  38. Takizawa K, Bazilevs Y, Tezduyar TE, Korobenko A (2020) Variational multiscale flow analysis in aerospace, energy and transportation technologies. In: Grama A, Sameh A (eds) Parallel algorithms in computational science and engineering, modeling and simulation in science, engineering and technology. Springer, pp 235–280, ISBN 978-3-030-43735-0. https://doi.org/10.1007/978-3-030-43736-7_8

  39. Bazilevs Y, Korobenko A, Deng X, Yan J (2016) FSI modeling for fatigue-damage prediction in full-scale wind-turbine blades. J Appl Mech 83(6):061010

    Article  Google Scholar 

  40. 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 

  41. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

  43. 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 

  44. 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 

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

    Article  MathSciNet  Google Scholar 

  46. Long CC, Marsden AL, Bazilevs Y (2013) Fluid-structure interaction simulation of pulsatile ventricular assist devices. Comput Mech 52:971–981. https://doi.org/10.1007/s00466-013-0858-3

    Article  MATH  Google Scholar 

  47. Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2014) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech 54:911–919. https://doi.org/10.1007/s00466-013-0931-y

    Article  MathSciNet  MATH  Google Scholar 

  48. Long CC, Marsden AL, Bazilevs Y (2014) Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech 54:921–932. https://doi.org/10.1007/s00466-013-0967-z

    Article  MathSciNet  MATH  Google Scholar 

  49. Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54:1055–1071. https://doi.org/10.1007/s00466-014-1059-4

    Article  MathSciNet  MATH  Google Scholar 

  50. Hsu M-C, Kamensky D, Xu F, Kiendl J, Wang C, Wu MCH, Mineroff J, Reali A, Bazilevs Y, Sacks MS (2015) Dynamic and fluid-structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models. Comput Mech 55:1211–1225. https://doi.org/10.1007/s00466-015-1166-x

    Article  MATH  Google Scholar 

  51. Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves. Comput Methods Appl Mech Eng 284:1005–1053

    Article  MathSciNet  MATH  Google Scholar 

  52. Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C (2019) Computational cardiovascular flow analysis with the variational multiscale methods. J Adv Eng Comput 3:366–405. https://doi.org/10.25073/jaec.201932.245

    Article  Google Scholar 

  53. Hughes TJR, Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C (2020) Computational cardiovascular analysis with the variational multiscale methods and isogeometric discretization. In: Grama A, Sameh A (eds) Parallel algorithms in computational science and engineering, modeling and simulation in science, engineering and technology. Springer, pp 151–193, ISBN 978-3-030-43735-0, https://doi.org/10.1007/978-3-030-43736-7_6

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  56. Wang C, Wu MCH, Xu F, Hsu M-C, Bazilevs Y (2017) Modeling of a hydraulic arresting gear using fluid-structure interaction and isogeometric analysis. Comput Fluids 142:3–14. https://doi.org/10.1016/j.compfluid.2015.12.004

    Article  MathSciNet  MATH  Google Scholar 

  57. Wu MCH, Kamensky D, Wang C, Herrema AJ, Xu F, Pigazzini MS, Verma A, Marsden AL, Bazilevs Y, Hsu M-C (2017) Optimizing fluid-structure interaction systems with immersogeometric analysis and surrogate modeling: application to a hydraulic arresting gear. Comput Methods Appl Mech Eng 316:668–693

    Article  MathSciNet  MATH  Google Scholar 

  58. Yan J, Deng X, Korobenko A, Bazilevs Y (2017) Free-surface flow modeling and simulation of horizontal-axis tidal-stream turbines. Comput Fluids 158:157–166. https://doi.org/10.1016/j.compfluid.2016.06.016

    Article  MathSciNet  MATH  Google Scholar 

  59. Yan J, Deng X, Xu F, Xu S, Zhu Q (2020) Numerical simulations of two back-to-back horizontal axis tidal stream turbines in free-surface flows. J Appl Mech 87(6):061001. https://doi.org/10.1115/1.4046317

    Article  Google Scholar 

  60. Augier B, Yan J, Korobenko A, Czarnowski J, Ketterman G, Bazilevs Y (2015) Experimental and numerical FSI study of compliant hydrofoils. Comput Mech 55:1079–1090. https://doi.org/10.1007/s00466-014-1090-5

    Article  MATH  Google Scholar 

  61. Yan J, Augier B, Korobenko A, Czarnowski J, Ketterman G, Bazilevs Y (2016) FSI modeling of a propulsion system based on compliant hydrofoils in a tandem configuration. Comput Fluids 141:201–211. https://doi.org/10.1016/j.compfluid.2015.07.013

