Aerodynamic Shape Optimization using Discrete Adjoint Formulation based on Overset Mesh System

  • Lee, Byung-Joon (School of Mechanical and Aerospace Engineering Seoul National University) ;
  • Yim, Jin-Woo (School of Mechanical and Aerospace Engineering Seoul National University) ;
  • Yi, Jun-Sok (School of Mechanical and Aerospace Engineering Seoul National University) ;
  • Kim, Chong-Am (School of Mechanical and Aerospace Engineering Seoul National University)
  • Published : 2007.06.30


A new design approach of complex geometries such as wing/body configuration is arranged by using overset mesh techniques under large scale computing environment. For an in-depth study of the flow physics and highly accurate design, several special overlapped structured blocks such as collar grid, tip-cap grid, and etc. which are commonly used in refined drag prediction are adopted to consider the applicability of the present design tools to practical problems. Various pre- and post-processing techniques for overset flow analysis and sensitivity analysis are devised or implemented to resolve overset mesh techniques into the design optimization problem based on Gradient Based Optimization Method (GBOM). In the pre-processing, the convergence characteristics of the flow solver and sensitivity analysis are improved by overlap optimization method. Moreover, a new post-processing method, Spline-Boundary Intersecting Grid (S-BIG) scheme, is proposed by considering the ratio of cell area for more refined prediction of aerodynamic coefficients and efficient evaluation of their sensitivities under parallel computing environment. With respect to the sensitivity analysis, discrete adjoint formulations for overset boundary conditions are derived by a full hand-differentiation. A smooth geometric modification on the overlapped surface boundaries and evaluation of grid sensitivities can be performed by mapping from planform coordinate to the surface meshes with Hicks-Henne function. Careful design works for the drag minimization problems of a transonic wing and a wing/body configuration are performed by using the newly-developed and -applied overset mesh techniques. The results from design applications demonstrate the capability of the present design approach successfully.


  1. William M. Chan, Reynaldo J. Gomez Ill, Stuart E. Rogers, Pieter G. Buning. Best Practices in Overset Grid Generation. AIAA Paper 2002-3191
  2. C. L. Rumsey, Robert T. Biedron. Computation of Flow Over a Drag Prediction Workshop Wing/Body Transport Configuration using CFL3D. NASA TM-2001-211262
  3. K. Leoviriyakit, S. Kim, and A. Jameson. Viscous Aerodynamic Shape Design Optimization of Wings including Planform Variables. AIAA Paper 2003-3498
  4. S. Choi, J. J. Alonso, S. Kim, I. Kroo, and M. Wintzer. Two-Level Multi-Fidelity Design Optimization Studies for Supersonic Jets. AlAA Paper 2005-0531
  5. B. J. Lee, C. Kim, and O. Rho. Optimal Shape Design of the S-Shaped Subsonic Intake Using NUHBS. AIAA Paper 2005-0455
  6. E .J. Nielsen, and W. K. Anderson. Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations. AIAA Paper 98-4809
  7. H. J. Kim, D. Sasaki, S. Obayashi, and K. Nakahashi. Aerodynamic Optimization of Supersonic Transport Wing Using Unstructured Adjoint Method. Adjoint Journal, 2001, 39(6): 1011-1020
  8. S. Nadarajah, A. Jameson. Studies of the Continuous and Discrete Adjoint Approaches to Viscous Automatic Aerodynamic Shape Optimization. AlAA Paper 2001-2530
  9. C. S. Kim, Chongam Kim, O. H. Hho. Feasibility Study of Constant Eddy-Viscosity Assumption in Gradient-Based Design Optimization. Journal of Aircraft, 2003, 40(6):1168-1176
  10. W. Liao, and H. M. Tsai. Aerodynamic Design Optimization by the Adjoint Equation Method on Overset Grids. AIAA Paper 2006-54
  11. Ralph W. Noack, and Davy M. Belk. Improved Interpolation for Viscous Overset Grids. AIAA. Paper 97-0199
  12. Norman E. Suhs, Stuert E. Rogers, and William E. Dietz. PEGASUS 5: An Automated Pre-processor for Overset-Crid CFD. AIAA Paper 2002-3186
  13. J. C. Vassberg, P. G. Buning, and C. L. Rumsey, Drag Prediction for the DLR-F4 Wing /Body using OVEHFLOW and CFL3D on an Overset Mesh. AIAA Paper 2002-0840
  14. R. L. Meakin. Object X-rays for Cutting Holes in Composite Overset Structured Grids. AIAA Paper 2001-2537
  15. D. M. Belk, and H. C. Maple, 'Automated Assembly of Structured Grids for Moving Body Problems', AIAA Paper 95-1680
  16. D. L. Brown, W. D. Henshaw, and D. J. Quinlan. Overture: Object-Oriented Tools for Overset Grid Applications. AIAA Paper 99-3130
  17. W. M. Chan and P. G. Buning. Zipper Grids for Force and Moment Computation on Overset Grids. AIAA Paper 95-1681
  18. Nathan Hariharan, Z. J. Wang, and P. G. Buning, Application of Conservative Chimera Methodology in Finite Difference Settings. AIAA Paper 97-0627
  19. Sung-soo Kim, Chongam Kim, Oh-hyun Rho, and Seung Kyu Hong. Cures for the Shock Instability: Development of Shock-Stable Hoe Scheme. Journal of Computational Physics, 2003, 185(2): 342-374
  20. J. R. R A Martins, I. M. Kroo. and J. J. Alonso. An Automated Method for Sensitivity Analysis using Complex Variables, AIAA Paper 2000-0869