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2018 | OriginalPaper | Chapter

Recent Advances in ALE-VMS and ST-VMS Computational Aerodynamic and FSI Analysis of Wind Turbines

Authors : Artem Korobenko, Yuri Bazilevs, Kenji Takizawa, Tayfun E. Tezduyar

Published in: Frontiers in Computational Fluid-Structure Interaction and Flow Simulation

Publisher: Springer International Publishing

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Abstract

We describe the recent advances made by our teams in ALE-VMS and ST-VMS computational aerodynamic and fluid–structure interaction (FSI) analysis of wind turbines. The ALE-VMS method is the variational multiscale version of the Arbitrary Lagrangian–Eulerian method. The VMS components are from the residual-based VMS method. The ST-VMS method is the VMS version of the Deforming-Spatial-Domain/Stabilized Space–Time method. The ALE-VMS and ST-VMS serve as the core methods in the computations. They are complemented by special methods that include the ALE-VMS versions for stratified flows, sliding interfaces and weak enforcement of Dirichlet boundary conditions, ST Slip Interface (ST-SI) method, NURBS-based isogeometric analysis, ST/NURBS Mesh Update Method (STNMUM), Kirchhoff–Love shell modeling of wind-turbine structures, and full FSI coupling. The VMS feature of the ALE-VMS and ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow, and the moving-mesh feature of the ALE and ST frameworks enables high-resolution computation near the rotor surface. The ST framework, in a general context, provides higher-order accuracy. The ALE-VMS version for sliding interfaces and the ST-SI enable moving-mesh computation of the spinning rotor. The mesh covering the rotor spins with it, and the sliding interface or the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-SI also enables prescribing the fluid velocity at the turbine rotor surface as weakly-enforced Dirichlet boundary condition. The STNMUM enables exact representation of the mesh rotation. The analysis cases reported include both the horizontal-axis and vertical-axis wind turbines, stratified and unstratified flows, standalone wind turbines, wind turbines with tower or support columns, aerodynamic interaction between two wind turbines, and the FSI between the aerodynamics and structural dynamics of wind turbines. Comparisons with experimental data are also included where applicable. The reported cases demonstrate the effectiveness of the ALE-VMS and ST-VMS computational analysis in wind-turbine aerodynamics and FSI.

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Literature
4.
go back to reference “Levelized cost of electricity renewable energy technologies”, Study, FRAUNHOFER INSTITUT FOR SOLAR ENERGY SYSTEMS ISE, November 2013. “Levelized cost of electricity renewable energy technologies”, Study, FRAUNHOFER INSTITUT FOR SOLAR ENERGY SYSTEMS ISE, November 2013.
5.
go back to reference N.N. Sørensen, J.A. Michelsen, and S. Schreck, “Navier–Stokes predictions of the NREL Phase VI rotor in the NASA Ames 80 ft × 120 ft wind tunnel”, Wind Energy, 5 (2002) 151–169.CrossRef N.N. Sørensen, J.A. Michelsen, and S. Schreck, “Navier–Stokes predictions of the NREL Phase VI rotor in the NASA Ames 80 ft × 120 ft wind tunnel”, Wind Energy, 5 (2002) 151–169.CrossRef
6.
go back to reference A.L. Pape and J. Lecanu, “3D Navier–Stokes computations of a stall-regulated wind turbine”, Wind Energy, 7 (2004) 309–324.CrossRef A.L. Pape and J. Lecanu, “3D Navier–Stokes computations of a stall-regulated wind turbine”, Wind Energy, 7 (2004) 309–324.CrossRef
7.
go back to reference F. Zahle, N.N. Sørensen, and J. Johansen, “Wind turbine rotor-tower interaction using an incompressible overset grid method”, Wind Energy, 12 (2009) 594–619.CrossRef F. Zahle, N.N. Sørensen, and J. Johansen, “Wind turbine rotor-tower interaction using an incompressible overset grid method”, Wind Energy, 12 (2009) 594–619.CrossRef
8.
go back to reference Y. Bazilevs, M.-C. Hsu, I. Akkerman, S. Wright, K. Takizawa, B. Henicke, T. Spielman, and T.E. Tezduyar, “3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics”, International Journal for Numerical Methods in Fluids, 65 (2011) 207–235, https://doi.org/10.1002/fld.2400.MATHCrossRef Y. Bazilevs, M.-C. Hsu, I. Akkerman, S. Wright, K. Takizawa, B. Henicke, T. Spielman, and T.E. Tezduyar, “3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics”, International Journal for Numerical Methods in Fluids, 65 (2011) 207–235, https://​doi.​org/​10.​1002/​fld.​2400.MATHCrossRef
10.
go back to reference Y. Li and P.M.C. Kim-Jong Paik, T. Xing, “Dynamic overset CFD simulations of wind turbine aerodynamics”, Renewable Energy, 37 (2012) 285–298.CrossRef Y. Li and P.M.C. Kim-Jong Paik, T. Xing, “Dynamic overset CFD simulations of wind turbine aerodynamics”, Renewable Energy, 37 (2012) 285–298.CrossRef
11.
go back to reference E. Guttierez, S. Primi, F. Taucer, P. Caperan, D. Tirelli, J. Mieres, I. Calvo, J. Rodriguez, F. Vallano, G. Galiotis, and D. Mouzakis, “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 Commission, 2003. E. Guttierez, S. Primi, F. Taucer, P. Caperan, D. Tirelli, J. Mieres, I. Calvo, J. Rodriguez, F. Vallano, G. Galiotis, and D. Mouzakis, “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 Commission, 2003.
12.
go back to reference C. Kong, J. Bang, and Y. Sugiyama, “Structural investigation of composite wind turbine blade considering various load cases and fatigue life”, Energy, 30 (2005) 2101–2114.CrossRef C. Kong, J. Bang, and Y. Sugiyama, “Structural investigation of composite wind turbine blade considering various load cases and fatigue life”, Energy, 30 (2005) 2101–2114.CrossRef
13.
go back to reference M.O.L. Hansen, J.N. Sørensen, S. Voutsinas, N. Sørensen, and H.A. Madsen, “State of the art in wind turbine aerodynamics and aeroelasticity”, Progress in Aerospace Sciences, 42 (2006) 285–330.CrossRef M.O.L. Hansen, J.N. Sørensen, S. Voutsinas, N. Sørensen, and H.A. Madsen, “State of the art in wind turbine aerodynamics and aeroelasticity”, Progress in Aerospace Sciences, 42 (2006) 285–330.CrossRef
14.
go back to reference F.M. Jensen, B.G. Falzon, J. Ankersen, and H. Stang, “Structural testing and numerical simulation of a 34 m composite wind turbine blade”, Composite Structures, 76 (2006) 52–61.CrossRef F.M. Jensen, B.G. Falzon, J. Ankersen, and H. Stang, “Structural testing and numerical simulation of a 34 m composite wind turbine blade”, Composite Structures, 76 (2006) 52–61.CrossRef
15.
go back to reference J. Kiendl, Y. Bazilevs, M.-C. Hsu, R. Wüchner, and K.-U. Bletzinger, “The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 2403–2416.MathSciNetMATHCrossRef J. Kiendl, Y. Bazilevs, M.-C. Hsu, R. Wüchner, and K.-U. Bletzinger, “The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 2403–2416.MathSciNetMATHCrossRef
16.