    Article  MathSciNet  MATH  Google Scholar 

  62. Helgedagsrud TA, Bazilevs Y, Mathisen KM, Oiseth OA (2019) Computational and experimental investigation of free vibration and flutter of bridge decks. Comput Mech 63:121–136. https://doi.org/10.1007/s00466-018-1587-4

    Article  MathSciNet  MATH  Google Scholar 

  63. Helgedagsrud TA, Bazilevs Y, Korobenko A, Mathisen KM, Oiseth OA (2019) Using ALE-VMS to compute aerodynamic derivatives of bridge sections. Comput Fluids 179:820–832. https://doi.org/10.1016/j.compfluid.2018.04.037

    Article  MathSciNet  MATH  Google Scholar 

  64. Helgedagsrud TA, Akkerman I, Bazilevs Y, Mathisen KM, Oiseth OA (2019) Isogeometric modeling and experimental investigation of moving-domain bridge aerodynamics. ASCE J Eng Mech 145:04019026. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001601

    Article  Google Scholar 

  65. Helgedagsrud TA, Bazilevs Y, Mathisen KM, Yan J, Oiseth OA (2019) Modeling and simulation of bridge-section buffeting response in turbulent flow. Math Models Methods Appl Sci 29:939–966. https://doi.org/10.1142/S0218202519410045

    Article  MathSciNet  MATH  Google Scholar 

  66. Helgedagsrud TA, Bazilevs Y, Mathisen KM, Oiseth OA (2019) ALE-VMS methods for wind-resistant design of long-span bridges. J Wind Eng Ind Aerodyn 191:143–153. https://doi.org/10.1016/j.jweia.2019.06.001

    Article  Google Scholar 

  67. Yan J, Korobenko A, Tejada-Martinez AE, Golshan R, Bazilevs Y (2017) A new variational multiscale formulation for stratified incompressible turbulent flows. Comput Fluids 158:150–156. https://doi.org/10.1016/j.compfluid.2016.12.004

    Article  MathSciNet  MATH  Google Scholar 

  68. Ravensbergen M, Helgedagsrud TA, Bazilevs Y, Korobenko A (2020) A variational multiscale framework for atmospheric turbulent flows over complex environmental terrains. Comput Methods Appl Mech Eng 368:113182. https://doi.org/10.1016/j.cma.2020.113182

    Article  MathSciNet  MATH  Google Scholar 

  69. Xu F, Moutsanidis G, Kamensky D, Hsu M-C, Murugan M, Ghoshal A, Bazilevs Y (2017) Compressible flows on moving domains: stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling. Comput Fluids 158:201–220. https://doi.org/10.1016/j.compfluid.2017.02.006

    Article  MathSciNet  MATH  Google Scholar 

  70. Murugan M, Ghoshal A, Xu F, Hsu M-C, Bazilevs Y, Bravo L, Kerner K (2017) Analytical study of articulating turbine rotor blade concept for improved off-design performance of gas turbine engines. J Eng Gas Turbines Power 139:102601–6

    Article  Google Scholar 

  71. Kozak N, Xu F, Rajanna MR, Bravo L, Murugan M, Ghoshal A, Bazilevs Y, Hsu M-C (2020) High-fidelity finite element modeling and analysis of adaptive gas turbine stator-rotor flow interaction at off-design conditions. J Mech 36:595–606

    Article  Google Scholar 

  72. Kozak N, Rajanna MR, Wu MCH, Murugan M, Bravo L, Ghoshal A, Hsu M-C, Bazilevs Y (2020) Optimizing gas turbine performance using the surrogate management framework and high-fidelity flow modeling. Energies 13:4283

    Article  Google Scholar 

  73. Bazilevs Y, Takizawa K, Wu MCH, Kuraishi T, Avsar R, Xu Z, Tezduyar TE (2021) Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method. Comput Mech 67:57–84. https://doi.org/10.1007/s00466-020-01919-w

    Article  MathSciNet  MATH  Google Scholar 

  74. Codoni D, Moutsanidis G, Hsu M-C, Bazilevs Y, Johansen C, Korobenko A (2021) Stabilized methods for high-speed compressible flows: toward hypersonic simulations. Comput Mech 67:785–809. https://doi.org/10.1007/s00466-020-01963-6

