Adjoint formulation for an embedded-boundary cartesian method

43rd AIAA Aerospace Sciences Meeting and Exhibit - Meeting Papers

Volumn , Issue , 2005, Pages 3341-3355

  Nemec, Marian ^a,b,c   Aftosmis, Michael J ^a,c   Murman, Scott M ^b,c   Pulliam, Thomas H ^b,c  

^a NASA AMES RESEARCH CENTER   (United States)

^b ELORET CORPORATION   (United States)

^c AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; LINEAR EQUATIONS; RUNGE KUTTA METHODS; SENSITIVITY ANALYSIS; TRANSONIC FLOW;

CARTESIAN METHOD; EMBEDDED BOUNDARIES;

BOUNDARY LAYERS;

EID: 30744472457     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2005-877     Document Type: Conference Paper

References (44)

1. Jameson, A., "Aerodynamic Design via Control Theory," Journal of Scientific Computing, Vol. 3, 1988, pp. 233-260, Also ICASE report 88-64.
2. Baysal, O. and Eleshaky, M. E., "Aerodynamic Sensitivity Analysis Methods for the Compressible Euler Equations," Journal of Fluids Engineering, Vol. 113, No. 4, 1991, pp. 681-688.
3. Reuther, J. J., Aerodynamic. Shape Optimization Using Control Theory, Ph.D. thesis, University of California Davis, 1996.
4. Anderson, W. K. and Venkatakrishnan, V., "Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation," Computers & Fluids, Vol. 28, 1999, pp. 443-480.
5. Giles, M. B. and Pierce, N. A., "An Introduction to the Adjoint Approach to Design," Flow. Turbulence, and Combustion, Vol. 65, No. 3/4, 2000, pp. 393-415.
6. Pierce, N. A. and Giles, M. B., "Adjoint Recovery of Superconvergent Functionals from PDE Approximations," SIAM Review, Vol. 42, No. 2, 2000, pp. 247-264.
7. Venditti, D. A. and Darmofal, D. L., "Anisotropic Grid Adaptation for Functional Outputs: Application to Two-Dimensional Viscous Flow," Journal of Computational Physics, Vol. 187, 2003, pp. 22-46.
8. Barth, T. J., "Numerical Methods and Error Estimation for Conservation Laws on Structured and Unstructured Meshes," Lecture notes, von Karman Institute for Fluid Dynamics, Series: 2003-04, Brussels, Belgium, March 2003.
9. Park, M. A., "Adjoint-Based, Three Dimensional Error Prediction and Grid Adaptation," AIAA Journal, Vol. 42, No. 9, 2004, pp. 1854-1862.
10. Pierce, N. A. and Giles, M. B., "Adjoint and defect error bounding and correction for functional estimates," Journal of Computational Physics, Vol. 200, 2004, pp. 769-794.
11. Korivi, V. M., Taylor III, A. C., Newman, P. A., Hou, G. W., and Jones, H. E., "An Approximately Factored Incremental Strategy for Calculating Consistent Discrete Aerodynamic Sensitivity Derivatives," Journal of Computational Physics, Vol. 113, No. 2, 1994, pp. 336-346.
12. Elliott, J. and Herling, W., "A Chimera Approach to Aerodynamic Shape Optimization for the Compressible, High-Re Navier Stokes Equations," AIAA Paper 2000-4729, Long Beach, CA, Sept. 2000.
13. Kim, C. S., Kim, C., and Rho, O. H., "Sensitivity Analysis for the Navier-Stokes Equations with Two-Equation Turbulence Models," AIAA Journal, Vol. 39, No. 5, 2001, pp. 838-845.
14. Nemec, M. and Zingg, D. W., "Newton-Krylov Algorithm for Aerodynamic Design Using the Navier-Stokes Equations," AIAA Journal, Vol. 40, No. 6, 2002, pp. 1146-1154.
15. Giles, M. B., Duta, M. C., Müller, J.-D., and Pierce, N. A., "Algorithm Developments for Discrete Adjoint Methods," AIAA Journal, Vol. 41, No. 2, 2003, pp. 198-204.
16. Nielsen, E. J., Lu, J., Park, M. A., and Darmofal, D. L., "An Implicit, Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids," Computers & Fluids, Vol. 33, 2004, pp. 1131-1155.
17. Mavriplis, D. J., "Formulation and Multigrid Solution of the Discrete Adjoint Problem on Unstructured Meshes," ICCFD 3, July 2004.
18. Barth, T. J., "Parallel CFD Algorithms on Unstructured Meshes, " Special Course on Parallel Computing in CFD, AGARD-R-807, Oct. 1995, pp. 7-1-7-41.
19. Anderson, W. K. and Bonhaus, D. L., "Airfoil Design on Unstructured Grids for Turbulent Flows," AIAA Journal, Vol. 37, No. 2, 1999, pp. 185-191.
20. Elliott, J. K., Aerodynamic Optimization Based on the Euler and Navier Stokes Equations Using Unstructured Grids, Ph.D. thesis, Massachusetts Institute of Technology, 1998.
