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Finite element methodology for modeling aircraft aerodynamics: development, simulation, and validation

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Abstract

In this work, we propose and validate a new stabilized compressible flow finite element framework for the simulation of aerospace applications. The framework is comprised of the streamline upwind/Petrov–Galerkin (SUPG)-based Navier–Stokes equations for compressible flows, the weakly enforced essential boundary conditions that act as a wall function, and the entropy-based discontinuity-capturing equation that acts as a shock-capturing operator. The accuracy and robustness of the framework is tested for various Mach numbers ranging from low-subsonic to transonic flow regimes. The aerodynamic simulations are carried out for 2D and 3D validation cases of flow around the NACA 0012 airfoil, RAE 2822 airfoil, ONERA M6 wing, and NASA Common Research Model (CRM) aircraft. The pressure coefficients obtained from the simulations of all cases are compared with experimental data. The computational results show good agreement with the experimental findings and demonstrate the accuracy and effectiveness of the finite element framework presented in this work for the simulation of aircraft aerodynamics.

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References

  1. Antoniadis AF, Tsoutsanis P, Drikakis D (2017) Assessment of high-order finite volume methods on unstructured meshes for RANS solutions of aeronautical configurations. Comput Fluids 146:86–104

    Article  MathSciNet  MATH  Google Scholar 

  2. Pulliam TH, Steger JL (1980) Implicit finite difference simulations of three-dimensional compressible flow. AIAA J 18:159–167

    Article  MATH  Google Scholar 

  3. Ballhaus WF, Goorjian PM (1977) Implicit finite difference computations of unsteady transonic flows about airfoils. AIAA J 15:1728–1735

    Article  MATH  Google Scholar 

  4. Donea J, Huerta A (2003) Finite element methods for flow problems. John Wiley & Sons, Chichester

    Book  Google Scholar 

  5. 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 

  6. 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

    Article  MathSciNet  MATH  Google Scholar 

  7. Hughes TJR, Mallet M (1986a) A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective–diffusive systems. Comput Methods Appl Mech Eng 58:305–328

    Article  MathSciNet  MATH  Google Scholar 

  8. Hughes TJR, Franca LP, Mallet A (1986a) A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier–Stokes equations and the second law of thermodynamics. Comput Methods Appl Mech Eng 54:223–234

    Article  MathSciNet  MATH  Google Scholar 

  9. Hughes TJR, Franca LP, Mallet M (1987) A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems. Comput Methods Appl Mech Eng 63:97–112

    Article  MATH  Google Scholar 

  10. Shakib F, Hughes TJR, Johan Z (1991) A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier–Stokes equations. Comput Methods Appl Mech Engrg 89:141–219

    Article  MathSciNet  Google Scholar 

  11. Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104:397–422

    Article  MATH  Google Scholar 

  12. Aliabadi SK, Tezduyar TE (1993) Space-time finite element computation of compressible flows involving moving boundaries and interfaces. Comput Methods Appl Mech Eng 107:209–223

    Article  MATH  Google Scholar 

  13. Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119:157–177

    Article  MATH  Google Scholar 

  14. Hauke G, Hughes TJR (1994) A unified approach to compressible and incompressible flows. Comput Methods Appl Mech Eng 113:389–396

    Article  MathSciNet  MATH  Google Scholar 

  15. Wren GP, Ray SE, Aliabadi SK, Tezduyar TE (1995) Space-time finite element computation of compressible flows between moving components. Int J Numer Meth Fluids 21:981–991

    Article  MATH  Google Scholar 

  16. Wren GP, Ray SE, Aliabadi SK, Tezduyar TE (1997) Simulation of flow problems with moving mechanical components, fluid-structure interactions and two-fluid interfaces. Int J Numer Meth Fluids 24:1433–1448

    Article  MATH  Google Scholar 

  17. Ray SE, Wren GP, Tezduyar TE (1997) Parallel implementations of a finite element formulation for fluid-structure interactions in interior flows. Parallel Comput 23:1279–1292

    Article  MathSciNet  MATH  Google Scholar 

  18. Mittal S, Tezduyar T (1998) A unified finite element formulation for compressible and incompressible flows using augumented conservation variables. Comput Methods Appl Mech Eng 161:229–243

    Article  MATH  Google Scholar 

  19. Ray SE, Tezduyar TE (2000) Fluid-object interactions in interior ballistics. Comput Methods Appl Mech Eng 190:363–372

