Over the past several decades, computational fluid dynamics has been increasingly used in the aerospace industry for the design and study of new and derivative aircraft. In this review we survey the CFD application process and note its place and importance within the everyday work of industry. Furthermore, the centrality of geometry and importance of turbulence models, higher-order numerical algorithms, output-based mesh adaptation, and numerical design optimization are discussed. Challenges in each area are noted and specific suggestions for investment are made. The review concludes with an outlook toward a future in which certification by analysis and model-based design are standard practice, along with a reminder of the steps necessary to lead the industry there.


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Literature Cited

  1. Alauzet F, Frey PJ, George PL, Mohammadi B. 2007. 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations. J. Comput. Phys. 222:2592–623
    [Google Scholar]
  2. Alauzet F, Loseille A. 2016. A decade of progress on anisotropic mesh adaptation for computational fluid dynamics. Comput.-Aided Des. 72:13–39
    [Google Scholar]
  3. Ashton N. 2017. Recalibrating delayed detached-eddy simulation to eliminate modelled-stress depletion Paper presented at 23rd AIAA Computational Fluid Dynamics Conference, Denver, CO, AIAA Pap2017–4281
  4. Ashton N, West A, Mendonça F. 2016. Flow dynamics past a 30P30N three-element airfoil using improved delayed detached-eddy simulation. AIAA J. 54:113657–67
    [Google Scholar]
  5. Balaras UPE, Piomelli U. 2002. Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34:349–74
    [Google Scholar]
  6. Bose ST, Park GI. 2018. Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mech. 50:535–61
    [Google Scholar]
  7. Boussinesq J. 1877. Essai sur la théorie des eaux courantes Paris: Impr. Natl.
  8. Buning P, Chiu I, Obayashi S, Rizk Y, Steger J. 1988. Numerical simulation of the integrated space shuttle vehicle in ascent Paper presented at 15th Atmospheric Flight Mechanics Conference, Minneapolis, MN, AIAA Pap1988–4359
  9. Bush R. 1988. A three dimensional zonal Navier-Stokes code for subsonic through hypersonic propulsion flowfields Paper presented at 24th Joint Propulsion Conference, Boston, AIAA Pap 2012-2830
  10. Bush R, Mani M. 2001. A two-equation large eddy stress model for high sub-grid shear Paper presented at 15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA, AIAA Pap 2001-2561
  11. Bush R, Power G, Towne C. 1998. WIND: the production flow solver of the NPARC Alliance Paper presented at 36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Pap 1997-935
  12. Cabot W, Moin P. 2000. Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow. Flow Turbul. Combust. 63:269–91
    [Google Scholar]
  13. Caplan P, Haimes R, Darmofal D, Galbraith M. 2019. Extension of local cavity operators to3d + t space-time mesh adaptation Paper presented at AIAA Scitech 2019 Forum, San Diego, CA, AIAA Pap 2019-1992
    [Google Scholar]
  14. Cary A, Dorgan A, Mani M. 2009. Towards accurate flow predictions using unstructured meshes Paper presented at 19th AIAA Computational Fluid Dynamics, San Antonio, TX, AIAA Pap 2009-3650
  15. Cascade Technol. 2021. Large-eddy simulation—our secret sauce Web Resour., Cascade Technol. Palo Alto, CA: https://www.cascadetechnologies.com/capabilities
  16. Cebeci T, Smith A. 1974. Analysis of Turbulent Boundary Layers New York: Academic
  17. Chakravarthy S, Szema KY, Goldberg U, Gorski J, Osher S. 1985. Application of a new class of high accuracy TVD schemes to the Navier-Stokes equations Paper presented at 23rd Aerospace Sciences Meeting, Reno, NV, AIAA Pap2012–165
  18. Chandrashekar P. 2013. Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations. Commun. Comput. Phys. 14:51252–86
    [Google Scholar]
  19. Cosner R. 1985. Integrated flowfield analysis methodology for fighter inlets Paper presented at Aircraft Design Systems and Operations Meeting, Colorado Springs, CO, AIAA Pap1985–3071
  20. Couchman BL, Darmofal DL, Allmaras S, Galbraith M. 2017. On the convergence of higher-order finite element methods to weak solutions Paper presented at 23rd AIAA Computational Fluid Dynamics Conference, Denver, CO, AIAA Pap2017–4274
  21. Darmofal D, Haimes R. 2005. Towards the next generation in CFD Paper presented at 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Pap2005–87