go back to reference Y. Bazilevs, M.-C. Hsu, J. Kiendl, and D.J. Benson, “A computational procedure for pre-bending of wind turbine blades”, International Journal for Numerical Methods in Engineering, 89 (2012) 323–336.MATHCrossRef Y. Bazilevs, M.-C. Hsu, J. Kiendl, and D.J. Benson, “A computational procedure for pre-bending of wind turbine blades”, International Journal for Numerical Methods in Engineering, 89 (2012) 323–336.MATHCrossRef
17.
go back to reference Y. Bazilevs, M.-C. Hsu, J. Kiendl, R. Wüchner, and K.-U. Bletzinger, “3D simulation of wind turbine rotors at full scale. Part II: Fluid–structure interaction modeling with composite blades”, International Journal for Numerical Methods in Fluids, 65 (2011) 236–253.MATHCrossRef Y. Bazilevs, M.-C. Hsu, J. Kiendl, R. Wüchner, and K.-U. Bletzinger, “3D simulation of wind turbine rotors at full scale. Part II: Fluid–structure interaction modeling with composite blades”, International Journal for Numerical Methods in Fluids, 65 (2011) 236–253.MATHCrossRef
18.
go back to reference S. Schreck, J. Lundquist, and W.Shaw, “U.s. department of energy workshop report: Research needs for wind resource characterization”, Technical Report NREL/TP-500-43521, National Renewable Energy Laboratory, 2008. S. Schreck, J. Lundquist, and W.Shaw, “U.s. department of energy workshop report: Research needs for wind resource characterization”, Technical Report NREL/TP-500-43521, National Renewable Energy Laboratory, 2008.
19.
go back to reference R. Barthelmie1, S. Frandsen, O. Rathmann, K. Hansen, E. Politis, J. Prospathopoulos, J. Schepers, K. Rados, D. Cabezn, W. Schlez, A. Neubert, and M. Heath, “Flow and wakes in large wind farms: Final report for upwind wp8”, Technical Report Report number Ris-R-1765(EN), Danmarks Tekniske Universitet, Ris Nationallaboratoriet for Bredygtig Energ, 2011. R. Barthelmie1, S. Frandsen, O. Rathmann, K. Hansen, E. Politis, J. Prospathopoulos, J. Schepers, K. Rados, D. Cabezn, W. Schlez, A. Neubert, and M. Heath, “Flow and wakes in large wind farms: Final report for upwind wp8”, Technical Report Report number Ris-R-1765(EN), Danmarks Tekniske Universitet, Ris Nationallaboratoriet for Bredygtig Energ, 2011.
21.
go back to reference T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs, “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement”, Computer Methods in Applied Mechanics and Engineering, 194 (2005) 4135–4195.MathSciNetMATHCrossRef T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs, “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement”, Computer Methods in Applied Mechanics and Engineering, 194 (2005) 4135–4195.MathSciNetMATHCrossRef
22.
go back to reference J.A. Cottrell, A. Reali, Y. Bazilevs, and T.J.R. Hughes, “Isogeometric analysis of structural vibrations”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 5257–5297.MathSciNetMATHCrossRef J.A. Cottrell, A. Reali, Y. Bazilevs, and T.J.R. Hughes, “Isogeometric analysis of structural vibrations”, Computer Methods in Applied Mechanics and Engineering, 195 (2006) 5257–5297.MathSciNetMATHCrossRef
23.
go back to reference Y. Bazilevs, L.B. da Veiga, J.A. Cottrell, T.J.R. Hughes, and G. Sangalli, “Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes”, Mathematical Models and Methods in Applied Sciences, 16 (2006) 1031–1090.MathSciNetMATHCrossRef Y. Bazilevs, L.B. da Veiga, J.A. Cottrell, T.J.R. Hughes, and G. Sangalli, “Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes”, Mathematical Models and Methods in Applied Sciences, 16 (2006) 1031–1090.MathSciNetMATHCrossRef
24.
go back to reference J.A. Cottrell, T.J.R. Hughes, and A. Reali, “Studies of refinement and continuity in isogeometric structural analysis”, Computer Methods in Applied Mechanics and Engineering, 196 (2007) 4160–4183.MATHCrossRef J.A. Cottrell, T.J.R. Hughes, and A. Reali, “Studies of refinement and continuity in isogeometric structural analysis”, Computer Methods in Applied Mechanics and Engineering, 196 (2007) 4160–4183.MATHCrossRef
25.
go back to reference W.A. Wall, M.A. Frenzel, and C. Cyron, “Isogeometric structural shape optimization”, Computer Methods in Applied Mechanics and Engineering, 197 (2008) 2976–2988.MathSciNetMATHCrossRef W.A. Wall, M.A. Frenzel, and C. Cyron, “Isogeometric structural shape optimization”, Computer Methods in Applied Mechanics and Engineering, 197 (2008) 2976–2988.MathSciNetMATHCrossRef
26.
go back to reference J.A. Cottrell, T.J.R. Hughes, and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Chichester, 2009.MATHCrossRef J.A. Cottrell, T.J.R. Hughes, and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Chichester, 2009.MATHCrossRef
27.
go back to reference J.A. Evans, Y. Bazilevs, I. Babus̆ka, and T.J.R. Hughes, “n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 1726–1741.MathSciNetMATHCrossRef J.A. Evans, Y. Bazilevs, I. Babus̆ka, and T.J.R. Hughes, “n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 1726–1741.MathSciNetMATHCrossRef
28.
go back to reference M.R. D\(\ddot {\text{o}}\)rfel, B. J\(\ddot {\text{u}}\)ttler, and B. Simeon, “Adaptive isogeometric analysis by local h-refinement with T-splines”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 264–275.MathSciNetMATHCrossRef M.R. D\(\ddot {\text{o}}\)rfel, B. J\(\ddot {\text{u}}\)ttler, and B. Simeon, “Adaptive isogeometric analysis by local h-refinement with T-splines”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 264–275.MathSciNetMATHCrossRef
29.
go back to reference Y. Bazilevs, V.M. Calo, J.A. Cottrell, J.A. Evans, T.J.R. Hughes, S. Lipton, M.A. Scott, and T.W. Sederberg, “Isogeometric analysis using T-splines”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 229–263.MathSciNetMATHCrossRef Y. Bazilevs, V.M. Calo, J.A. Cottrell, J.A. Evans, T.J.R. Hughes, S. Lipton, M.A. Scott, and T.W. Sederberg, “Isogeometric analysis using T-splines”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 229–263.MathSciNetMATHCrossRef
30.
go back to reference F. Auricchio, L. Beir\(\tilde {\text{a}}\)o da Veiga, C. Lovadina, and A. Reali, “The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: Mixed FEMs versus NURBS-based approximations”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 314–323.MathSciNetMATHCrossRef F. Auricchio, L. Beir\(\tilde {\text{a}}\)o da Veiga, C. Lovadina, and A. Reali, “The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: Mixed FEMs versus NURBS-based approximations”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 314–323.MathSciNetMATHCrossRef
31.
go back to reference W. Wang and Y. Zhang, “Wavelets-based NURBS simplification and fairing”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 290–300.MathSciNetMATHCrossRef W. Wang and Y. Zhang, “Wavelets-based NURBS simplification and fairing”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 290–300.MathSciNetMATHCrossRef
32.
go back to reference E. Cohen, T. Martin, R.M. Kirby, T. Lyche, and R.F. Riesenfeld, “Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 334–356.MathSciNetMATHCrossRef E. Cohen, T. Martin, R.M. Kirby, T. Lyche, and R.F. Riesenfeld, “Analysis-aware modeling: Understanding quality considerations in modeling for isogeometric analysis”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 334–356.MathSciNetMATHCrossRef
33.