    Article  MATH  Google Scholar 

  20. Hauke G (2001) Simple stabilizing matrices for the computation of compressible flows in primitive variables. Comput Methods Appl Mech Eng 190:6881–6893

    Article  MATH  Google Scholar 

  21. Hughes TJR, Scovazzi G, Tezduyar TE (2010) Stabilized methods for compressible flows. J Sci Comput 43:343–368

    Article  MathSciNet  MATH  Google Scholar 

  22. 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

    Article  MathSciNet  MATH  Google Scholar 

  23. 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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  25. Hughes TJR, Mallet M, Mizukami A (1986b) 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 

  26. Hughes TJR, Mallet M (1986b) A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective–diffusive systems. Comput Methods Appl Mech Eng 58:329–339

    Article  MathSciNet  MATH  Google Scholar 

  27. Almeida RC, Galeão AC (1996) An adaptive Petrov-Galerkin formulation for the compressible Euler and Navier-Stokes equations. Comput Methods Appl Mech Eng 129:157–176

    Article  MathSciNet  MATH  Google Scholar 

  28. Hauke G, Hughes TJR (1998) A comparative study of different sets of variables for solving compressible and incompressible flows. Comput Methods Appl Mech Eng 153:1–44

    Article  MathSciNet  MATH  Google Scholar 

  29. Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195:1621–1632

    Article  MathSciNet  MATH  Google Scholar 

  30. Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ\(\beta \) shock-capturing. Comput Mech 38:469–481

    Article  MATH  Google Scholar 

  31. Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ\(\beta \) shock-capturing. Comput Fluids 36:147–159

    Article  MATH  Google Scholar 

  32. Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZ\(\beta \) shock-capturing. Int J Numer Meth Fluids 54:695–706

    Article  MathSciNet  MATH  Google Scholar 

  33. Rispoli F, Saavedra R, Menichini F, Tezduyar TE (2009) Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZ\(\beta \) shock-capturing. J Appl Mech 76:021209

    Article  Google Scholar 

  34. Rispoli F, Delibra G, Venturini P, Corsini A, Saavedra R, Tezduyar TE (2015) Particle tracking and particle-shock interaction in compressible-flow computations with the V-SGS stabilization and YZ\(\beta \) shock-capturing. Comput Mech 55:1201–1209

    Article  MathSciNet  MATH  Google Scholar 

  35. 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

    Article  MathSciNet  MATH  Google Scholar 

  36. Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36:12–26

    Article  MathSciNet  MATH  Google Scholar 

  37. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2007) Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput Methods Appl Mech Eng 196:4853–4862

    Article  MathSciNet  MATH  Google Scholar 

  38. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2010) Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. Comput Methods Appl Mech Eng 199:780–790

    Article  MathSciNet  MATH  Google Scholar 

  39. 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

    Article  MathSciNet  MATH  Google Scholar 

  40. 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 

  41. Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: Validation and the role of weakly enforced boundary conditions. Comput Mech 50:499–511

    Article  MathSciNet  Google Scholar 

  42. Hsu M-C, Akkerman I, Bazilevs Y (2014) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy 17:461–481

    Article  Google Scholar 

  43. Xu S, Gao B, Hsu M-C, Ganapathysubramanian B (2019) A residual-based variational multiscale method with weak imposition of boundary conditions for buoyancy-driven flows. Comput Methods Appl Mech Eng 352:345–368

    Article  MathSciNet  MATH  Google Scholar 

  44. Golshan R, Tejada-Martínez AE, Juha M, Bazilevs Y (2015) Large-eddy simulation with near-wall modeling using weakly enforced no-slip boundary conditions. Comput Fluids 118:172–181

    Article  MathSciNet  MATH  Google Scholar 

  45. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

  47. Xu F, Bazilevs Y, Hsu M-C (2019) Immersogeometric analysis of compressible flows with application to aerodynamic simulation of rotorcraft. Math Models Methods Appl Sci 29:905–938

    Article  MathSciNet  MATH  Google Scholar 

  48. 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 

  49. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  51. Sturek WB, Ray S, Aliabadi S, Waters C, Tezduyar TE (1997) Parallel finite element computation of missile aerodynamics. Int J Numer Meth Fluids 24:1417–1432