    Article  MathSciNet  Google Scholar 

  75. Bayram AM, Korobenko A (2020) Variational multiscale framework for cavitating flows. Comput Mech 66:49–67. https://doi.org/10.1007/s00466-020-01840-2

    Article  MathSciNet  MATH  Google Scholar 

  76. Cen H, Zhou Q, Korobenko A (2021) Variational multiscale framework for cavitating flows. Comput Fluids 214:104765. https://doi.org/10.1016/j.compfluid.2020.104765

    Article  MathSciNet  MATH  Google Scholar 

  77. Zhu Q, Liu Z, Yan J (2021) Machine learning for metal additive manufacturing: predicting temperature and melt pool fluid dynamics using physics-informed neural networks. Comput Mech 67:619–635. https://doi.org/10.1007/s00466-020-01952-9

    Article  MathSciNet  MATH  Google Scholar 

  78. Xu S, Liu N, Yan J (2019) Residual-based variational multi-scale modeling for particle-laden gravity currents over flat and triangular wavy terrains. Comput Fluids 188:114–124

    Article  MathSciNet  MATH  Google Scholar 

  79. Yan J, Yan W, Lin S, Wagner G (2018) A fully coupled finite element formulation for liquid-solid-gas thermo-fluid flow with melting and solidification. Comput Methods Appl Mech Eng 336:444–470

    Article  MathSciNet  MATH  Google Scholar 

  80. Yan J, Lin SS, Bazilevs Y, Wagner G (2019) Isogeometric analysis of multi-phase flows with surface tension and with application to dynamics of rising bubbles. Comput Fluids 179:777–789

    Article  MathSciNet  MATH  Google Scholar 

  81. Zhao Z, Zhu Q, Yan J (2021) A thermal multi-phase flow model for directed energy deposition processes via a moving signed distance function. Comput Methods Appl Mech Eng 373:113518

    Article  MathSciNet  MATH  Google Scholar 

  82. Zhao Z, Yan J (2020) Variational multi-scale modeling of interfacial flows with a balanced-force surface tension model. Mech Res Commun. https://doi.org/10.1016/j.mechrescom.2020.103608

    Article  Google Scholar 

  83. Zhu Q, Xu F, Xu S, Hsu M-C, Yan J (2020) An immersogeometric formulation for free-surface flows with application to marine engineering problems. Comput Methods Appl Mech Eng 361:112748

    Article  MathSciNet  MATH  Google Scholar 

  84. Zhu Q, Yan J, Tejada-Martínez A, Bazilevs Y (2020) Variational multiscale modeling of Langmuir turbulent boundary layers in shallow water using isogeometric analysis. Mech Res Commun 108:103570. https://doi.org/10.1016/j.mechrescom.2020.103570

    Article  Google Scholar 

  85. Zhu Q, Yan J (2021) A moving-domain CFD solver in FEniCS with applications to tidal turbine simulations in turbulent flows. Comput Math Appl 81:532–546

    Article  MathSciNet  MATH  Google Scholar 

  86. Hsu M-C, Wang C, Xu F, Herrema AJ, Krishnamurthy A (2016) Direct immersogeometric fluid flow analysis using B-rep CAD models. Comput Aided Geom Des 43:143–158

    Article  MathSciNet  MATH  Google Scholar 

  87. Xu F, Schillinger D, Kamensky D, Varduhn V, Wang C, Hsu M-C (2016) The tetrahedral finite cell method for fluids: immersogeometric analysis of turbulent flow around complex geometries. Comput Fluids 141:135–154

    Article  MathSciNet  MATH  Google Scholar 

  88. Wang C, Xu F, Hsu M-C, Krishnamurthy A (2017) Rapid B-rep model preprocessing for immersogeometric analysis using analytic surfaces. Comput Aided Geom Des 52–53:190–204

    Article  MathSciNet  MATH  Google Scholar 

  89. Xu S, Xu F, Kommajosula A, Hsu M-C, Ganapathysubramanian B (2019) Immersogeometric analysis of moving objects in incompressible flows. Comput Fluids 189:24–33

    Article  MathSciNet  MATH  Google Scholar 

  90. Xu S, Gao B, Lofquist A, Fernando M, Hsu M-C, Sundar H, Ganapathysubramanian B (2020) An octree-based immersogeometric approach for modeling inertial migration of particles in channels. Comput Fluids 214:104764

    Article  MathSciNet  MATH  Google Scholar 

  91. Kamensky D, Evans JA, Hsu M-C (2015) Stability and conservation properties of collocated constraints in immersogeometric fluid-thin structure interaction analysis. Commun Comput Phys 18:1147–1180