go back to reference V. Srinivasan, S. Radhakrishnan, and G. Subbarayan, “Coordinated synthesis of hierarchical engineering systems”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 392–404.MATHCrossRef V. Srinivasan, S. Radhakrishnan, and G. Subbarayan, “Coordinated synthesis of hierarchical engineering systems”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 392–404.MATHCrossRef
34.
go back to reference Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, and G. Scovazzi, “Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows”, Computer Methods in Applied Mechanics and Engineering, 197 (2007) 173–201.MathSciNetMATHCrossRef Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, and G. Scovazzi, “Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows”, Computer Methods in Applied Mechanics and Engineering, 197 (2007) 173–201.MathSciNetMATHCrossRef
35.
go back to reference Y. Bazilevs, C. Michler, V.M. Calo, and T.J.R. Hughes, “Weak Dirichlet boundary conditions for wall-bounded turbulent flows”, Computer Methods in Applied Mechanics and Engineering, 196 (2007) 4853–4862.MathSciNetMATHCrossRef Y. Bazilevs, C. Michler, V.M. Calo, and T.J.R. Hughes, “Weak Dirichlet boundary conditions for wall-bounded turbulent flows”, Computer Methods in Applied Mechanics and Engineering, 196 (2007) 4853–4862.MathSciNetMATHCrossRef
36.
go back to reference Y. Bazilevs, C. Michler, V.M. Calo, and T.J.R. Hughes, “Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 780–790.MathSciNetMATHCrossRef Y. Bazilevs, C. Michler, V.M. Calo, and T.J.R. Hughes, “Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 780–790.MathSciNetMATHCrossRef
37.
go back to reference I. Akkerman, Y. Bazilevs, V.M. Calo, T.J.R. Hughes, and S. Hulshoff, “The role of continuity in residual-based variational multiscale modeling of turbulence”, Computational Mechanics, 41 (2008) 371–378.MathSciNetMATHCrossRef I. Akkerman, Y. Bazilevs, V.M. Calo, T.J.R. Hughes, and S. Hulshoff, “The role of continuity in residual-based variational multiscale modeling of turbulence”, Computational Mechanics, 41 (2008) 371–378.MathSciNetMATHCrossRef
39.
go back to reference Y. Bazilevs and I. Akkerman, “Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual–based variational multiscale method”, Journal of Computational Physics, 229 (2010) 3402–3414.MathSciNetMATHCrossRef Y. Bazilevs and I. Akkerman, “Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual–based variational multiscale method”, Journal of Computational Physics, 229 (2010) 3402–3414.MathSciNetMATHCrossRef
40.
go back to reference T. Elguedj, Y. Bazilevs, V.M. Calo, and T.J.R. Hughes, “B-bar and F-bar projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order nurbs elements”, Computer Methods in Applied Mechanics and Engineering, 197 (2008) 2732–2762.MATHCrossRef T. Elguedj, Y. Bazilevs, V.M. Calo, and T.J.R. Hughes, “B-bar and F-bar projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order nurbs elements”, Computer Methods in Applied Mechanics and Engineering, 197 (2008) 2732–2762.MATHCrossRef
41.
go back to reference S. Lipton, J.A. Evans, Y. Bazilevs, T. Elguedj, and T.J.R. Hughes, “Robustness of isogeometric structural discretizations under severe mesh distortion”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 357–373.MATHCrossRef S. Lipton, J.A. Evans, Y. Bazilevs, T. Elguedj, and T.J.R. Hughes, “Robustness of isogeometric structural discretizations under severe mesh distortion”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 357–373.MATHCrossRef
42.
go back to reference D.J. Benson, Y. Bazilevs, E. De Luycker, M.-C. Hsu, M. Scott, T.J.R. Hughes, and T. Belytschko, “A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM”, International Journal for Numerical Methods in Engineering, 83 (2010) 765–785.MathSciNetMATH D.J. Benson, Y. Bazilevs, E. De Luycker, M.-C. Hsu, M. Scott, T.J.R. Hughes, and T. Belytschko, “A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM”, International Journal for Numerical Methods in Engineering, 83 (2010) 765–785.MathSciNetMATH
43.
go back to reference D.J. Benson, Y. Bazilevs, M.-C. Hsu, and T.J.R. Hughes, “Isogeometric shell analysis: The Reissner–Mindlin shell”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 276–289.MathSciNetMATHCrossRef D.J. Benson, Y. Bazilevs, M.-C. Hsu, and T.J.R. Hughes, “Isogeometric shell analysis: The Reissner–Mindlin shell”, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 276–289.MathSciNetMATHCrossRef
44.
go back to reference J. Kiendl, K.-U. Bletzinger, J. Linhard, and R. Wüchner, “Isogeometric shell analysis with Kirchhoff–Love elements”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3902–3914.MathSciNetMATHCrossRef J. Kiendl, K.-U. Bletzinger, J. Linhard, and R. Wüchner, “Isogeometric shell analysis with Kirchhoff–Love elements”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3902–3914.MathSciNetMATHCrossRef
45.
go back to reference Y. Zhang, Y. Bazilevs, S. Goswami, C. Bajaj, and T.J.R. Hughes, “Patient-specific vascular nurbs modeling for isogeometric analysis of blood flow”, Computer Methods in Applied Mechanics and Engineering, 196 (2007) 2943–2959.MathSciNetMATHCrossRef Y. Zhang, Y. Bazilevs, S. Goswami, C. Bajaj, and T.J.R. Hughes, “Patient-specific vascular nurbs modeling for isogeometric analysis of blood flow”, Computer Methods in Applied Mechanics and Engineering, 196 (2007) 2943–2959.MathSciNetMATHCrossRef
46.
go back to reference Y. Bazilevs, V.M. Calo, Y. Zhang, and T.J.R. Hughes, “Isogeometric fluid–structure interaction analysis with applications to arterial blood flow”, Computational Mechanics, 38 (2006) 310–322.MathSciNetCrossRefMATH Y. Bazilevs, V.M. Calo, Y. Zhang, and T.J.R. Hughes, “Isogeometric fluid–structure interaction analysis with applications to arterial blood flow”, Computational Mechanics, 38 (2006) 310–322.MathSciNetCrossRefMATH
47.
go back to reference Y. Bazilevs, V.M. Calo, T.J.R. Hughes, and Y. Zhang, “Isogeometric fluid–structure interaction: theory, algorithms, and computations”, Computational Mechanics, 43 (2008) 3–37.MathSciNetMATHCrossRef Y. Bazilevs, V.M. Calo, T.J.R. Hughes, and Y. Zhang, “Isogeometric fluid–structure interaction: theory, algorithms, and computations”, Computational Mechanics, 43 (2008) 3–37.MathSciNetMATHCrossRef
48.
go back to reference J.G. Isaksen, Y. Bazilevs, T. Kvamsdal, Y. Zhang, J.H. Kaspersen, K. Waterloo, B. Romner, and T. Ingebrigtsen, “Determination of wall tension in cerebral artery aneurysms by numerical simulation”, Stroke, 39 (2008) 3172–3178.CrossRef J.G. Isaksen, Y. Bazilevs, T. Kvamsdal, Y. Zhang, J.H. Kaspersen, K. Waterloo, B. Romner, and T. Ingebrigtsen, “Determination of wall tension in cerebral artery aneurysms by numerical simulation”, Stroke, 39 (2008) 3172–3178.CrossRef
49.
go back to reference Y. Bazilevs and T.J.R. Hughes, “NURBS-based isogeometric analysis for the computation of flows about rotating components”, Computational Mechanics, 43 (2008) 143–150.MATHCrossRef Y. Bazilevs and T.J.R. Hughes, “NURBS-based isogeometric analysis for the computation of flows about rotating components”, Computational Mechanics, 43 (2008) 143–150.MATHCrossRef
50.
go back to reference F. Cirak, M. Ortiz, and P. Schr\(\ddot {\text{o}}\)der, “Subdivision surfaces: a new paradigm for thin shell analysis”, International Journal for Numerical Methods in Engineering, 47 (2000) 2039–2072. F. Cirak, M. Ortiz, and P. Schr\(\ddot {\text{o}}\)der, “Subdivision surfaces: a new paradigm for thin shell analysis”, International Journal for Numerical Methods in Engineering, 47 (2000) 2039–2072.