  22. Fidkowski K. 2012. An output-based dynamic order refinement strategy for unsteady aerodynamics Paper presented at 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, AIAA Pap2012–77
  23. Goc KA, Bose S, Moin P. 2020. Wall-modeled large eddy simulation of an aircraft in landing configuration Paper presented at AIAA Aviation 2020 Forum (Online), AIAA Pap2020–3002
  24. Goc KA, Bose ST, Moin P. 2022. Large eddy simulation of the NASA High-Lift Common Research Model Paper presented at AIAA Scitech 2022 Forum, San Diego, CA, AIAA Pap2022–1556
  25. Goc KA, Lehmkuhl O, Park GI, Bose ST, Moin P 2021. Large eddy simulation of aircraft at affordable cost: a milestone in computational fluid dynamics. Flow 1:E14
    [Google Scholar]
  26. Hayes WD. 1947. Linearized supersonic flow Tech. Rep. AL-222, North American Aviation Los Angeles, CA:
  27. Holst KR, Glasby RS, Erwin JT, Stefanski DL, Coder JG. 2019. High-order shock capturing techniques using HPCMP CREATE™-AV kestrel Paper presented at AIAA Scitech 2019 Forum, San Diego, CA, AIAA Pap2019–1345
  28. Honein AE, Moin P. 2004. Higher entropy conservation and numerical stability of compressible turbulence simulations. J. Comput. Phys. 201:2531–45
    [Google Scholar]
  29. Jameson A. 1987. Successes and challenges in computational aerodynamics Paper presented at 8th Computational Fluid Dynamics Conference, Honolulu, HI, AIAA Pap1987–1184
  30. Jameson A. 2008. Formulation of kinetic energy preserving conservative schemes for gas dynamics and direct numerical simulation of one-dimensional viscous compressible flow in a shock tube using entropy and kinetic energy preserving schemes. J. Sci. Comput. 34:188–208
    [Google Scholar]
  31. Jameson A, Caughey D. 1977. A finite volume method for transonic potential flow calculations Paper presented at 3rd Computational Fluid Dynamics Conference, Albuquerque, NM, AIAA Pap1977–635
  32. Jameson A, Schmidt W, Turkel E. 1981. Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes Paper presented at 14th Fluid and Plasma Dynamics Conference, Palo Alto, CA, AIAA Pap1981–1259
  33. Johnson FT, Tinoco EN, Yu NJ. 2005. Thirty years of development and application of CFD at Boeing Commercial Airplanes, Seattle. Comput. Fluids 34:101115–51
    [Google Scholar]
  34. Jones RT. 1946. Properties of low-aspect-ratio pointed wings at speeds below and above the speed of sound Tech. Rep. 835, NACA (Natl. Adv. Comm. Aeronaut.) Washington, DC:
  35. Kamenetskiy DS, Bussoletti JE, Hilmes CL, Venkatakrishnan V, Wigton LB, Johnson FT. 2014. Numerical evidence of multiple solutions for the Reynolds-averaged Navier–Stokes equations. AIAA J. 52:81686–98
    [Google Scholar]
  36. Krakos JA, Darmofal DL. 2010. Effect of small-scale output unsteadiness on adjoint-based sensitivity. AIAA J. 48:112611–23
    [Google Scholar]
  37. Kuya Y, Kawai S. 2020. Stable, non-dissipative and physically-consistent kinetic energy and entropy preserving (KEEP) schemes for compressible flows Paper presented at AIAA Scitech 2020 Forum, Orlando, FL, AIAA Pap2020–0565
  38. Lakebrink MT, Mani M. 2018. Numerical investigation of dynamic distortion and flow control in a serpentine diffuser Paper presented at 2018 AIAA Aerospace Sciences Meeting, Kissimmee, FL, AIAA Pap 2018-1283
  39. Larsson J, Kawai S. 2010. Wall-modeling in large eddy simulation: length scales, grid resolution and accuracy. Annual Research Briefs 202039–46 Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  40. Larsson J, Kawai S, Bodart J, Bermejo-Moreno I. 2016. Large eddy simulation with modeled wall-stress: recent progress and future directions. Mech. Eng. Rev. 3:115–00418
    [Google Scholar]
  41. Larsson J, Wang Q. 2014. The prospect of using large eddy and detached eddy simulations in engineering design, and the research required to get there. Philos. Trans. R. Soc. A 372:202220130329
    [Google Scholar]
  42. Lee HB, Ghia U, Bayyuk S, Oberkampf W, Roy CJ et al. 2016. Development and use of engineering standards for computational fluid dynamics for complex aerospace systems Paper presented at 46th AIAA Fluid Dynamics Conference, Washington, DC, AIAA Pap2016–3811
  43. Lehmkuhl O, Park G, Bose S, Moin P. 2019. Large-eddy simulation of practical aeronautical flows at stall conditions. Proceedings of the Summer Program 201887–96 Stanford, CA: Cent. Turbul. Res.