    Article  MathSciNet  MATH  Google Scholar 

  92. Kamensky D, Evans JA, Hsu M-C, Bazilevs Y (2017) Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid-thin structure interaction analysis, with application to heart valve modeling. Comput Math Appl 74:2068–2088. https://doi.org/10.1016/j.camwa.2017.07.006

    Article  MathSciNet  MATH  Google Scholar 

  93. Kamensky D, Hsu M-C, Yu Y, Evans JA, Sacks MS, Hughes TJR (2017) Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines. Comput Methods Appl Mech Eng 314:408–472

    Article  MathSciNet  MATH  Google Scholar 

  94. Xu F, Morganti S, Zakerzadeh R, Kamensky D, Auricchio F, Reali A, Hughes TJR, Sacks MS, Hsu M-C (2018) A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis. Int J Numer Methods Biomed Eng 34:e2938

    Article  MathSciNet  Google Scholar 

  95. Yu Y, Kamensky D, Hsu M-C, Lu XY, Bazilevs Y, Hughes TJR (2018) Error estimates for projection-based dynamic augmented Lagrangian boundary condition enforcement, with application to fluid-structure interaction. Math Models Methods Appl Sci 28:2457–2509. https://doi.org/10.1142/S0218202518500537

    Article  MathSciNet  MATH  Google Scholar 

  96. Wu MCH, Zakerzadeh R, Kamensky D, Kiendl J, Sacks MS, Hsu M-C (2018) An anisotropic constitutive model for immersogeometric fluid-structure interaction analysis of bioprosthetic heart valves. J Biomech 74:23–31

    Article  Google Scholar 

  97. Wu MCH, Muchowski HM, Johnson EL, Rajanna MR, Hsu M-C (2019) Immersogeometric fluid-structure interaction modeling and simulation of transcatheter aortic valve replacement. Comput Methods Appl Mech Eng 357:112556

    Article  MathSciNet  MATH  Google Scholar 

  98. Johnson EL, Wu MCH, Xu F, Wiese NM, Rajanna MR, Herrema AJ, Ganapathysubramanian B, Hughes TJR, Sacks MS, Hsu M-C (2020) Thinner biological tissues induce leaflet flutter in aortic heart valve replacements. Proc Natl Acad Sci 117:19007–19016

    Article  Google Scholar 

  99. Xu F, Johnson EL, Wang C, Jafari A, Yang C-H, Sacks MS, Krishnamurthy A, Hsu M-C (2021) Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement. Mech Res Commun. https://doi.org/10.1016/j.mechrescom.2020.103604

    Article  Google Scholar 

  100. 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. https://doi.org/10.1002/fld.2221

    Article  MATH  Google Scholar 

  101. 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 7–24

  102. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36. https://doi.org/10.1109/2.237441

    Article  MATH  Google Scholar 

  103. Terahara T, Takizawa K, Tezduyar TE, Tsushima A, Shiozaki K (2020) Ventricle-valve-aorta flow analysis with the space-time isogeometric discretization and topology change. Comput Mech 65:1343–1363. https://doi.org/10.1007/s00466-020-01822-4

    Article  MathSciNet  MATH  Google Scholar 

  104. 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. https://doi.org/10.1007/s00466-013-0880-5

    Article  MATH  Google Scholar 

  105. Takizawa K, Tezduyar TE, Avsar R (2020) A low-distortion mesh moving method based on fiber-reinforced hyperelasticity and optimized zero-stress state. Comput Mech 65:1567–1591. https://doi.org/10.1007/s00466-020-01835-z

    Article  MathSciNet  MATH  Google Scholar 

  106. Tonon P, Sanches RAK, Takizawa K, Tezduyar TE (2021) A linear-elasticity-based mesh moving method with no cycle-to-cycle accumulated distortion. Comput Mech 67:413–434. https://doi.org/10.1007/s00466-020-01941-y

    Article  MathSciNet  MATH  Google Scholar 

  107. Tezduyar TE, Takizawa K (2019) Space-time computations in practical engineering applications: a summary of the 25-year history. Comput Mech 63:747–753. https://doi.org/10.1007/s00466-018-1620-7

    Article  MATH  Google Scholar 

  108. 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. https://doi.org/10.1142/S0218202513400058