    Article  MATH  Google Scholar 

  52. 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 

  53. 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 

  54. 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

    Article  MathSciNet  MATH  Google Scholar 

  55. 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

    Article  MathSciNet  MATH  Google Scholar 

  56. Ladson C. L.(1988) Effects of independent variation of Mach and Reynolds numbers on the low-speed aerodynamic characteristics of the NACA 0012 airfoil section. NASA Technical Report TM-4074, NASA,

  57. Gregory N, O’Reilly C L(1970) Low-speed aerodynamic characteristics of NACA 0012 aerofoil section, including the effects of upper-surface roughness simulating hoar frost. NASA Technical Report R &M3726, NASA,

  58. Harris C D(1981) Two-dimensional aerodynamic characteristics of the NACA 0012 airfoil in the Langley 8-Foot Transonic Pressure Tunnel. NASA Technical Report TM-81927, NASA,

  59. Cook P H, McDonald M A, Firmin M C P(1979) Aerofoil RAE 2822 – pressure distributions, and boundary layer and wake measurements. AGARD Report AR-138, AGARD,

  60. Schmitt V, Charpin F (1979)Pressure distributions on the ONERA-M6-Wing at transonic Mach numbers. AGARD Report AR-138, AGARD,

  61. Vassberg J, Dehaan M, Rivers M, Wahls R Development of a Common Research Model for applied CFD validation studies. In AIAA 2008-6919, Honolulu, Hawaii, 2008. 26th AIAA applied aerodynamics conference

  62. Rivers MB, Dittberner A (2014) Experimental investigations of the NASA Common Research Model. J Aircr 51:1183–1193

    Article  Google Scholar 

  63. NASA Common Research Model. https://commonresearchmodel.larc.nasa.gov/. [Accessed 31 March 2022]

  64. Le Beau G. J, Tezduyar T. E(1991) Finite element computation of compressible flows with the SUPG formulation. In Advances in Finite Element Analysis in Fluid Dynamics, FED-Vol.123, pp 21–27, New York, ASME

  65. Hughes TJR, Feijóo GR, Mazzei L, Quincy JB (1998) The variational multiscale method-A paradigm for computational mechanics. Comput Methods Appl Mech Eng 166:3–24

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  68. Pope SB (2000) Turbulent Flows. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  69. 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 

  70. Hughes TJR, Sangalli G (2007) Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM J Numer Anal 45:539–557

    Article  MathSciNet  MATH  Google Scholar 

  71. Masud A, Calderer R (2011) A variational multiscale method for incompressible turbulent flows: Bubble functions and fine scale fields. Comput Methods Appl Mech Eng 200:2577–2593

    Article  MathSciNet  MATH  Google Scholar 

  72. 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

    Article  MathSciNet  MATH  Google Scholar 

  73. Masud A, Calderer R (2013) Residual-based turbulence models for moving boundary flows: hierarchical application of variational multiscale method and three-level scale separation. Int J Numer Meth Fluids 73(3):284–305

    Article  MathSciNet  MATH  Google Scholar 

  74. Bazilevs Y, Yan J, de Stadler M, Sarkar S (2014) Computation of the flow over a sphere at \(Re\) = 3700: a comparison of uniform and turbulent inflow conditions. J Appl Mech 81:121003

    Article  Google Scholar 

  75. 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

    Article  MathSciNet  MATH  Google Scholar 

  76. Calderer R, Zhu L, Gibson R, Masud A (2015) Residual-based turbulence models and arbitrary Lagrangian-Eulerian framework for free surface flows. Math Models Methods Appl Sci 25(12):2287–2317

    Article  MathSciNet  MATH  Google Scholar 

  77. Yang L, Badia S, Codina R (2016) A pseudo-compressible variational multiscale solver for turbulent incompressible flows. Comput Mech 58:1051–1069

    Article  MathSciNet  MATH  Google Scholar 

  78. Yan J, Korobenko A, Tejada-Martínez AE, Golshan R, Bazilevs Y (2017) A new variational multiscale formulation for stratified incompressible turbulent flows. Comput Fluids 158:150–156

    Article  MathSciNet  MATH  Google Scholar 

  79. Korobenko A, Bazilevs Y, Takizawa K, Tezduyar TE (2019) Computer Modeling of Wind Turbines: 1. ALE-VMS and ST-VMS Aerodynamic and FSI Analysis. Archives Comput Methods Eng 26:1059–1099