51.
go back to reference F. Cirak and M. Ortiz, “Fully C1-conforming subdivision elements for finite deformation thin shell analysis”, International Journal for Numerical Methods in Engineering, 51 (2001) 813–833.MATHCrossRef F. Cirak and M. Ortiz, “Fully C1-conforming subdivision elements for finite deformation thin shell analysis”, International Journal for Numerical Methods in Engineering, 51 (2001) 813–833.MATHCrossRef
52.
go back to reference F. Cirak, M.J. Scott, E.K. Antonsson, M. Ortiz, and P. Schr\(\ddot {\text{o}}\)der, “Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision”, Computer-Aided Design, 34 (2002) 137–148.CrossRef F. Cirak, M.J. Scott, E.K. Antonsson, M. Ortiz, and P. Schr\(\ddot {\text{o}}\)der, “Integrated modeling, finite-element analysis, and engineering design for thin-shell structures using subdivision”, Computer-Aided Design, 34 (2002) 137–148.CrossRef
53.
go back to reference T.J.R. Hughes, W.K. Liu, and T.K. Zimmermann, “Lagrangian–Eulerian finite element formulation for incompressible viscous flows”, Computer Methods in Applied Mechanics and Engineering, 29 (1981) 329–349.MathSciNetMATHCrossRef T.J.R. Hughes, W.K. Liu, and T.K. Zimmermann, “Lagrangian–Eulerian finite element formulation for incompressible viscous flows”, Computer Methods in Applied Mechanics and Engineering, 29 (1981) 329–349.MathSciNetMATHCrossRef
54.
go back to reference T.J.R. Hughes, “Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods”, Computer Methods in Applied Mechanics and Engineering, 127 (1995) 387–401.MathSciNetMATHCrossRef T.J.R. Hughes, “Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods”, Computer Methods in Applied Mechanics and Engineering, 127 (1995) 387–401.MathSciNetMATHCrossRef
55.
go back to reference T.J.R. Hughes, A.A. Oberai, and L. Mazzei, “Large eddy simulation of turbulent channel flows by the variational multiscale method”, Physics of Fluids, 13 (2001) 1784–1799.MATHCrossRef T.J.R. Hughes, A.A. Oberai, and L. Mazzei, “Large eddy simulation of turbulent channel flows by the variational multiscale method”, Physics of Fluids, 13 (2001) 1784–1799.MATHCrossRef
56.
go back to reference Y. Bazilevs and T.J.R. Hughes, “Weak imposition of Dirichlet boundary conditions in fluid mechanics”, Computers and Fluids, 36 (2007) 12–26.MathSciNetMATHCrossRef Y. Bazilevs and T.J.R. Hughes, “Weak imposition of Dirichlet boundary conditions in fluid mechanics”, Computers and Fluids, 36 (2007) 12–26.MathSciNetMATHCrossRef
57.
go back to reference J. Nitsche, “Uber ein variationsprinzip zur losung von Dirichlet-problemen bei verwendung von teilraumen, die keinen randbedingungen unterworfen sind”, Abh. Math. Univ. Hamburg, 36 (1971) 9–15.MATHCrossRef J. Nitsche, “Uber ein variationsprinzip zur losung von Dirichlet-problemen bei verwendung von teilraumen, die keinen randbedingungen unterworfen sind”, Abh. Math. Univ. Hamburg, 36 (1971) 9–15.MATHCrossRef
58.
go back to reference D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini, “Unified analysis of Discontinuous Galerkin methods for elliptic problems”, SIAM Journal of Numerical Analysis, 39 (2002) 1749–1779.MathSciNetMATHCrossRef D.N. Arnold, F. Brezzi, B. Cockburn, and L.D. Marini, “Unified analysis of Discontinuous Galerkin methods for elliptic problems”, SIAM Journal of Numerical Analysis, 39 (2002) 1749–1779.MathSciNetMATHCrossRef
59.
go back to reference Y. Bazilevs, A. Korobenko, J. Yan, A. Pal, S. Gohari, and S. Sarkar, “ALE–VMS formulation for stratified turbulent incompressible flows with applications”, Mathematical Models and Methods in Applied Sciences, 25 (12) (2015) 2349–2375.MathSciNetMATHCrossRef Y. Bazilevs, A. Korobenko, J. Yan, A. Pal, S. Gohari, and S. Sarkar, “ALE–VMS formulation for stratified turbulent incompressible flows with applications”, Mathematical Models and Methods in Applied Sciences, 25 (12) (2015) 2349–2375.MathSciNetMATHCrossRef
60.
go back to reference J. Yan, A. Korobenko, A. Tejada-Martinez, R. Golshan, and Y. Bazilevs, “A new variational multiscale formulation for stratified incompressible turbulent flows”, Computers & Fluids, 158 (2017) 150–156.MathSciNetMATHCrossRef J. Yan, A. Korobenko, A. Tejada-Martinez, R. Golshan, and Y. Bazilevs, “A new variational multiscale formulation for stratified incompressible turbulent flows”, Computers & Fluids, 158 (2017) 150–156.MathSciNetMATHCrossRef
61.
go back to reference A. Korobenko, J. Yan, S. Gohari, S. Sarkar, and Y. Bazilevs, “FSI simulation of two back-to-back wind turbines in atmospheric boundary layer flow”, Computers & Fluids, 158 (2017) 167–175.MathSciNetMATHCrossRef A. Korobenko, J. Yan, S. Gohari, S. Sarkar, and Y. Bazilevs, “FSI simulation of two back-to-back wind turbines in atmospheric boundary layer flow”, Computers & Fluids, 158 (2017) 167–175.MathSciNetMATHCrossRef
62.
go back to reference M.-C. Hsu, I. Akkerman, and Y. Bazilevs, “High-performance computing of wind turbine aerodynamics using isogeometric analysis”, Computers and Fluids, 49 (2011) 93–100.MathSciNetMATHCrossRef M.-C. Hsu, I. Akkerman, and Y. Bazilevs, “High-performance computing of wind turbine aerodynamics using isogeometric analysis”, Computers and Fluids, 49 (2011) 93–100.MathSciNetMATHCrossRef
63.
go back to reference Y. Bazilevs, M.-C. Hsu, and M.A. Scott, “Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines”, Computer Methods in Applied Mechanics and Engineering, 249–252 (2012) 28–41.MathSciNetMATHCrossRef Y. Bazilevs, M.-C. Hsu, and M.A. Scott, “Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines”, Computer Methods in Applied Mechanics and Engineering, 249–252 (2012) 28–41.MathSciNetMATHCrossRef
64.
go back to reference M.-C. Hsu, I. Akkerman, and Y. Bazilevs, “Finite element simulation of wind turbine aerodynamics: Validation study using NREL Phase VI experiment”, Wind Energy, 17 (2014) 461–481.CrossRef M.-C. Hsu, I. Akkerman, and Y. Bazilevs, “Finite element simulation of wind turbine aerodynamics: Validation study using NREL Phase VI experiment”, Wind Energy, 17 (2014) 461–481.CrossRef
65.