    Article  MathSciNet  MATH  Google Scholar 

  109. Takizawa K, Tezduyar TE, Kolesar R (2015) FSI modeling of the Orion spacecraft drogue parachutes. Comput Mech 55:1167–1179. https://doi.org/10.1007/s00466-014-1108-z

    Article  MATH  Google Scholar 

  110. 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. https://doi.org/10.1007/s00466-013-0888-x

    Article  MATH  Google Scholar 

  111. Takizawa K, Tezduyar TE, Mochizuki H, Hattori H, Mei S, Pan L, Montel K (2015) Space-time VMS method for flow computations with slip interfaces (ST-SI). Math Models Methods Appl Sci 25:2377–2406. https://doi.org/10.1142/S0218202515400126

    Article  MathSciNet  MATH  Google Scholar 

  112. Otoguro Y, Mochizuki H, Takizawa K, Tezduyar TE (2020) Space-time variational multiscale isogeometric analysis of a tsunami-shelter vertical-axis wind turbine. Comput Mech 66:1443–1460. https://doi.org/10.1007/s00466-020-01910-5

    Article  MathSciNet  MATH  Google Scholar 

  113. 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. https://doi.org/10.1115/1.4005073

    Article  MATH  Google Scholar 

  114. 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. https://doi.org/10.1007/s00466-012-0759-x

    Article  MATH  Google Scholar 

  115. 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. https://doi.org/10.1007/s00466-012-0758-y

    Article  MATH  Google Scholar 

  116. Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time interface-tracking with topology change (ST-TC). Comput Mech 54:955–971. https://doi.org/10.1007/s00466-013-0935-7

    Article  MathSciNet  MATH  Google Scholar 

  117. Takizawa K, Tezduyar TE, Buscher A (2015) Space-time computational analysis of MAV flapping-wing aerodynamics with wing clapping. Comput Mech 55:1131–1141. https://doi.org/10.1007/s00466-014-1095-0

    Article  Google Scholar 

  118. Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486. https://doi.org/10.1142/S0218202514500250

    Article  MathSciNet  MATH  Google Scholar 

  119. 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. https://doi.org/10.1007/s00466-012-0760-4

    Article  MathSciNet  MATH  Google Scholar 

  120. 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. https://doi.org/10.1007/s00466-012-0790-y

    Article  MathSciNet  MATH  Google Scholar 

  121. Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T, Tezduyar TE (2016) A geometrical-characteristics study in patient-specific FSI analysis of blood flow in the thoracic aorta. In: Bazilevs Y, Takizawa K (eds) Advances in computational fluid-structure interaction and flow simulation: new methods and challenging computations, modeling and simulation in science, engineering and technology. Springer, pp 379–386, ISBN 978-3-319-40825-5. https://doi.org/10.1007/978-3-319-40827-9_29

  122. Takizawa K, Tezduyar TE, Uchikawa H, Terahara T, Sasaki T, Shiozaki K, Yoshida A, Komiya K, Inoue G (2018) Aorta flow analysis and heart valve flow and structure analysis. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty—2018, modeling and simulation in science, engineering and technology. Springer, pp 29–89, ISBN 978-3-319-96468-3. https://doi.org/10.1007/978-3-319-96469-0_2

  123. Takizawa K, Tezduyar TE, Uchikawa H, Terahara T, Sasaki T, Yoshida A (2019) Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization. Comput Fluids 179:790–798. https://doi.org/10.1016/j.compfluid.2018.05.025

    Article  MathSciNet  MATH  Google Scholar 

  124. Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time fluid mechanics computation of heart valve models. Comput Mech 54:973–986. https://doi.org/10.1007/s00466-014-1046-9

    Article  MATH  Google Scholar 

  125. Takizawa K, Tezduyar TE (2016) New directions in space-time computational methods. In: Bazilevs Y, Takizawa K (eds) Advances in computational fluid-structure interaction and flow simulation: new methods and challenging computations, modeling and simulation in science, engineering and technology. Springer, pp 159–178, ISBN 978-3-319-40825-5. https://doi.org/10.1007/978-3-319-40827-9_13

  126. Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2018) Heart valve flow computation with the Space-Time Slip Interface Topology Change (ST-SI-TC) method and Isogeometric Analysis (IGA). In: Wriggers P, Lenarz T (eds) Biomedical technology: modeling, experiments and simulation. lecture notes in applied and computational mechanics. Springer, pp 77–99, ISBN 978-3-319-59547-4. https://doi.org/10.1007/978-3-319-59548-1_6