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  81. 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

    Article  MathSciNet  MATH  Google Scholar 

  82. 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

    Article  MathSciNet  MATH  Google Scholar 

  83. Zhu Q, Yan J, Tejada-Martínez AE, Bazilevs Y (2020) Variational multiscale modeling of Langmuir turbulent boundary layers in shallow water using Isogeometric Analysis. Mech Res Commun 108:103570

    Article  Google Scholar 

  84. Cen H, Zhou Q, Korobenko A (2021) Simulation of stably stratified turbulent channel flow using residual-based variational multiscale method and isogeometric analysis. Computers & Fluids 214:104765

    Article  MathSciNet  MATH  Google Scholar 

  85. Aydinbakar L, Takizawa K, Tezduyar TE, Kuraishi T (2021) Space-time VMS isogeometric analysis of the Taylor-Couette flow. Comput Mech 67:1515–1541

    Article  MathSciNet  MATH  Google Scholar 

  86. Wilcox DC (2006) Turbulence Modeling for CFD, 3rd edn. DCW Industries Inc, La Cañada, CA

    Google Scholar 

  87. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–75

    Article  MathSciNet  MATH  Google Scholar 

  88. Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319

    Article  MathSciNet  MATH  Google Scholar 

  89. 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 

  90. Shakib F, Hughes TJR, Johan Z (1989) A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis. Comput Methods Appl Mech Eng 75:415-456

  91. NASA Langley Research Center Turbulence Modeling Resource: 2D NACA 0012 Airfoil Validation. https://turbmodels.larc.nasa.gov/naca0012_val.html. [Accessed 31 March 2022]

  92. NPARC Alliance CFD Verification and Validation: RAE 2822 Transonic Airfoil – Study #4. https://www.grc.nasa.gov/www/wind/valid/raetaf/raetaf04/raetaf04.html. [Accessed 31 March 2022]

  93. NPARC Alliance CFD Verification and Validation: RAE 2822 Transonic Airfoil. https://www.grc.nasa.gov/www/wind/valid/raetaf/raetaf.html. [Accessed 31 March 2022]

  94. NASA Langley Research Center Turbulence Modeling Resource: 3D ONERA M6 Wing Validation. https://turbmodels.larc.nasa.gov/onerawingnumerics_val.html. [Accessed 31 March 2022]

  95. NPARC Alliance CFD Verification and Validation: ONERA M6 Wing. https://www.grc.nasa.gov/www/wind/valid/m6wing/m6wing.html. [Accessed 31 March 2022]

  96. NASA Langley Research Center Turbulence Modeling Resource: 3D ONERA M6 Wing Validation – SA-neg Model Results. https://turbmodels.larc.nasa.gov/onerawingnumerics_val_sa.html. [Accessed 31 March 2022]

  97. NPARC Alliance CFD Verification and Validation: ONERA M6 Wing – Study #1. https://www.grc.nasa.gov/www/wind/valid/m6wing/m6wing01/m6wing01.html. [Accessed 31 March 2022]

  98. 6th AIAA CFD Drag Prediction Workshop. https://aiaa-dpw.larc.nasa.gov/Workshop6/workshop6.html. [Accessed 31 March 2022]

  99. 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 

  100. 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

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by the U.S. Naval Air Systems Command (NAVAIR) under Grant No. N68335-20-C-0899. This support is gratefully acknowledged. Y. Bazilevs was also partially supported by the NSF Award No. 1854436.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Iowa State University, Ames, IA, 50011, USA

    Manoj R. Rajanna & Ming-Chen Hsu

  2. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Emily L. Johnson

  3. Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada

    David Codoni & Artem Korobenko

  4. School of Engineering, Brown University, Providence, RI, 02912, USA

    Yuri Bazilevs

  5. Global Engineering & Materials, Inc., Princeton, NJ, 08540, USA

    Ning Liu & Jim Lua

  6. Structures Division, Naval Air Systems Command (NAVAIR), Patuxent River, MD, 20670, USA

    Nam Phan

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  1. Manoj R. Rajanna
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Rajanna, M.R., Johnson, E.L., Codoni, D. et al. Finite element methodology for modeling aircraft aerodynamics: development, simulation, and validation. Comput Mech 70, 549–563 (2022). https://doi.org/10.1007/s00466-022-02178-7

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