go back to reference A. Korobenko, M.-C. Hsu, I. Akkerman, J. Tippmann, and Y. Bazilevs, “Structural mechanics modeling and FSI simulation of wind turbines”, Mathematical Models and Methods in Applied Sciences, 23 (2013) 249–272.MathSciNetMATHCrossRef A. Korobenko, M.-C. Hsu, I. Akkerman, J. Tippmann, and Y. Bazilevs, “Structural mechanics modeling and FSI simulation of wind turbines”, Mathematical Models and Methods in Applied Sciences, 23 (2013) 249–272.MathSciNetMATHCrossRef
70.
go back to reference J. Yan, A. Korobenko, X. Deng, and Y. Bazilevs, “Computational free-surface fluid–structure interaction with application to floating offshore wind turbines”, Computers and Fluids, 141 (2016) 155–174,MathSciNetMATHCrossRef J. Yan, A. Korobenko, X. Deng, and Y. Bazilevs, “Computational free-surface fluid–structure interaction with application to floating offshore wind turbines”, Computers and Fluids, 141 (2016) 155–174,MathSciNetMATHCrossRef
72.
go back to reference Y. Bazilevs, A. Korobenko, X. Deng, and J. Yan, “FSI modeling for fatigue-damage prediction in full-scale wind-turbine blades”, Journal of Applied Mechanics, 83 (6) (2016) 061010.CrossRef Y. Bazilevs, A. Korobenko, X. Deng, and J. Yan, “FSI modeling for fatigue-damage prediction in full-scale wind-turbine blades”, Journal of Applied Mechanics, 83 (6) (2016) 061010.CrossRef
73.
go back to reference Y. Bazilevs, J.R. Gohean, T.J.R. Hughes, R.D. Moser, and Y. Zhang, “Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3534–3550.MathSciNetMATHCrossRef Y. Bazilevs, J.R. Gohean, T.J.R. Hughes, R.D. Moser, and Y. Zhang, “Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device”, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 3534–3550.MathSciNetMATHCrossRef
74.
go back to reference Y. Bazilevs, M.-C. Hsu, D. Benson, S. Sankaran, and A. Marsden, “Computational fluid–structure interaction: Methods and application to a total cavopulmonary connection”, Computational Mechanics, 45 (2009) 77–89.MathSciNetMATHCrossRef Y. Bazilevs, M.-C. Hsu, D. Benson, S. Sankaran, and A. Marsden, “Computational fluid–structure interaction: Methods and application to a total cavopulmonary connection”, Computational Mechanics, 45 (2009) 77–89.MathSciNetMATHCrossRef
75.
go back to reference Y. Bazilevs, M.-C. Hsu, Y. Zhang, W. Wang, X. Liang, T. Kvamsdal, R. Brekken, and J. Isaksen, “A fully-coupled fluid–structure interaction simulation of cerebral aneurysms”, Computational Mechanics, 46 (2010) 3–16.MathSciNetMATHCrossRef Y. Bazilevs, M.-C. Hsu, Y. Zhang, W. Wang, X. Liang, T. Kvamsdal, R. Brekken, and J. Isaksen, “A fully-coupled fluid–structure interaction simulation of cerebral aneurysms”, Computational Mechanics, 46 (2010) 3–16.MathSciNetMATHCrossRef
76.
go back to reference Y. Bazilevs, M.-C. Hsu, Y. Zhang, W. Wang, T. Kvamsdal, S. Hentschel, and J. Isaksen, “Computational fluid–structure interaction: Methods and application to cerebral aneurysms”, Biomechanics and Modeling in Mechanobiology, 9 (2010) 481–498.CrossRef Y. Bazilevs, M.-C. Hsu, Y. Zhang, W. Wang, T. Kvamsdal, S. Hentschel, and J. Isaksen, “Computational fluid–structure interaction: Methods and application to cerebral aneurysms”, Biomechanics and Modeling in Mechanobiology, 9 (2010) 481–498.CrossRef
77.
go back to reference M.-C. Hsu and Y. Bazilevs, “Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations”, Finite Elements in Analysis and Design, 47 (2011) 593–599.MathSciNetCrossRef M.-C. Hsu and Y. Bazilevs, “Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations”, Finite Elements in Analysis and Design, 47 (2011) 593–599.MathSciNetCrossRef
82.
go back to reference M.-C. Hsu, D. Kamensky, F. Xu, J. Kiendl, C. Wang, M.C.H. Wu, J. Mineroff, A. Reali, Y. Bazilevs, and M.S. Sacks, “Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models”, Computational Mechanics, 55 (2015) 1211–1225, https://doi.org/10.1007/s00466-015-1166-x.MATHCrossRef M.-C. Hsu, D. Kamensky, F. Xu, J. Kiendl, C. Wang, M.C.H. Wu, J. Mineroff, A. Reali, Y. Bazilevs, and M.S. Sacks, “Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models”, Computational Mechanics, 55 (2015) 1211–1225, https://​doi.​org/​10.​1007/​s00466-015-1166-x.MATHCrossRef
83.
go back to reference D. Kamensky, M.-C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks, and T.J.R. Hughes, “An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves”, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 1005–1053.MathSciNetMATHCrossRef D. Kamensky, M.-C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks, and T.J.R. Hughes, “An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves”, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 1005–1053.MathSciNetMATHCrossRef
84.
go back to reference I. Akkerman, Y. Bazilevs, D.J. Benson, M.W. Farthing, and C.E. Kees, “Free-surface flow and fluid–object interaction modeling with emphasis on ship hydrodynamics”, Journal of Applied Mechanics, 79 (2012) 010905.CrossRef I. Akkerman, Y. Bazilevs, D.J. Benson, M.W. Farthing, and C.E. Kees, “Free-surface flow and fluid–object interaction modeling with emphasis on ship hydrodynamics”, Journal of Applied Mechanics, 79 (2012) 010905.CrossRef
85.
go back to reference I. Akkerman, J. Dunaway, J. Kvandal, J. Spinks, and Y. Bazilevs, “Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS”, Computational Mechanics, 50 (2012) 719–727.CrossRef I. Akkerman, J. Dunaway, J. Kvandal, J. Spinks, and Y. Bazilevs, “Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS”, Computational Mechanics, 50 (2012) 719–727.CrossRef
87.
go back to reference M.C.H. Wu, D. Kamensky, C. Wang, A.J. Herrema, F. Xu, M.S. Pigazzini, A. Verma, A.L. Marsden, Y. Bazilevs, and M.-C. Hsu, “Optimizing fluid–structure interaction systems with immersogeometric analysis and surrogate modeling: Application to a hydraulic arresting gear”, Computer Methods in Applied Mechanics and Engineering, (2017), Published online. https://doi.org/10.1016/j.cma.2016.09.032.MathSciNetCrossRef M.C.H. Wu, D. Kamensky, C. Wang, A.J. Herrema, F. Xu, M.S. Pigazzini, A. Verma, A.L. Marsden, Y. Bazilevs, and M.-C. Hsu, “Optimizing fluid–structure interaction systems with immersogeometric analysis and surrogate modeling: Application to a hydraulic arresting gear”, Computer Methods in Applied Mechanics and Engineering, (2017), Published online. https://​doi.​org/​10.​1016/​j.​cma.​2016.​09.​032.MathSciNetCrossRef
103.
