Perspectives on Simulation Based Aerodynamic Design

  • A. Jameson
  • L. Martinelli
  • J. Alonso
  • J. Vassberg
  • J. Reuther
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 78)


This paper reviews the status of advanced computational simulation techniques in the aerodynamic design of modern aircraft. An outline of the aircraft design process is provided, and the most relevant trade-offs between disciplines are presented to justify the leading role that aerodynamic design plays in this truly multidisciplinary process. A control theory based adjoint approach which considerably reduces the computational cost of the calculation of design sensitivities is presented. Our experience with this method is described with the help of several computational design examples that cover a substantial range of objective functions, computational models, and geometric complexity. Using the adjoint method, entire design optimization calculations can be completed with a computational cost equivalent to only a few (typically less than ten) analysis runs. In comparison with current practice in an industrial setting, the design approach presented in this paper can yield large computational savings as well as reduced turn around times that can be used to either decrease the time to market or to increase the number of design iterations within a given time frame.


Mach Number Drag Reduction AIAA Paper Lift Coefficient Adjoint Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    M. Van Dyke. An Album of Fluid Motion. The Parabolic Press, Stanford, 1982.Google Scholar
  2. [2]
    D.R. Chapman, H. Mark, and M.W. Pirtle. Computers vs. wind tunnels in aerodynamic flow simulations. Astronautics and Aeronautics, 13(4): 22–30, 35, 1975.Google Scholar
  3. [31.
    J.T. Oden, L. Demkowicz, T. Liszka, and W. Rachowicz. h-p adaptive finite element methods for compressible and incompressible flows. In S. L. Venneri A. K. Noor, editor, Proceedings of the Symposium on Computational Technology on Flight Vehicles, pages 523534, Washington, D.C., November 1990. Pergamon.Google Scholar
  4. [4]
    L. Martinelli and A. Jameson. Validation of a multigrid method for the Reynolds averaged equations. AIAA paper 88–0414, 1988.Google Scholar
  5. [5]
    W.H. Jou. Boeing Memorandum AERO-B113B-L92–018, September 1992. To Joseph Shang.Google Scholar
  6. [6]
    M.H. Ha. The impact of turbulence modelling on the numerical prediction of flows. In M. Napolitano and F. Solbetta, editors, Proc. of the 13th International Conference on Numerical Methods in Fluid Dynamics, pages 27–46, Rome, Italy, July 1992. Springer Verlag, 1993.Google Scholar
  7. [71.
    ECARP. European Computational Aerodynamics Research Project, Validation of CFD Codes and Assessment of Turbulence Models Vieweg.Google Scholar
  8. [8]
    T. Cebeci and A.M.O. Smith. Analysis of Turbulent Boundary Layers. Academic Press, 1974.Google Scholar
  9. [9]
    B. Baldwin and H. Lomax. Thin layer approximation and algebraic model for separated turbulent flow. AIAA Paper 78–257, 1978.Google Scholar
  10. [10]
    D. Degani and L. Schiff. Computation of turbulent supersonic flows around pointed bodies having crossflow separation. J. Comp. Phys., 66: 173–196, 1986.zbMATHCrossRefGoogle Scholar
  11. [11]
    L. Martinelli, A. Jameson, and E. Malfa. Numerical simulation of three-dimensional vortex flows over delta wing configurations. In M. Napolitano and F. Solbetta, editors, Proc. 13th International Confrence on Numerical Methods in Fluid Dynamics, pages 534–538, Rome, Italy, July 1992. Springer Verlag, 1993.Google Scholar
  12. [12]
    D. Johnson and L. King. A mathematically simple turbulence closure model for attached and separated turbulent boundary layers. AIAA Journal, 23: 1684–1692, 1985.Google Scholar
  13. (13]
    C.L. Rumsey and V.N. Vatsa. A comparison of the predictive capabilities of several turbulence models using upwind and centered - difference computer codes. AIAA Paper 93–0192, AIAA 31st Aerospace Sciences Meeting, Reno, NV, January 1993.Google Scholar
  14. [14]
    T.J. Kao, T.Y. Su, and N.J. Yu. Navier-Stokes calculations for transport wing-body configurations with nacelles and struts. AIAA Paper 93–2945, AIAA 24th Fluid Dynamics Conference, Orlando, July 1993.Google Scholar
  15. [15]
    W.P. Jones and B.E. Launder. The calculation of low-Reynolds-number phenomena with a two-equation model of turbulence. Int. J. of Heat Tran., 16: 1119–1130, 1973.CrossRefGoogle Scholar