    [Google Scholar]
  44. Levy D, Laflin K, Vassberg J, Tinoco E, Mani M et al. 2013. Summary of data from the Fifth AIAA CFD Drag Prediction Workshop Paper presented at 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, AIAA Pap2013–46
  45. Lozano-Durán A, Bose ST, Moin P 2021. Performance of wall-modeled LES for external aerodynamics in the NASA juncture flow. arXiv:2101.00331 [physics.flu-dyn]. https://doi.org/10.48550/arXiv.2107.01506
  46. Mani A, Park D. 2021. Macroscopic forcing method: a tool for turbulence modeling and analysis of closures. Phys. Rev. Fluids 6:5054607
    [Google Scholar]
  47. Mani M, Babcock D, Winkler C, Spalart P. 2013. Predictions of a supersonic turbulent flow in a square duct Paper presented at 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, AIAA Pap2013–860
  48. Mani M, Cary A, Ramakrishnan S 2004. A structured and hybrid-unstructured grid Euler and Navier-Stokes solver for general geometry Paper presented at 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Pap2004–524
  49. Mani M, Ladd J, Cain A, Bush R 1997. An assessment of one-and two-equation turbulence models for internal and external flows Paper presented at 28th Fluid Dynamics Conference, Snowmass Village, CO, AIAA Pap 1997-2010
  50. Mani M, Winkler C. 2016. Investigation of shielding parameters in SA/DDES Intern. Memo., Boeing Arlington, VA:
  51. Mauery T, Alonso J, Cary A, Lee V, Malecki R et al. 2021. A guide for aircraft certification by analysis Contract. Rep. 20210015404, NASA Langley Res. Cent. Hampton, VA:
  52. Mayfield M 2020. JUST IN: Air Force ‘Digital Century Series’ acquisition concept nearing milestone. National Defense July 14. https://www.nationaldefensemagazine.org/articles/2020/7/14/air-force-digital-century-series-concept-approaching-new
    [Google Scholar]
  53. McLean J, Randall J. 1979. Computer program to calculate three-dimensional boundary layer flows over wings with wall mass transfer Contract. Rep. 3123, NASA Langley Res. Cent. Hampton, VA:
  54. Menter FR. 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32:81598–605
    [Google Scholar]
  55. Menter FR 2016. Stress-blended eddy simulation (SBES)—a new paradigm in hybrid RANS-LES modeling. Progress in Hybrid RANS-LES Modelling Y Hoarau, SH Peng, D Schwamborn, A Revell 27–37 Cham, Switz: Springer
    [Google Scholar]
  56. Michal T, Krakos J. 2012. Anisotropic mesh adaptation through edge primitive operations Paper presented at 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, AIAA Pap2012–159
  57. Michal T, Krakos J, Kamenetskiy D, Galbraith M, Ursachi CI et al. 2021. Comparing unstructured adaptive mesh solutions for the high lift common research airfoil. AIAA J. 59:93566–84
    [Google Scholar]
  58. Murman EM, Cole JD. 1971. Calculation of plane steady transonic flows. AIAA J. 9:1114–21
    [Google Scholar]
  59. Nishikawa H, Liu Y. 2018. Third-order edge-based scheme for unsteady problems Paper presented at 2018 Fluid Dynamics Conference, Atlanta, AIAA Pap2018–4166
  60. Oberkampf WL, Smith B. 2014. Assessment criteria for computational fluid dynamics validation benchmark experiments Paper presented at 52nd Aerospace Sciences Meeting, National Harbor, MD, AIAA Pap 2014-0205
  61. Park GI, Moin P. 2014. An improved dynamic non-equilibrium wall-model for large eddy simulation. Phys. Fluids 26:015108
    [Google Scholar]
  62. Park MA. 2008. Anisotropic output-based adaptation with tetrahedral cut cells for compressible flows PhD Thesis, Mass. Inst. Technol. Cambridge, MA:
  63. Park MA, Loseille A, Krakos J, Michal TR, Alonso JJ 2016. Unstructured grid adaptation: status, potential impacts, and recommended investments towards CFD Vision 2030 Paper presented at 46th AIAA Fluid Dynamics Conference, Washington, DC, AIAA Pap2016–3323
  64. Power G, Cooper G, Sirbaugh J. 1995. NPARC 2.2 -- features and capabilities Paper presented at 31st Joint Propulsion Conference and Exhibit, San Diego, CA, AIAA Pap 1995–2609
  65. Reyhner T. 1981. Transonic potential flow computation about three-dimensional inlets, ducts, and bodies. AIAA J. 19:91112–21
    [Google Scholar]
  66. Roe PL. 1981. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:2357–72
    [Google Scholar]
  67. Rubbert PE. 1994. CFD and the changing world of airplane design. ICAS Proceedings 1994lvii–lxxxiii Washington, DC: AIAA
    [Google Scholar]
  68. Rumsey C 2021. Turbulence modeling resource Web Resour., NASA Langley Res. Cent. Hampton, VA: https://turbmodels.larc.nasa.gov/
  69. Rumsey CL, Slotnick JP, Long M, Stuever R, Wayman T. 2011. Summary of the First AIAA CFD High-Lift Prediction Workshop. J. Aircr. 48:62068–79
    [Google Scholar]
  70. Rumsey CL, Slotnick JP, Sclafani AJ. 2019. Overview and summary of the Third AIAA High Lift Prediction Workshop. J. Aircr. 56:2621–44
    [Google Scholar]
  71. Schaefer JA, Cary AW, Mani M, Spalart PR. 2017. Uncertainty quantification and sensitivity analysis of SA turbulence model coefficients in two and three dimensions Paper presented at 55th AIAA Aerospace Sciences Meeting, Grapevine, TX, AIAA Pap2017–1710
  72. Schumann JE, Toosi S, Larsson J. 2020. Assessment of grid anisotropy effects on large-eddy-simulation models with different length scales. AIAA J. 58:104522–33
    [Google Scholar]
  73. Sheshadri A, Crabill JA. 2015. Mesh deformation and shock capturing techniques for high-order simulation of unsteady compressible flows on dynamic meshes Paper presented at 53rd AIAA Aerospace Sciences Meeting, Kissimmee, FL, AIAA Pap2015–1741
  74. Shur ML, Spalart PR, Strelets MK, Travin AK. 2008. A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Int. J. Heat Fluid Flow 29:61638–49
    [Google Scholar]
  75. Slotnick JP, Khodadoust A, Alonso J, Darmofal D, Gropp W et al. 2014. CFD Vision 2030 study: a path to revolutionary computational aerosciences Contract. Rep. 2014-218178 NASA Langley Res. Cent. Hampton, VA:
  76. Slotnick JP, Wayman T, Simpson D, Fowler S. 2017. HiLiftPW-3 case 2 results Slides presented at 3rd AIAA CFD High Lift Prediction Workshop Denver, CO: June 3–4
  77. Smith B. 1997. A nonequilibrium turbulent viscosity function for the k-l two equation turbulence model Paper presented at 28th Fluid Dynamics Conference, Snowmass Village, CO, AIAA Pap1997–1959
    [Google Scholar]
  78. Sorenson RL. 1980. A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation Tech. Memo. 81198, NASA Ames Res. Cent. Moffett Field, CA:
  79. Spalart PR. 2000. Strategies for turbulence modelling and simulations. Int. J. Heat Fluid Flow 21:3252–63
    [Google Scholar]
  80. Spalart PR. 2001. Young-person's guide to detached-eddy simulation grids NASA Contract. Rep. 2001-211032 NASA Langley Res. Cent Hampton, VA:
  81. Spalart PR, Allmaras S 1992. A one-equation turbulence model for aerodynamic flows Paper presented at 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Pap1992–439
  82. Spalart PR, Deck S, Shur ML, Squires KD, Strelets MK, Travin A. 2006. A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20:3181–95
    [Google Scholar]
  83. Spalart PR, Jou W-H, Strelets M, Allmaras SR 1997. Comments on the feasibility of LES for wings, and on hybrid RANS/LES approach. Advances in DNS/LES: Proceedings of 1st AFOSR International Conference on DNS/LES C Liu, Z Liu, L Sakell 137–48 Dayton, OH: Greyden
