Table of Contents Author Guidelines Submit a Manuscript
International Journal of Aerospace Engineering
Volume 2013, Article ID 928904, 11 pages
http://dx.doi.org/10.1155/2013/928904
Research Article

Interpolation of Transonic Flows Using a Proper Orthogonal Decomposition Method

École Polytechnique de Montréal, Department of Mechanical Engineering, 2900 Boulevard Edouard-Montpetit, Montréal, QC, Canada H3T 1J4

Received 9 April 2013; Revised 23 July 2013; Accepted 25 July 2013

Academic Editor: R. Ganguli

Copyright © 2013 Benoit Malouin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. D. Salas, “Digital flight: the last CFD aeronautical grand challenge,” Journal of Scientific Computing, vol. 28, no. 2-3, pp. 479–505, 2006. View at Publisher · View at Google Scholar · View at Scopus
  2. P. LeGresley and J. Alonso, “Airfoil design optimization using reduced order models based on proper orthogonal decomposition,” in Proceedings of the Fluids Conference and Exhibit, AIAA Paper, Denver, Colo, USA, 2000.
  3. D. Alonso, A. Velazquez, and J. M. Vega, “A method to generate computationally efficient reduced order models,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 33–36, pp. 2683–2691, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. J. Burkardt, M. Gunzburger, and H.-C. Lee, “POD and CVT-based reduced-order modeling of Navier-Stokes flows,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 1–3, pp. 337–355, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. K. Lee, S. K. Rallabhandi, and D. N. Mavris, “Aerodynamic data reconstruction via probabilistic principal component analysis,” in Proceedings of the 46th AIAA Aerospace Sciences Meeting and Exhibit, January 2008. View at Scopus
  6. L. S. Lorente, J. M. Vega, and A. Velazquez, “Generation of aerodynamic databases using high-order singular value decomposition,” Journal of Aircraft, vol. 45, no. 5, pp. 1779–1788, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. P. LeGresley, Application of proper orthogonal decomposition (POD) to design decomposition methods [Ph.D. thesis], Stanford University, 2005.
  8. B. T. Tan, Proper orthogonal decomposition extensions and their applications in steady aerodynamics [Ph.D. thesis], City University, 2003.
  9. T. Bui-Thanh, M. Damodaran, and K. Willcox, “Proper orthogonal decomposition extensions for para metric applications in transonic aerodynamics,” in Proceedings of the 15th AIAA Computational Fluid Dynamics Conference, vol. 4213 of AIAA Paper, p. 2003, 2003.
  10. D. Alonso, J. M. Vega, and A. Velazquez, “Reduced-order model for viscous aerodynamic flow past an airfoil,” AIAA Journal, vol. 48, no. 9, pp. 1946–1958, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Alonso, J. M. Vega, A. Velazquez, and V. de Pablo, “Reduced-order modeling of three-dimensi external aerodynamic flows,” Journal of Aerospace Engineering, vol. 25, no. 4, pp. 588–599, 2011. View at Google Scholar
  12. L. Sirovich, “Turbulence and the dynamics of coherent structures. I-Coherent structures. II-Symmetries and transformations. III- Dynamics and scaling,” Quarterly of Applied Mathematics, vol. 45, pp. 561–571, 1987. View at Google Scholar
  13. D. J. Lucia, P. I. King, and P. S. Beran, “Reduced order modeling of a two-dimensional flow with moving shocks,” Computers and Fluids, vol. 32, no. 7, pp. 917–938, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. B. I. Epureanu, “A parametric analysis of reduced order models of viscous flows in turbomachinery,” Journal of Fluids and Structures, vol. 17, no. 7, pp. 971–982, 2003. View at Publisher · View at Google Scholar · View at Scopus
  15. W. Cazemier, R. W. C. P. Verstappen, and A. E. P. Veldman, “Proper orthogonal decomposition and low-dimensional models for driven cavity flows,” Physics of Fluids, vol. 10, no. 7, pp. 1685–1699, 1998. View at Google Scholar · View at Scopus
  16. D. J. Lucia and P. S. Beran, “Projection methods for reduced order models of compressible flows,” Journal of Computational Physics, vol. 188, no. 1, pp. 252–280, 2003. View at Publisher · View at Google Scholar · View at Scopus
  17. K. C. Hall, J. P. Thomas, and E. H. Dowell, “Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows,” AIAA Journal, vol. 38, no. 10, pp. 1853–1862, 2000. View at Google Scholar · View at Scopus
  18. T. Lieu, C. Farhat, and M. Lesoinne, “Reduced-order fluid/structure modeling of a complete aircraft configuration,” Computer Methods in Applied Mechanics and Engineering, vol. 195, no. 41–43, pp. 5730–5742, 2006. View at Publisher · View at Google Scholar · View at Scopus
  19. P. G. A. Cizmas, B. R. Richardson, T. A. Brenner, T. J. O'Brien, and R. W. Breault, “Acceleration techniques for reduced-order models based on proper orthogonal decomposition,” Journal of Computational Physics, vol. 227, no. 16, pp. 7791–7812, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. T. Bui-Thanh, K. Willcox, and O. Ghattas, “Parametric reduced-order models for probabilistic analysis of unsteady aerodynamic applications,” AIAA Journal, vol. 46, no. 10, pp. 2520–2529, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Taeibi-Rahni, F. Sabetghadam, and M. K. Moayyedi, “Low-dimensional proper orthogonal decomposition modeling as a fast approach of aerodynamic data estimation,” Journal of Aerospace Engineering, vol. 23, no. 1, pp. 44–54, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. B. Malouin, Prediction of aerodynamic coefficients using proper orthogonal decomposition [M.S. thesis], École Polytechnique de Montréal, 2010.
  23. R. Zimmermann and S. Görtz, “Non-linear POD-based reduced order models for steady turbulent aerodynamics,” in Proceedings of the RAeS Conference Applied Aerodynamics: Capabilities and Future Requirements, RAeS, Bristol, UK, July 2010.
  24. K. Kunisch and S. Volkwein, “Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics,” SIAM Journal on Numerical Analysis, vol. 40, no. 2, pp. 492–515, 2002. View at Publisher · View at Google Scholar · View at Scopus
  25. M. Rathinam and L. R. Petzold, “A new look at proper orthogonal decomposition,” SIAM Journal on Numerical Analysis, vol. 41, no. 5, pp. 1893–1925, 2003. View at Publisher · View at Google Scholar · View at Scopus
  26. K. Carlberg and C. Farhat, “A low-cost, goal-oriented “compact proper orthogonal decomposition” basis for model reduction of static systems,” International Journal for Numerical Methods in Engineering, vol. 86, no. 3, pp. 381–402, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. M. C. Kennedy and A. O'Hagan, “Predicting the output from a complex computer code when fast approximations are available,” Biometrika, vol. 87, no. 1, pp. 1–13, 2000. View at Google Scholar · View at Scopus