  127. Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2017) Heart valve flow computation with the integrated space-time VMS, slip interface, topology change and isogeometric discretization methods. Comput Fluids 158:176–188. https://doi.org/10.1016/j.compfluid.2016.11.012

    Article  MathSciNet  MATH  Google Scholar 

  128. Terahara T, Takizawa K, Tezduyar TE, Bazilevs Y, Hsu M-C (2020) Heart valve isogeometric sequentially-coupled FSI analysis with the space-time topology change method. Comput Mech 65:1167–1187. https://doi.org/10.1007/s00466-019-01813-0

    Article  MathSciNet  MATH  Google Scholar 

  129. Takizawa K, Terahara T, Tezduyar TE (2020) Space-time flow computation with contact between the moving solid surfaces. Springer, Berlin

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  131. Takizawa K, Tezduyar TE, Kuraishi T, Tabata S, Takagi H (2016) Computational thermo-fluid analysis of a disk brake. Comput Mech 57:965–977. https://doi.org/10.1007/s00466-016-1272-4

    Article  MathSciNet  MATH  Google Scholar 

  132. Komiya K, Kanai T, Otoguro Y, Kaneko M, Hirota K, Zhang Y, Takizawa K, Tezduyar TE, Nohmi M, Tsuneda T, Kawai M, Isono M (2019) Computational analysis of flow-driven string dynamics in a pump and residence time calculation. IOP Conf Ser Earth Environ Sci 240:062014. https://doi.org/10.1088/1755-1315/240/6/062014

    Article  Google Scholar 

  133. Kanai T, Takizawa K, Tezduyar TE, Komiya K, Kaneko M, Hirota K, Nohmi M, Tsuneda T, Kawai M, Isono M (2019) Methods for computation of flow-driven string dynamics in a pump and residence time. Math Models Methods Appl Sci 29:839–870. https://doi.org/10.1142/S021820251941001X

    Article  MathSciNet  MATH  Google Scholar 

  134. Otoguro Y, Takizawa K, Tezduyar TE (2018) A general-purpose NURBS mesh generation method for complex geometries. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty—2018, modeling and simulation in science, engineering and technology. Springer, pp 399–434, ISBN 978-3-319-96468-3, https://doi.org/10.1007/978-3-319-96469-0_10

  135. Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Avsar R, Zhang Y (2019) Space-time VMS flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle. Comput Mech 64:1403–1419. https://doi.org/10.1007/s00466-019-01722-2

    Article  MathSciNet  MATH  Google Scholar 

  136. Kuraishi T, Takizawa K, Tezduyar TE (2018) Space-time computational analysis of tire aerodynamics with actual geometry, road contact and tire deformation. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty—2018, modeling and simulation in science, engineering and technology. Springer, pp 337–376, ISBN 978-3-319-96468-3. https://doi.org/10.1007/978-3-319-96469-0_8

  137. Kuraishi T, Takizawa K, Tezduyar TE (2019) Tire aerodynamics with actual tire geometry, road contact and tire deformation. Comput Mech 63:1165–1185. https://doi.org/10.1007/s00466-018-1642-1

    Article  MathSciNet  MATH  Google Scholar 

  138. Kuraishi T, Takizawa K, Tezduyar TE (2019) Space-time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film. Comput Mech 64:1699–1718. https://doi.org/10.1007/s00466-019-01746-8

    Article  MATH  Google Scholar 

  139. Tezduyar TE, Takizawa K, Kuraishi T (2020) Space-time computational FSI and flow analysis: 2004 and beyond. Springer, Berlin

    Google Scholar 

  140. Kuraishi T, Takizawa K, Tezduyar TE (2019) Space-time isogeometric flow analysis with built-in Reynolds-equation limit. Math Models Methods Appl Sci 29:871–904. https://doi.org/10.1142/S0218202519410021

    Article  MathSciNet  MATH  Google Scholar 

  141. Takizawa K, Tezduyar TE, Terahara T (2016) Ram-air parachute structural and fluid mechanics computations with the space-time isogeometric analysis (ST-IGA). Comput Fluids 141:191–200. https://doi.org/10.1016/j.compfluid.2016.05.027

    Article  MathSciNet  MATH  Google Scholar 

  142. Takizawa K, Tezduyar TE, Kanai T (2017) Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. Math Models Methods Appl Sci 27:771–806. https://doi.org/10.1142/S0218202517500166

    Article  MathSciNet  MATH  Google Scholar 

  143. Kanai T, Takizawa K, Tezduyar TE, Tanaka T, Hartmann A (2019) Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization. Comput Mech 63:301–321. https://doi.org/10.1007/s00466-018-1595-4