  16. [16]
    D.C. Wilcox. A half a century historical review of the k-w model. AIAA Paper 91–0615, AIAA 29th Aerospace Sciences Meeting, Reno, NV, January 1991.Google Scholar
  17. [17]
    C.G. Speziale, E.C. Anderson, and R. Abid. A critical evaluation of two-equation models for near wall turbulence. AIAA Paper 90–1481, June 1990.Google Scholar
  18. [18]
    R. Abid, C.G. Speziale, and S. Thangam. Application of a new k-T model to near wall turbulent flows. AIAA Paper 91–0614, AIAA 29th Aerospace Sciences Meeting, Reno, NV, January 1991.Google Scholar
  19. [19]
    F. Menter. Zonal two-equation k-w turbulence models for aerodynamic flows. AIAA Paper 93–2906, AIAA 24th Fluid Dynamics Meeting, Orlando, July 1993.Google Scholar
  20. [20]
    T.J. Coakley. Numerical simulation of viscous transonic airfoil flows. AIAA Paper 87–0416, AIAA 25th Aerospace Sciences Meeting, Reno, NV, January 1987.Google Scholar
  21. [21]
    F. Liu and X. Zheng. A strongly coupled time-marching method for solving the NavierStokes and is — w turbulence model equations with multigrid. J. Comp. Phys., 128: 289–300, 1996.MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    B. R. Smith. A near wall model for the k — l two equation turbulence model. AIAA paper 94–2386, AIAA 25th Fluid Dynamics Conference, Colorado Springs, CO, June 1994.Google Scholar
  23. [23]
    B.S. Baldwin and T.J. Barth. A one-equation turbulence transport model for high Reynolds number wall-bounded flows. AIAA Paper 91–0610, AIAA 29th Aerospace Sciences Meeting, Reno, NV, January 1991.Google Scholar
  24. [24]
    P. Spalart and S. Allmaras A one-equation turbulent model for aerodynamic flows. AIAA Paper 92–0439, AIAA 30th Aerospace Sciences Meeting, Reno, NV, January 1992.Google Scholar
  25. [25]
    J.E. Melton, S.A. Pandya, and J.L. Steger. 3D Euler flow solutions using unstructured Cartesian and prismatic grids. AIAA Paper 93–0331, Reno, NV, January 1993.Google Scholar
  26. [26]
    S.S. Samant, J.E. Bussoletti, F.T. Johnson, R.H. Burkhart, B.L. Everson, R.G. Melvin, D.P. Young, L.L. Erickson, and M.D. Madson. TRANAIR: A computer code for transonic analyses of arbitrary configurations. AIAA Paper 87–0034, 1987.Google Scholar
  27. [27]
    M. Berger and R.J. LeVeque. An adaptive Cartesian mesh algorithm for the Euler equations in arbitrary geometries. AIAA Paper 89–1930, 1989.Google Scholar
  28. [28]
    A.M. Landsberg, J.P. Boris, W. Sandberg, and T.R. Young. Naval ship superstructure design: Complex three-dimensional flows using an efficient, parallel method. High Performance Computing 1993: Grand Challenges in Computer Simulation, 1993.Google Scholar
  29. [29]
    N.P. Weatherill and C.A. Forsey. Grid generation and flow calculations for aircraft geometries. J. Aircraft, 22: 855–860, 1985.CrossRefGoogle Scholar
  30. [30]
    K. Sawada and S. Takanashi. A numerical investigation on wing/nacelle interferences of USB configuration. AIAA paper 87–0455, AIAA 25th Aerospace Sciences Meeting, Reno, NV, January 1987.Google Scholar
  31. [31]
    J.A. Benek, P.G. Buning, and J.L. Steger. A 3-D Chimera grid embedding technique. AIAA Paper 85–1523, AIAA 7th Computational Fluid Dynamics Conference, Cincinnati, OH, 1985.Google Scholar
  32. [32]
    J.A. Benek, T.L. Donegan, and N.E. Subs. Extended Chimera grid embedding scheme with applications to viscous flows. AIAA Paper 87–1126, AIAA 8th Computational Fluid Dynamics Conference, Honolulu, HI, 1987.Google Scholar
  33. [33]
    J. Vassberg. Multi-block mesh extrusion driven by a globally elliptic system. In 5th U.S. National Congress on Computational Mechanics, 2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, CO, August 1999.Google Scholar
  34. [34]
    B. Delaunay. Sur la sphere vide. Bull. Acad. Science USSR VII: Class Scil, Mat. Nat., pages 793–800, 1934.Google Scholar
  35. [35]
    T. J. Barth. Aspects of unstructured grids and finite volume solvers for the Euler and Navier Stokes equations. In von Karman Institute for Fluid Dynamics Lecture Series Notes 1994–05, Brussels, 1994.Google Scholar
  36. [36]
    G. Voronoi. Nouvelles applications des parametres continus a la theorie des formes quadratiques. Deuxieme memoire: Recherches sur les parallelloedres primitifs. J. Reine Angew. Math., 134: 198–287, 1908.zbMATHGoogle Scholar
  37. [37]
    R. Lohner and P. Parikh. Generation of three-dimensional unstructured grids by the advancing front method. AIAA Paper 88–0515, Reno, NV, January 1988.Google Scholar