go back to reference A.N. Brooks and T.J.R. Hughes, “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations”, Computer Methods in Applied Mechanics and Engineering, 32 (1982) 199–259.MathSciNetMATHCrossRef A.N. Brooks and T.J.R. Hughes, “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations”, Computer Methods in Applied Mechanics and Engineering, 32 (1982) 199–259.MathSciNetMATHCrossRef
105.
go back to reference Y. Bazilevs, K. Takizawa, and T.E. Tezduyar, Computational Fluid–Structure Interaction: Methods and Applications. Wiley, February 2013, ISBN: 978-0470978771.MATHCrossRef Y. Bazilevs, K. Takizawa, and T.E. Tezduyar, Computational Fluid–Structure Interaction: Methods and Applications. Wiley, February 2013, ISBN:​ 978-0470978771.MATHCrossRef
129.
go back to reference K. Takizawa, T.E. Tezduyar, H. Uchikawa, T. Terahara, T. Sasaki, K. Shiozaki, A. Yoshida, K. Komiya, and G. Inoue, “Aorta flow analysis and heart valve flow and structure analysis”, to appear in a special volume to be published by Springer, 2018. K. Takizawa, T.E. Tezduyar, H. Uchikawa, T. Terahara, T. Sasaki, K. Shiozaki, A. Yoshida, K. Komiya, and G. Inoue, “Aorta flow analysis and heart valve flow and structure analysis”, to appear in a special volume to be published by Springer, 2018.
131.
go back to reference K. Takizawa, T.E. Tezduyar, T. Terahara, and T. Sasaki, “Heart valve flow computation with the Space–Time Slip Interface Topology Change (ST-SI-TC) method and Isogeometric Analysis (IGA)”, in P. Wriggers and T. Lenarz, editors, Biomedical Technology: Modeling, Experiments and Simulation, Lecture Notes in Applied and Computational Mechanics, 77–99, Springer, 2018, ISBN: 978-3-319-59547-4. K. Takizawa, T.E. Tezduyar, T. Terahara, and T. Sasaki, “Heart valve flow computation with the Space–Time Slip Interface Topology Change (ST-SI-TC) method and Isogeometric Analysis (IGA)”, in P. Wriggers and T. Lenarz, editors, Biomedical Technology: Modeling, Experiments and Simulation, Lecture Notes in Applied and Computational Mechanics, 77–99, Springer, 2018, ISBN:​ 978-3-319-59547-4.
138.
go back to reference Y. Otoguro, K. Takizawa, and T.E. Tezduyar, “A general-purpose NURBS mesh generation method for complex geometries”, to appear in a special volume to be published by Springer, 2018. Y. Otoguro, K. Takizawa, and T.E. Tezduyar, “A general-purpose NURBS mesh generation method for complex geometries”, to appear in a special volume to be published by Springer, 2018.
140.
go back to reference T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Space–time computational analysis of tire aerodynamics with actual geometry, road contact and tire deformation”, to appear in a special volume to be published by Springer, 2018. T. Kuraishi, K. Takizawa, and T.E. Tezduyar, “Space–time computational analysis of tire aerodynamics with actual geometry, road contact and tire deformation”, to appear in a special volume to be published by Springer, 2018.
143.
go back to reference M.-C. Hsu and Y. Bazilevs, “Fluid–structure interaction modeling of wind turbines: simulating the full machine”, Computational Mechanics, 50 (2012) 821–833.MATHCrossRef M.-C. Hsu and Y. Bazilevs, “Fluid–structure interaction modeling of wind turbines: simulating the full machine”, Computational Mechanics, 50 (2012) 821–833.MATHCrossRef
147.
go back to reference C. Johnson, Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Sweden, 1987.MATH C. Johnson, Numerical solution of partial differential equations by the finite element method. Cambridge University Press, Sweden, 1987.MATH
148.
go back to reference S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 2nd ed. Springer, 2002. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 2nd ed. Springer, 2002.
149.
152.
go back to reference T.J.R. Hughes, L.P. Franca, and M. Balestra, “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”, Computer Methods in Applied Mechanics and Engineering, 59 (1986) 85–99.MathSciNetMATHCrossRef T.J.R. Hughes, L.P. Franca, and M. Balestra, “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”, Computer Methods in Applied Mechanics and Engineering, 59 (1986) 85–99.MathSciNetMATHCrossRef
154.
go back to reference T.J.R. Hughes, G.R. Feijóo, L. Mazzei, and J.-B. Quincy, “The variational multiscale method–A paradigm for computational mechanics”, Computer Methods in Applied Mechanics and Engineering, 166 (1998) 3–24.MathSciNetMATHCrossRef T.J.R. Hughes, G.R. Feijóo, L. Mazzei, and J.-B. Quincy, “The variational multiscale method–A paradigm for computational mechanics”, Computer Methods in Applied Mechanics and Engineering, 166 (1998) 3–24.MathSciNetMATHCrossRef
155.
go back to reference T.J.R. Hughes and G. Sangalli, “Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods”, SIAM Journal of Numerical Analysis, 45 (2007) 539–557.MathSciNetMATHCrossRef T.J.R. Hughes and G. Sangalli, “Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods”, SIAM Journal of Numerical Analysis, 45 (2007) 539–557.MathSciNetMATHCrossRef
156.
go back to reference F. Shakib, T.J.R. Hughes, and Z. Johan, “A multi-element group preconditionined GMRES algorithm for nonsymmetric systems arising in finite element analysis”, Computer Methods in Applied Mechanics and Engineering, 75 (1989) 415–456.MathSciNetMATHCrossRef F. Shakib, T.J.R. Hughes, and Z. Johan, “A multi-element group preconditionined GMRES algorithm for nonsymmetric systems arising in finite element analysis”, Computer Methods in Applied Mechanics and Engineering, 75 (1989) 415–456.MathSciNetMATHCrossRef
157.
go back to reference T.J.R. Hughes and M. Mallet, “A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems”, Computer Methods in Applied Mechanics and Engineering, 58 (1986) 305–328.MathSciNetMATHCrossRef T.J.R. Hughes and M. Mallet, “A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems”, Computer Methods in Applied Mechanics and Engineering, 58 (1986) 305–328.MathSciNetMATHCrossRef
159.
go back to reference B.E. Launder and D.B. Spalding, “The numerical computation of turbulent flows”, Computer Methods in Applied Mechanics and Engineering, 3 (1974) 269–289.MATHCrossRef B.E. Launder and D.B. Spalding, “The numerical computation of turbulent flows”, Computer Methods in Applied Mechanics and Engineering, 3 (1974) 269–289.MATHCrossRef
160.
go back to reference D.C. Wilcox, Turbulence Modeling for CFD. DCW Industries, La Canada, CA, 1998. D.C. Wilcox, Turbulence Modeling for CFD. DCW Industries, La Canada, CA, 1998.
161.
go back to reference R. Golshan, A. Tejada-Martínez, M. Juha, and Y. Bazilevs, “Large-eddy simulation with near-wall modeling using weakly enforced no-slip boundary conditions”, Computers & Fluids, 118 (2015) 172–181.MathSciNetMATHCrossRef R. Golshan, A. Tejada-Martínez, M. Juha, and Y. Bazilevs, “Large-eddy simulation with near-wall modeling using weakly enforced no-slip boundary conditions”, Computers & Fluids, 118 (2015) 172–181.MathSciNetMATHCrossRef
175.
go back to reference A. Corsini, C. Menichini, F. Rispoli, A. Santoriello, and T.E. Tezduyar, “A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms”, Journal of Applied Mechanics, 76 (2009) 021211, https://doi.org/10.1115/1.3062967.CrossRef A. Corsini, C. Menichini, F. Rispoli, A. Santoriello, and T.E. Tezduyar, “A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms”, Journal of Applied Mechanics, 76 (2009) 021211, https://​doi.​org/​10.​1115/​1.​3062967.CrossRef
176.