    Article  MathSciNet  MATH  Google Scholar 

  144. Aydinbakar L, Takizawa K, Tezduyar TE, Matsuda D (2021) U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization. Comput Mech 67:823–843. https://doi.org/10.1007/s00466-020-01965-4

    Article  MathSciNet  Google Scholar 

  145. Aydinbakar L, Takizawa K, Tezduyar TE, Kuraishi T (2021) Space-time VMS isogeometric analysis of the Taylor–Couette flow. Comput Mech 67:1515–1541. https://doi.org/10.1007/s00466-021-02004-6

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  149. Takizawa K, Tezduyar TE, Sasaki T (2018) Estimation of element-based zero-stress state in arterial FSI computations with isogeometric wall discretization. In: Wriggers P, Lenarz T (eds) Biomedical technology: modeling, experiments and simulation. lecture notes in applied and computational mechanics. Springer, pp 101–122, ISBN 978-3-319-59547-4. https://doi.org/10.1007/978-3-319-59548-1_7

  150. Takizawa K, Tezduyar TE, Sasaki T (2017) Aorta modeling with the element-based zero-stress state and isogeometric discretization. Comput Mech 59:265–280. https://doi.org/10.1007/s00466-016-1344-5

    Article  MathSciNet  Google Scholar 

  151. Sasaki T, Takizawa K, Tezduyar TE (2019) Medical-image-based aorta modeling with zero-stress-state estimation. Comput Mech 64:249–271. https://doi.org/10.1007/s00466-019-01669-4

    Article  MathSciNet  MATH  Google Scholar 

  152. Takizawa K, Tezduyar TE, Sasaki T (2019) Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping. Comput Mech 63:681–700. https://doi.org/10.1007/s00466-018-1616-3

    Article  MathSciNet  MATH  Google Scholar 

  153. 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 89:323–336

    Article  MATH  Google Scholar 

  154. Bazilevs Y, Deng X, Korobenko A, di Scalea FL, Todd MD, Taylor SG (2015) Isogeometric fatigue damage prediction in large-scale composite structures driven by dynamic sensor data. J Appl Mech 82:091008

    Article  Google Scholar 

  155. Kiendl J, Hsu M-C, Wu MCH, Reali A (2015) Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials. Comput Methods Appl Mech Eng 291:280–303

    Article  MathSciNet  MATH  Google Scholar 

  156. Hsu M-C, Wang C, Herrema AJ, Schillinger D, Ghoshal A, Bazilevs Y (2015) An interactive geometry modeling and parametric design platform for isogeometric analysis. Comput Math Appl 70:1481–1500

    Article  MathSciNet  MATH  Google Scholar 

  157. Herrema AJ, Wiese NM, Darling CN, Ganapathysubramanian B, Krishnamurthy A, Hsu M-C (2017) A framework for parametric design optimization using isogeometric analysis. Comput Methods Appl Mech Eng 316:944–965

    Article  MathSciNet  MATH  Google Scholar 

  158. Benzaken J, Herrema AJ, Hsu M-C, Evans JA (2017) A rapid and efficient isogeometric design space exploration framework with application to structural mechanics. Comput Methods Appl Mech Eng 316:1215–1256

    Article  MathSciNet  MATH  Google Scholar 

  159. Kamensky D, Xu F, Lee C-H, Yan J, Bazilevs Y, Hsu M-C (2018) A contact formulation based on a volumetric potential: Application to isogeometric simulations of atrioventricular valves. Comput Methods Appl Mech Eng 330:522–546

    Article  MathSciNet  MATH  Google Scholar 

  160. Herrema AJ, Johnson EL, Proserpio D, Wu MCH, Kiendl J, Hsu M-C (2019) Penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches with application to composite wind turbine blades. Comput Methods Appl Mech Eng 346:810–840

    Article  MathSciNet  MATH  Google Scholar 

  161. Herrema AJ, Kiendl J, Hsu M-C (2019) A framework for isogeometric-analysis-based optimization of wind turbine blade structures. Wind Energy 22:153–170

    Article  Google Scholar 

  162. Johnson EL, Hsu M-C (2020) Isogeometric analysis of ice accretion on wind turbine blades. Comput Mech 66:311–322

    Article  MathSciNet  MATH  Google Scholar 

  163. Hughes TJR, Mallet M, Mizukami A (1986) A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput Methods Appl Mech Eng 54:341–355

