Optimum Transonic Wing Design Using Control Theory

  • Antony Jameson
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 73)


While aerodynamic prediction methods based CFD are now well established, and quite accurate and robust, the ultimate need in the design process is to find the optimum shape which maximizes the aerodynamic performance. One way to approach this objective is to view it as a control problem, in which the wing is treated as a device which controls the flow to produce lift with minimum drag, while meeting other requirements such as low structure weight, sufficient fuel volume, and stability and control constrains. Here we apply the theory of optimal control of systems governed by partial differential equations with boundary control, in this case through changing the shape of the boundary. Using this theory, we can find the Frechet derivative (infinitely dimensional gradient) of the cost function with respect to the shape by solving an adjoint problem, and then we can make an improvement by making a modification in a descent direction. For example, the cost function might be the drag coefficient at a fixed lift, or the lift to drag ratio. During the last decade, this method has been intensively developed, and has proved to be very effective for improving wing section shapes for fixed wing planform [3, 4, 8, 9, 10, 11, 13, 14].


Computational Fluid Dynamics Drag Coefficient 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. Jameson, W. Schmidt, and E. Turkei, Numerical Solution of the Euler equations by finite volume methods using Runger-Kutta time stepping schemes, AIAA Paper 81-1259, June, 1981.Google Scholar
  2. [2]
    A. Jameson and T.J. Baker, Improvements to the Aircraft Euler Method, AIAA Paper 87-0353, 25th AIAA Aerospace Sciences Meeting, Reno, January, 1987.Google Scholar
  3. [3]
    A. Jameson, Aerodynamic Design via Control Theory, Princeton University Report MAE 1824, ICASE Report No. 88-64, November, 1988, also J. of Scientific Computing, Vol. 3, pp. 233–260, 1988.Google Scholar
  4. [4]
    A. Jameson, Computational Aerodynamics for Aircraft Design, Science, Vol. 245, pp. 361–371, 1989.ADSCrossRefGoogle Scholar
  5. [5]
    T.J. Barth, Apects of unstructured grids and finite volume solvers for the Euler and Navier-Stokes equations, AIAA Paper 91-0237, 29th AIAA Aerospace Sciences Meeting, Reno, January, 1994.Google Scholar
  6. [6]
    J. Elliot and J. Peraire, Aerodynamic design using unstructured meshes, AIAA Paper 96-1941, 33rd AIAA Aerospace Sciences Meeting, Reno, January, 1996.Google Scholar
  7. [7]
    K. Anderson and V. Venkatakrishnan, Aerodynamic Design Optimization on Unstructured grids using a continuous adjoint formulation, AIAA Paper 97-0643, 34th AIAA Aerospace Sciences Meeting, Reno, January, 1997.Google Scholar
  8. [8]
    A. Jameson, L. Martinelli, and N. Pierce, Optimum Aerodynamic Design Using the Navier-Stokes Equations, Theoret. Comput. Fluid Dynamics, 10, pp. 213–237, 1998.ADSzbMATHCrossRefGoogle Scholar
  9. [9]
    A. Jameson, A Perspective on Computational Algorithms for Aerodynamic Shape Analysis and Design, Sixth Taiwan National Conference on Computational Fluid Dynamics, Taitung, Taiwan ROC, August, 1999, Progress in Aerospace Sciences, Elsvier, 2001.Google Scholar
  10. [10]
    A. Jameson and L. Martinelli, Aerodynamic Shape Optimization Techniques Based on Control Theory, CIME (International Mathematical Summer Center), Martina Franca, Italy, 1999.Google Scholar
  11. [11]
    J. C. Vassberg and A. Jameson, Computational Fluid Dynamics for Aerodynamic Design: Its Current and Future Impact, AIAA 2001-0538, 39th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, January, 2001.Google Scholar
  12. [12]
    S. E. Cliff, S.D. Thomas, T. J. Baker, A. Jameson, and R. M. Hicks, Aerodynamic Shape optimization using unstructured grid method, AIAA Paper 02-5550, 9th AIAA Symposium on Multidisciplinary Analysis and Optimization, Atlanta, September, 2002.Google Scholar
  13. [13]
    J. C. Vassberg and A. Jameson, Aerodynamic Shape Optimization of a Reno Race Plane, International Journal of Vehicle Design, vol.28 no.4, pp. 318–338, 2002.CrossRefGoogle Scholar
  14. [14]
    S. Kim, J.J. Alonso, and A. Jameson, Design Optimization of High-Lift Configurations Using a Viscous Continuous Adjoint Method, AIAA-2002-0844, 40th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, January, 2002.Google Scholar
  15. [15]
    O. Pironneau, Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York, 1984.zbMATHCrossRefGoogle Scholar
  16. [16]
    J.L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, 1971, Translated by S.K. Mitter.zbMATHCrossRefGoogle Scholar
  17. [17]
    A. Jameson, Optimum Aerodynamic Design Using Control Theory, Computational Fluid Dynamics Review 1995, Wiley, 1995.Google Scholar
  18. [18]
    A. Jameson, L. Martinelli, and J. Vassberg, Using CFD for Aerodynamics-A critical Assesment, Proceedings of ICASE 2002, Toronto, Canada, September 8–13, 2002.Google Scholar
  19. [19]
    A. Jameson and S. Kim, Reduction of the Adjoint Gradient Formula in the Continuous Limit, AIAA Paper, 41st AIAA Aerospace Sciences Meeting, Reno January, 2003.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Antony Jameson
    • 1
  1. 1.Thomas V Jones Professor of Engineering, Department of Aeronautics and AstronauticsStanford UniversityStanfordUSA

Personalised recommendations