184.
go back to reference K. Takizawa, T.E. Tezduyar, and Y. Otoguro, “Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations”, Computational Mechanics, published online, https://doi.org/10.1007/s00466-018-1557-x, April 2018. K. Takizawa, T.E. Tezduyar, and Y. Otoguro, “Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations”, Computational Mechanics, published online, https://​doi.​org/​10.​1007/​s00466-018-1557-x, April 2018.
185.
go back to reference M.-C. Hsu, I. Akkerman, and Y. Bazilevs, “Wind turbine aerodynamics using ALE-VMS: Validation and role of weakly enforced boundary conditions”, Computational Mechanics, 50 (2012) 499–511.MathSciNetMATHCrossRef M.-C. Hsu, I. Akkerman, and Y. Bazilevs, “Wind turbine aerodynamics using ALE-VMS: Validation and role of weakly enforced boundary conditions”, Computational Mechanics, 50 (2012) 499–511.MathSciNetMATHCrossRef
186.
go back to reference Y. Otoguro, K. Takizawa, T.E. Tezduyar, K. Nagaoka, and S. Mei, “Turbocharger turbine and exhaust manifold flow computation with the Space–Time Variational Multiscale Method and Isogeometric Analysis”, Computers & Fluids, submitted, 2018. Y. Otoguro, K. Takizawa, T.E. Tezduyar, K. Nagaoka, and S. Mei, “Turbocharger turbine and exhaust manifold flow computation with the Space–Time Variational Multiscale Method and Isogeometric Analysis”, Computers & Fluids, submitted, 2018.
187.
go back to reference S.B. Raknes, X. Deng, Y. Bazilevs, D.J. Benson, K.M. Mathisen, and T. Kvamsdal, “Isogeometric rotation-free bending-stabilized cables: Statics, dynamics, bending strips and coupling with shells”, Computer Methods in Applied Mechanics and Engineering, 263 (2013) 127–143.MathSciNetMATHCrossRef S.B. Raknes, X. Deng, Y. Bazilevs, D.J. Benson, K.M. Mathisen, and T. Kvamsdal, “Isogeometric rotation-free bending-stabilized cables: Statics, dynamics, bending strips and coupling with shells”, Computer Methods in Applied Mechanics and Engineering, 263 (2013) 127–143.MathSciNetMATHCrossRef
188.
go back to reference L. Piegl and W. Tiller, The NURBS Book (Monographs in Visual Communication), 2nd ed. Springer-Verlag, New York, 1997.MATHCrossRef L. Piegl and W. Tiller, The NURBS Book (Monographs in Visual Communication), 2nd ed. Springer-Verlag, New York, 1997.MATHCrossRef
189.
go back to reference T. Belytschko, W.K. Liu, and B. Moran, Nonlinear Finite Elements for Continua and Structures. Wiley, 2000.MATH T. Belytschko, W.K. Liu, and B. Moran, Nonlinear Finite Elements for Continua and Structures. Wiley, 2000.MATH
190.
go back to reference M. Bischoff, W.A. Wall, K.-U. Bletzinger, and E. Ramm, “Models and finite elements for thin-walled structures”, in E. Stein, R. de Borst, and T.J.R. Hughes, editors, Encyclopedia of Computational Mechanics, Vol. 2, Solids, Structures and Coupled Problems, Chapter 3, Wiley, 2004. M. Bischoff, W.A. Wall, K.-U. Bletzinger, and E. Ramm, “Models and finite elements for thin-walled structures”, in E. Stein, R. de Borst, and T.J.R. Hughes, editors, Encyclopedia of Computational Mechanics, Vol. 2, Solids, Structures and Coupled Problems, Chapter 3, Wiley, 2004.
191.
go back to reference J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed. CRC Press, Boca Raton, FL, 2004.CrossRef J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed. CRC Press, Boca Raton, FL, 2004.CrossRef
192.
go back to reference Y. Guo and M. Ruess, “Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures”, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 881–905.MathSciNetMATHCrossRef Y. Guo and M. Ruess, “Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures”, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 881–905.MathSciNetMATHCrossRef
193.
go back to reference J. Chung and G.M. Hulbert, “A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method”, Journal of Applied Mechanics, 60 (1993) 371–75.MathSciNetMATHCrossRef J. Chung and G.M. Hulbert, “A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-α method”, Journal of Applied Mechanics, 60 (1993) 371–75.MathSciNetMATHCrossRef
194.
go back to reference H. Melbø and T. Kvamsdal, “Goal oriented error estimators for Stokes equations based on variationally consistent postprocessing”, Computer Methods in Applied Mechanics and Engineering, 192 (2003) 613–633.MathSciNetMATHCrossRef H. Melbø and T. Kvamsdal, “Goal oriented error estimators for Stokes equations based on variationally consistent postprocessing”, Computer Methods in Applied Mechanics and Engineering, 192 (2003) 613–633.MathSciNetMATHCrossRef
195.
go back to reference E.H. van Brummelen, V.V. Garg, S. Prudhomme, and K.G. van der Zee, “Flux evaluation in primal and dual boundary-coupled problems”, Journal of Applied Mechanics, 79 (2011) 010904.CrossRef E.H. van Brummelen, V.V. Garg, S. Prudhomme, and K.G. van der Zee, “Flux evaluation in primal and dual boundary-coupled problems”, Journal of Applied Mechanics, 79 (2011) 010904.CrossRef
196.
go back to reference T.E. Tezduyar, M. Behr, S. Mittal, and A.A. Johnson, “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, (1992) 7–24. T.E. Tezduyar, M. Behr, S. Mittal, and A.A. Johnson, “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, (1992) 7–24.
200.
go back to reference T. Tezduyar, “Finite element interface-tracking and interface-capturing techniques for flows with moving boundaries and interfaces”, in Proceedings of the ASME Symposium on Fluid-Physics and Heat Transfer for Macro- and Micro-Scale Gas-Liquid and Phase-Change Flows (CD-ROM), ASME Paper IMECE2001/HTD-24206, ASME, New York, New York, (2001). T. Tezduyar, “Finite element interface-tracking and interface-capturing techniques for flows with moving boundaries and interfaces”, in Proceedings of the ASME Symposium on Fluid-Physics and Heat Transfer for Macro- and Micro-Scale Gas-Liquid and Phase-Change Flows (CD-ROM), ASME Paper IMECE2001/HTD-24206, ASME, New York, New York, (2001).
203.
go back to reference T.E. Tezduyar, S. Sathe, M. Senga, L. Aureli, K. Stein, and B. Griffin, “Finite element modeling of fluid–structure interactions with space–time and advanced mesh update techniques”, in Proceedings of the 10th International Conference on Numerical Methods in Continuum Mechanics (CD-ROM), Zilina, Slovakia, (2005). T.E. Tezduyar, S. Sathe, M. Senga, L. Aureli, K. Stein, and B. Griffin, “Finite element modeling of fluid–structure interactions with space–time and advanced mesh update techniques”, in Proceedings of the 10th International Conference on Numerical Methods in Continuum Mechanics (CD-ROM), Zilina, Slovakia, (2005).