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  166. Tezduyar TE (2001) Adaptive determination of the finite element stabilization parameters. In: Proceedings of the ECCOMAS computational fluid dynamics conference (2001) CD-ROM. Swansea, Wales

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

    Article  MathSciNet  MATH  Google Scholar 

  168. 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. Volume 3: Fluids, Chapter 17, Wiley, ISBN 978-0-470-84699-5, https://doi.org/10.1002/0470091355.ecm069

  169. 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. https://doi.org/10.1007/s00466-011-0614-5

    Article  MATH  Google Scholar 

  170. Castorrini A, Corsini A, Rispoli F, Venturini P, Takizawa K, Tezduyar TE (2016) SUPG/PSPG computational analysis of rain erosion in wind-turbine blades. In: Bazilevs Y, Takizawa K (eds) Advances in computational fluid-structure interaction and flow simulation: new methods and challenging computations, modeling and simulation in science, engineering and technology. Springer, pp 77–96, ISBN 978-3-319-40825-5, https://doi.org/10.1007/978-3-319-40827-9_7

  171. Castorrini A, Corsini A, Rispoli F, Venturini P, Takizawa K, Tezduyar TE (2019) Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion. Comput Mech 64:1133–1153. https://doi.org/10.1007/s00466-019-01697-0

    Article  MathSciNet  MATH  Google Scholar 

  172. Takizawa K, Tezduyar TE, Otoguro Y (2018) Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations. Comput Mech 62:1169–1186. https://doi.org/10.1007/s00466-018-1557-x

    Article  MathSciNet  MATH  Google Scholar 

  173. Takizawa K, Ueda Y, Tezduyar TE (2019) A node-numbering-invariant directional length scale for simplex elements. Math Models Methods Appl Sci 29:2719–2753. https://doi.org/10.1142/S0218202519500581

    Article  MathSciNet  Google Scholar 

  174. Otoguro Y, Takizawa K, Tezduyar TE (2020) Element length calculation in B-spline meshes for complex geometries. Comput Mech 65:1085–1103. https://doi.org/10.1007/s00466-019-01809-w

    Article  MathSciNet  MATH  Google Scholar 

  175. Ueda Y, Otoguro Y, Takizawa K, Tezduyar TE (2020) Element-splitting-invariant local-length-scale calculation in B-spline meshes for complex geometries. Math Models Methods Appl Sci 30:2139–2174. https://doi.org/10.1142/S0218202520500402

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  177. 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. https://doi.org/10.1016/S0045-7825(01)00310-3

    Article  MATH  Google Scholar 

  178. 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. https://doi.org/10.1016/S0045-7825(01)00311-5

    Article  MATH  Google Scholar 

  179. Moghadam ME, Bazilevs Y, Hsia T-Y, Vignon-Clementel IE, Marsden AL, M. of Congenital Hearts Alliance (MOCHA) (2011) A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput Mech 48:277–291. https://doi.org/10.1007/s00466-011-0599-0

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Acknowledgements

This work was supported in part by Rice–Waseda research agreement. The work was also supported in part by ARO Grant W911NF-17-1-0046 (first and fourth authors), top Global University Project of Waseda University (fourth author), and China Scholarship Council (No. 201906710089) (second author). We are grateful to Artem Korobenko (University of Calgary), Jinhu Yan (University of Illinois at Urbana-Champaign) and Yuri Bazilevs (Brown University) for providing us the velocity data at a plane 10 m downstream of the lead turbine in their computations [5].

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Authors and Affiliations

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

    Takashi Kuraishi, Fulin Zhang & Tayfun E. Tezduyar

  2. College of Water Conservancy and Hydropower Engineering, Hohai University, 1 Xikang Road, Nanjing, 210024, Jiangsu, China

    Fulin Zhang

  3. Department of Modern Mechanical Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Kenji Takizawa

  4. Faculty of Science and Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Tayfun E. Tezduyar

Authors
  1. Takashi Kuraishi
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  2. Fulin Zhang
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  3. Kenji Takizawa
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  4. Tayfun E. Tezduyar
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Corresponding author

Correspondence to Kenji Takizawa.

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Kuraishi, T., Zhang, F., Takizawa, K. et al. Wind turbine wake computation with the ST-VMS method, isogeometric discretization and multidomain method: I. Computational framework. Comput Mech 68, 113–130 (2021). https://doi.org/10.1007/s00466-021-02022-4

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  • DOI: https://doi.org/10.1007/s00466-021-02022-4

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