  38. [38]
    A. Jameson. The present status, challenges, and future developments in Computational Fluid Dynamics Technical report, 77th AGARD Fluid Dynamics Panel Symposium, Seville, October 1995.Google Scholar
  39. [39]
    A. Jameson and L. Martinell. Mesh refinement and modelling errors in flow simulation. AIAA paper 96–2050, AIAA 27th Fluid Dynamics Conference, New Orleans, LA, June 1996.Google Scholar
  40. [40]
    J. Reuther, J.J. Alonso, M.J. Rimlinger, and A. Jameson. Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on parallel computers. AIAA paper 96–4045, 6th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, September 1996.Google Scholar
  41. [41]
    J. Reuther, A. Jameson, J. Farmer, L. Martinelli, and D. Saunders. Aerodynamic shape optimization of complex aircraft configurations via an adjoint formulation. AIAA paper 960094, 34th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 1996.Google Scholar
  42. [42]
    J. Reuther, A. Jameson, J. J. Alonso, M. J. Rimlinger, and D. Saunders. Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers. AIAA paper 97–0103, 35th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 1997.Google Scholar
  43. [43]
    J. Reuther, J. J. Alonso, J. C. Vassberg, A. Jameson, and L. Martinelli. An efficient multiblock method for aerodynamic analysis and design on distributed memory systems. AIAA paper 97–1893, June 1997.Google Scholar
  44. [44]
    A. Jameson. Optimum aerodynamic design via boundary control. In AGARD-VKI Lecture Series, Optimum Design Methods in Aerodynamics. von Karman Institute for Fluid Dynamics, 1994.Google Scholar
  45. [45]
    J. Reuther and A. Jameson. Aerodynamic shape optimization of wing and wing-body configurations using control theory. AIAA paper 95–0123, 33rd Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 1995.Google Scholar
  46. [46]
    J. Reuther and A. Jameson. Supersonic wing and wing-body shape optimization using an adjoint formulation. Technical report, The Forum on CFD for Design and Optimization, (IMECE 95 ), San Francisco, California, November 1995.Google Scholar
  47. [47]
    A. Jameson. Multigrid algorithms for compressible flow calculations. In W. Hackbusch and U. Trottenberg, editors, Lecture Notes in Mathematics, Vol. 1228, pages 166–201. Proceedings of the 2nd European Conference on Multigrid Methods, Cologne, 1985, Springer-Verlag, 1986.Google Scholar
  48. [48]
    Jameson A. and J. Vassberg. Studies of alternative numerical optimization methods Beach, CA.Google Scholar
  49. [49]
    J. L. Lions. Optimal Control of Systems Governed by Partial Diferential Equations. Springer-Verlag, New York, 1971. Translated by S.K. Mitter.Google Scholar
  50. [50]
    A. Jameson. Aerodynamic design via control theory. Journal of Scientific Computing, 3: 233–260, 1988.zbMATHCrossRefGoogle Scholar
  51. [51]
    A. Jameson, L. Martinelli, and N. A. Pierce. Optimum aerodynamic design using the Navier-Stokes equations. Theoretical and Computational Fluid Dynamics, 10: 213–237, 1998.zbMATHCrossRefGoogle Scholar
  52. [52]
    A. Jameson, N. Pierce, and L. Martinelli. Optimum aerodynamic design using the NavierStokes equations. AIAA paper 97–0101, January 1997.Google Scholar
  53. [53]
    A. Jameson and L. Martinelli. Aerodynamic shape optimization techniques based on control theory. In Course on “Computational Mathematics Driven by Industrial Applications”,Martina Franca, Italy, 1999. Fondazione CIME International Mathematical Summer Center.Google Scholar
  54. [54]
    P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. User’s guide for npsol (version 4.0): A fortran package for nonlinear programming. Technical Report SOL 86–2, Department of Operations Research, Stanford University, Jan. 1986.Google Scholar
  55. [55]
    A. Jameson. Optimum aerodynamic design using control theory. Computational Fluid Dynamics Review, pages 495–528, 1995.Google Scholar
  56. [56]
    J. Gallman, J. Reuther, N. Pfeiffer, W. Forrest, and D. Bernstorf. Business jet wing design using aerodynamic shape optimization. AIAA paper 96–0554, 34th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • A. Jameson
    • 1
  • L. Martinelli
    • 1
  • J. Alonso
    • 1
  • J. Vassberg
    • 1
  • J. Reuther
    • 1
  1. 1.Department of Aeronautics & AstronauticsStanford UniversityStanfordUSA

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