    [Google Scholar]
  84. Spalart PR, Shur M. 1997. On the sensitization of turbulence models to rotation and curvature. Aerosp. Sci. Technol. 1:5297–302
    [Google Scholar]
  85. Stookesberry D. 2001. CFD modeling of F/A-18E/F abrupt wing stall—a discussion of lessons learned Paper presented at 15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA, AIAA Pap2001–2662
  86. Strelets M. 2001. Detached eddy simulation of massively separated flows Paper presented at 39th Aerospace Sciences Meeting and Exhibit Reno, NV:2001–879
  87. Taylor NJ, Haimes R. 2018. Geometry modelling: underlying concepts and requirements for computational simulation (invited) Paper presented at 2018 Fluid Dynamics Conference, Atlanta, AIAA Pap2018–3402
  88. Thompson JF, Thames FC, Mastin CW. 1974. Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies. J. Comput. Phys. 15:3299–319
    [Google Scholar]
  89. Tinoco E. 2008. Validation and minimizing CFD uncertainty for commercial aircraft applications Paper presented at 26th AIAA Applied Aerodynamics Conference, Honolulu, HI, AIAA Pap 2008–6902
  90. Tramel R, Nichols R 1997. A highly efficient numerical method for overset-mesh moving-body problems Paper presented at 13th Computational Fluid Dynamics Conference, Snowmass Village, CO, AIAA Pap 1997–2040
  91. Ursachi CI, Galbraith M, Allmaras SR, Darmofal D. 2020. Output-based adaptive RANS solutions using higher-order FEM on a multi-element airfoil Paper presented at AIAA Aviation 2020 Forum (Online), AIAA Pap2020–3220
  92. Van Leer B. 1979. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 32:1101–36
    [Google Scholar]
  93. Vassberg J, Tinoco E, Mani M, Rider B, Zickuhr T et al. 2010. Summary of the Fourth AIAA CFD Drag Prediction Workshop Paper presented at 28th AIAA Applied Aerodynamics Conference, Chicago, AIAA Pap2010–4547
  94. Vatsa VN, Thomas JL, Wedan BW. 1989. Navier-Stokes computations of a prolate spheroid at angle of attack. J. Aircr. 26:11986–93
    [Google Scholar]
  95. Venditti DA, Darmofal DL. 2003. Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows. J. Comput. Phys. 187:122–46
    [Google Scholar]
  96. Verhoff A, O'Neil P 1981. Extension of FLO codes to transonic flow prediction for fighter configurations. Transonic Aerodynamics D Nixon 467–87 Reston, VA: AIAA
    [Google Scholar]
  97. Walden A, Nielsen EJ, Zubair M, Linford JC, Wohlbier JG et al. 2017. Unstructured-grid CFD algorithms on many-core architectures Poster presented at International Supercomputing Conference for High Performance Computing, Networking, Storage, and Analysis Denver, CO: Nov. 12–17
  98. Wang Q, Moin P, Iaccarino G. 2009. Minimal repetition dynamic checkpointing algorithm for unsteady adjoint calculation. SIAM J. Sci. Comput. 31:2549–67
    [Google Scholar]
  99. Wang ZJ, Fidkowski K, Abgrall R, Bassi F, Caraeni D et al. 2013. High-order CFD methods: current status and perspective. Int. J. Numer. Methods Fluids 72:8811–45
    [Google Scholar]
  100. Winkler C, Dorgan A, Mani M. 2011. Scale adaptive simulations of turbulent flows on unstructured grids Paper presented at 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI, AIAA Pap2011–3559
  101. Winkler C, Dorgan A, Mani M. 2012. A reduced dissipation approach for unsteady flows on unstructured grids Paper presented at 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, AIAA Pap2012–0570
  102. Winkler CM, Dorgan AJ, Mani M. 2013. Refinement of a two-equation hybrid RANS/LES model in BCFD Paper presented at 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, AIAA Pap2013–3079

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