Convergence studies of the time accurate and non-linear frequency domain methods for optimum shape design

International Journal of Computational Fluid Dynamics

Volumn 21, Issue 5-6, 2007, Pages 189-207

  Nadarajah, Siva K ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Adjoint method; Frequency domain; Optimization; Time accurate; Unsteady flow

Indexed keywords

EID: 35448938710     PISSN: 10618562     EISSN: 10290257     Source Type: Journal    
DOI: 10.1080/10618560701577328     Document Type: Article

References (37)

1. Anderson, W.K. and Venkatakrishnan, V., Aerodynamic design optimisation on unstructured grids with a continuous adjoint formulation. Comput. Fluids, 1999, 28(4-5), 443-480.
2. Collis, S., Ghayour, K., Heinkenschloss, M.,, Ulbrich, M. and Ulbrich, S., Optimal control of unsteady compressible viscous flows. Int. J. Numer. Methods Fluids, 2002, 40(11), 1401-1429.
3. Davis, S.S., NACA 64A010 (NASA Ames model) oscillatory pitching, AGARD Report 702, August 1982. In Compendium of Unsteady Aerodynamic Measurements 1982.
4. Duta, M.C., Giles, M.B. and Campobasso, M.S., The harmonic adjoint approach to unsteady turbomachinery design. Int. J. Numer. Methods Fluids, 2002, 40, 323-332, October.
5. Elliot, J. and Peraire, J., Aerodynamic design using unstructured meshes, AIAA Paper 96-1941 1996.
6. Frigo, M. and Johnson, S.G., Fastest Fourier transform in the west (fftw) version 2.1.5. http://www/fftw/org 1998.
7. Gallman, J., Reuther, J., Pfeiffer, N., Forrest, W. and Bernstorf, D., Business jet wing design using aerodynamic shape optimisation, AIAA Paper 96-0554, 34th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 1996.
8. Giles, M.B., Duta, M., Muller, J. and Pierce, N., Algorithm developments for discrete adjoint methods. AIAA J., 2003,15(5), 1131 -1145, May.
9. Hall, K.C., Seminar on harmonic balance techniques, Technical Report, Presented to the Aerospace Computing Lab, Stanford University, 2000.
10. Hall, K.C., Thomas, J.P. and Clark, W.S., Computation of unsteady non-linear flows in cascades using a harmonic balance technique, Technical Report, 9th International Symposium on Unsteady Aerodynamics, Aeroacoustics, and Aeroelasticity of Turbomachines, Lyon, France, September 2000.
11. Jameson, A., Computational aerodynamics for aircraft design. Science, 1989, 245, 361-371.
12. Jameson, A. and Baker, T.J., Solution of the Euler equations for complex configurations, AIAA Paper 83-1929, AIAA 6th Computational Fluid Dynamics Conference, Danvers, MA, July 1983.
13. Jameson, A. and Vassberg, J.C., Studies of alternative numerical optimisation methods applied to the brachistochrone problem, OptiCON 99, 1999.
14. Jameson, A., Schmidt, W. and Turkel, E., Numerical solutions of the Euler equations by finite volume methods with Runge-Kutta time stepping schemes, AIAA Paper 81-1259, January 1981.
15. Kim, H. and Nakahashi, K., Unstructured adjoint method for Navier-Stokes equations. JSME Int. J. Ser. B Fluids Therm. Eng., 2005, 48(2), 202-207, May.
16. Kim, H., Kim, C. and Rho, O., Optimal flow control using unsteady sensitivity analysis. Trans, Jpn. Soc. Aeronaut. Space Sci., 2005, 48, 102-109.
17. Lee, S. and Kwon, O., Aerodynamic shape optimisation of hovering rotor blades in transonic flow using unstructured meshes. AIAA J., 2006, 44(8), 1816-1825.
18. Leoviriyakit, K. and Jameson, A., Case studies in aero-structural wing planform, and section optimisation, AIAA Paper 2004-5372, 22nd AIAA Applied Aerodynamics Conference, Providence, RI, August 2004.
19. Mani, K. and Mavriplis, D., An unsteady discrete adjoint formulation for two-dimensional flow problems with deforming meshes, AIAA 2007-0060, Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 2007.
20. Mavriplis, D., Multigrid solution of the discrete adjoint for optimisation problems on unstructured meshes. AIAA J., 2006,44,42-50, January.
21. McCroskey, W.J., Unsteady airfoils. Annu. Rev. Fluid Mech., 1982, 14, 285-311.
22. McMullen, M.,, The Application of Non-Linear Frequency Domain Methods to the Euler and Navier-Stokes Equations. Phd dissertation, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, March, 2003.
23. McMullen, M., Jameson, A. and Alonso, J., Acceleration of convergence to a periodic steady state in turbomachinery flows, AIAA Paper 01-0152, 39th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2001.
24. McMullen, M., Jameson, A. and Alonso, J., Application of a non-linear frequency domain solver to the Euler and Navier-Stokes equations, AIAA Paper 02-0120,40th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2002.
25. Mohammadi, B. and Pironneau, O., Shape optimisation in fluid mechanics. Annu. Rev. Fluid Mech., 2005, 36, 255-279.
26. Nadarajah, S., The Discrete Adjoint Approach to Aerodynamic Shape Optimization. PhD dissertation, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, January 2003.
27. Nadarajah, S. and Jameson, A., Optimal control of unsteady flows using a time accurate method, AIAA Paper 02-5436, 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimisation Conference, Atlanta, GA, September 2002.
28. Nadarajah, S. and Jameson, A., Optimum, shape design for unsteady three-dimensional viscous flows using a non-linear frequency domain method, AIAA Paper 06-3455, AIAA 25th Applied Aerodynamics Conference, San Francisco, CA, June 2006.
29. Nadarajah, S., Jameson, A. and Alonso, J.J., An adjoint method for the calculation of remote sensitivities in supersonic flow, AIAA Paper 02-0261, 40th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2002.
30. Nadarajah, S., McMullen, M. and Jameson, A., Non-linear frequency domain method based optimum shape design for unsteady three-dimensional flows, AIAA Paper 06-1052, AIAA 44th Aero-space Sciences Meeting and Exhibit, Reno, NV, January 2006.
31. Nemec, M., Zingg, D. and Pulliam, T.H., Multipoint and multi-objective aerodynamic shape optimisation. AIAA J., June 2004, 42(6), 1057-1065.
32. Nielsen, E., Lu, J., Park, M.A. and Darmofal, D., An implicit, exact dual adjoint solution method for turbulent flows on unstructured grids. Comput. Fluids, 2004, 33(9), 1131-1155.
33. Reuther, J., Cliff, S., Hicks, R. and van Dam, C.R, Practical, design optimisation of wing/body configurations using the Euler equations, AIAA Paper 92-2633, 1992.
34. Reuther, J., Alonso, J.J., Martins, J.R.R.A. and Smith, S.C., A coupled aero-structural optimisation method for complete aircraft configurations, AIAA Paper 99-0187, 37th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 1999.
35. Rumpfkeil, M. and Zingg, D., A general, framework for the optimal control of unsteady flows with applications, AIAA 07-1128, Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 2007.
36. Soto, O., Löhner, R. and Yang, C., An adjoint-based design methodology for cfd problems. Int. J. Numer. Methods Heat Fluid Flow, 2004, 14(6), 734-759.
37. Thomas, J.P., Hall, K.C. and Dowell, E.H., A discrete adjoint approach for modelling unsteady aerodynamic design sensitivities, AIAA Paper 03-0041, 41th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2003.