204.
go back to reference T.J.R. Hughes and J. Winget, “Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis”, International Journal for Numerical Methods in Engineering, 15 (1980) 1862–1867.MathSciNetMATHCrossRef T.J.R. Hughes and J. Winget, “Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis”, International Journal for Numerical Methods in Engineering, 15 (1980) 1862–1867.MathSciNetMATHCrossRef
205.
go back to reference O. Rodrigues, “Des lois geometriques qui regissent les deplacements dun systeme solide dans lespace, et de la variation des coordonnees provenant de ces deplacements consideres independamment des causes qui peuvent les produire”, Journal de Mathematiques, 5 (1840) 380–440. O. Rodrigues, “Des lois geometriques qui regissent les deplacements dun systeme solide dans lespace, et de la variation des coordonnees provenant de ces deplacements consideres independamment des causes qui peuvent les produire”, Journal de Mathematiques, 5 (1840) 380–440.
206.
go back to reference B. Gayen, S. Sarkar, and J.R. Taylor, “Large eddy simulation of a stratified boundary layer under an oscillatory current”, Journal of Fluid Mechanics, 643 (2010) 233–266.MATHCrossRef B. Gayen, S. Sarkar, and J.R. Taylor, “Large eddy simulation of a stratified boundary layer under an oscillatory current”, Journal of Fluid Mechanics, 643 (2010) 233–266.MATHCrossRef
207.
go back to reference B. Gayen and S. Sarkar, “Direct and large-eddy simulations of internal tide generation at a near-critical slope.”, Journal of Fluid Mechanics, 681 (2011) 48–79.MathSciNetMATHCrossRef B. Gayen and S. Sarkar, “Direct and large-eddy simulations of internal tide generation at a near-critical slope.”, Journal of Fluid Mechanics, 681 (2011) 48–79.MathSciNetMATHCrossRef
208.
go back to reference R. Beare, M. Macvean, A. Holtslag, J. Cuxart, I. Esau, J.-C. Golaz, M. Jimenez, M. Khairoutdinov, B. Kosovic, D. Lewellen, T. Lund, J. Lundquist, A. Mccabe, A. Moene, Y. Noh, S. Raasch, and P. Sullivan, “An intercomparison of large-eddy simulations of the stable boundary layer”, Boundary-Layer Meteor., 118 (2006) 247–272.CrossRef R. Beare, M. Macvean, A. Holtslag, J. Cuxart, I. Esau, J.-C. Golaz, M. Jimenez, M. Khairoutdinov, B. Kosovic, D. Lewellen, T. Lund, J. Lundquist, A. Mccabe, A. Moene, Y. Noh, S. Raasch, and P. Sullivan, “An intercomparison of large-eddy simulations of the stable boundary layer”, Boundary-Layer Meteor., 118 (2006) 247–272.CrossRef
209.
go back to reference D.T. Griffith and T.D. Ashwill, “The sandia 100-meter all-glass baseline wind turbine blade: Snl100-00”, SANDIA REPORT, SAND2011-3779, (2011). D.T. Griffith and T.D. Ashwill, “The sandia 100-meter all-glass baseline wind turbine blade: Snl100-00”, SANDIA REPORT, SAND2011-3779, (2011).
210.
go back to reference J. Jonkman, S. Butterfield, W. Musial, and G. Scott, “Definition of a 5-MW reference wind turbine for offshore system development”, Technical Report NREL/TP-500-38060, National Renewable Energy Laboratory, 2009. J. Jonkman, S. Butterfield, W. Musial, and G. Scott, “Definition of a 5-MW reference wind turbine for offshore system development”, Technical Report NREL/TP-500-38060, National Renewable Energy Laboratory, 2009.
211.
go back to reference R. Bravo, S. Tullis, and S. Ziada, “Performance testing of a small vertical-axis wind turbine”, Proceedings of the 21st Canadian Congress of Applied Mechanics, (2007) 470–471. R. Bravo, S. Tullis, and S. Ziada, “Performance testing of a small vertical-axis wind turbine”, Proceedings of the 21st Canadian Congress of Applied Mechanics, (2007) 470–471.
212.
213.
go back to reference J.O. Dabiri, “Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays”, Journal of Renewable and Sustainable Energy, 3 (2011) 043104.CrossRef J.O. Dabiri, “Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays”, Journal of Renewable and Sustainable Energy, 3 (2011) 043104.CrossRef
215.
go back to reference Y. Bazilevs, M.-C. Hsu, J. Kiendl, and D.J. Benson, “A computational procedure for prebending of wind turbine blades”, International Journal for Numerical Methods in Engineering, 89 (2012) 323–336.MATHCrossRef Y. Bazilevs, M.-C. Hsu, J. Kiendl, and D.J. Benson, “A computational procedure for prebending of wind turbine blades”, International Journal for Numerical Methods in Engineering, 89 (2012) 323–336.MATHCrossRef
217.
go back to reference N. Hill, R. Dominy, G. Ingram, and J. Dominy, “Darrieus turbines: the physics of self-starting”, Proc. IMechE Part A: J. Power and Energy, 223(1) (2009) 21–29.CrossRef N. Hill, R. Dominy, G. Ingram, and J. Dominy, “Darrieus turbines: the physics of self-starting”, Proc. IMechE Part A: J. Power and Energy, 223(1) (2009) 21–29.CrossRef
218.
go back to reference J.R. Baker, “Features to aid or enable self starting of pitched low solidity vertical axis wind turbines”, J. Wind Eng. Ind. Aerodyn., 15 (1983) 369–380.CrossRef J.R. Baker, “Features to aid or enable self starting of pitched low solidity vertical axis wind turbines”, J. Wind Eng. Ind. Aerodyn., 15 (1983) 369–380.CrossRef
219.
go back to reference Y. Osawa and T. Tezduyar, “A multi-domain method for 3D computation of wake flow behind a circular cylinder”, Computational Fluid Dynamics Journal, 8 (1999) 296–308. Y. Osawa and T. Tezduyar, “A multi-domain method for 3D computation of wake flow behind a circular cylinder”, Computational Fluid Dynamics Journal, 8 (1999) 296–308.
223.
go back to reference M. Jalali, N. Rapaka, and S. Sarkar, “Tidal flow over topography: effect of excursion number on wave energetics and turbulence”, Journal of Fluid Mechanics, 750 (2014) 259–283.CrossRef M. Jalali, N. Rapaka, and S. Sarkar, “Tidal flow over topography: effect of excursion number on wave energetics and turbulence”, Journal of Fluid Mechanics, 750 (2014) 259–283.CrossRef
224.
go back to reference S. Gohari and S. Sarkar, “Tidal flow over topography: effect of excursion number on wave energetics and turbulence”, Boundary-Layer Meteorology, (2016), Accepted for publication. S. Gohari and S. Sarkar, “Tidal flow over topography: effect of excursion number on wave energetics and turbulence”, Boundary-Layer Meteorology, (2016), Accepted for publication.
225.
go back to reference Y. Bazilevs, A. Korobenko, X. Deng, and J. Yan, “Fluid–structure interaction modeling for fatigue-damage prediction in full-scale wind-turbine blades”, Journal of Applied Mechanics, 83 (6) (2016) 061010.CrossRef Y. Bazilevs, A. Korobenko, X. Deng, and J. Yan, “Fluid–structure interaction modeling for fatigue-damage prediction in full-scale wind-turbine blades”, Journal of Applied Mechanics, 83 (6) (2016) 061010.CrossRef
Metadata
Title
Recent Advances in ALE-VMS and ST-VMS Computational Aerodynamic and FSI Analysis of Wind Turbines
Authors
Artem Korobenko
Yuri Bazilevs
Kenji Takizawa
Tayfun E. Tezduyar
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-96469-0_7

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