21. Giering, R. and Kaminski, T., "Recipes for Adjoint Code Construction," A CM Transactions on Mathematical Software, Vol. 24, No. 4, 1998, pp. 437-474.
22. Mohammadi, B. and Pironneau, O., Applied Shape Optimization for Fluids, Oxford University Press, New York, USA, 2001.
23. Taylor III, A. C., Green, L. L., Newman, P. A., and Putko, M. M., "Some Advanced Concepts in Discrete Aerodynamic Sensitivity Analysis, " AIAA Journal, Vol. 41, No. 7, 2003, pp. 1224-1229.
24. Cusdin, P. and Müller, J.-D., "Deriving Linear and Adjoint Codes for CFD using Automatic Differentiation," Preprint submitted to AIAA J., www.ea.qub.ac.uk/jmueller/.
25. Cusdin, P. and Müller, J.-D., "Generating Efficient Code with Automatic Differentiation," 4th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), edited by P. Neittaanmäki, T. Rossi, K. Majava, and O. Pironneau, July 2004.
26. Aftosmis, M. J., "Solution Adaptive Cartesian Grid Methods for Aerodynamic Flows with Complex Geometries," Lecture notes, von Karman Institute for Fluid Dynamics, Series: 1997-02, Brussels, Belgium, March 1997.
27. Aftosmis, M. J., Berger, M. J., and Melton, J. E., "Robust and Efficient Cartesian Mesh Generation for Componenet-Based Geometry," AIAA Journal, Vol. 36, No. 6, 1998, pp. 952-960.
28. Aftosmis, M. J., Berger, M. J., and Adomavicius, G., "A Parallel Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries," AIAA Paper 2000-0808, Reno, NV, Jan. 2000.
29. Nemec, M., Aftosmis, M. J., and Pulliam, T. H., "CAD-Based Aerodynamic Design of Complex Configurations Using a Cartesian Method," AIAA Paper 2004-0113, Reno, NV, Jan. 2004.
30. Aftosmis, M. J. and Berger, M. J., "Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries," AIAA Paper 2002-0863, Reno, NV, Jan. 2002.
31. Melvin, R. G., Huffman, W. P., Young, D. P., Johnson, F. T., Hilmes, C. L., and Bieterman, M. B., "Recent Progress in Aerodynamic Design Optimization," International Journal for Numerical Methods in Fluids, Vol. 30, 1999, pp. 205-216.
32. Young, D. P., Melvin, R. G., Bieterman, M. B., Johnson, F. T., and Samant, S. S., "A Locally Refined Rectangular Grid Finite Element Method: Application to Computational Fluid Dynamics and Computational Physics," Journal of Computational Physics, Vol. 92, No. 1, 1991, pp. 1-66.
33. Dadone, A. and Grossman, B., "Efficient Fluid Dynamic Design Optimization Using Cartesian Grids," AIAA Paper 2003-3959, Orlando, FL, June 2003.
34. Dadone, A. and Grossman, B., "Ghost-Cell Method for Inviscid Two-Dimensional Flows on Cartesian Grids," AIAA Journal, Vol. 42, No. 12, 2004, pp. 2499-2507.
35. van Leer, B., "Flux-Vector Splitting for the Euler Equations," ICASE Report 82-30, Sept. 1982.
36. Aftosmis, M. J., Berger, M. J., and Murman, S. M., "Applications of Space-Filling-Curves to Cartesian Methods for CFD," AIAA Paper 2004-1232, Reno, NV, Jan. 2004.
37. Berger, M. J., Aftosmis, M. J., and Murman, S. M., "Analysis of Slope Limiters on Irregular Grids," AIAA Paper 2005-0490, Reno, NV, Jan. 2005.
38. Giles, M. B. and Pierce, N. A., "Analytic Adjoint Solutions for the Quasi-One-Dimensional Euler Equations," Journal of Fluid Mechanics, Vol. 426, 2001, pp. 327-345.
39. Nielsen, E. J., Anderson, W. K., Walters, R. W., and Keyes, D. E., "Application of Newton - Krylov Methodology to a Three-Dimensional Unstructured Euler Code," AIAA Paper 95 1733-CP, 1995.
40. Nemec, M., Optimal Shape Design of Aerodynamic Configurations: A Niwton Krylov Approach, Ph.D. thesis, University of Toronto, 2003, http://oddjob.utias.utoronto.ca/marian/.
41. Burgreen, G. W., Three-Dimensional Aerodynamic Shape Optimization Using Discrete Sensitivity Analysis, Ph.D. thesis, Old Dominion University, 1994.
42. Giles, M. B., "On the Use of Runge - Kutta Time-Marching and Multigrid for the Solution of Steady Adjoint equations," Oxford University Computing Laboratory 00/10, June 2000.
43. Carr, M. P. and Pallister, K. C., "Pressure Distributions Measured on Research Wing M100 Mounted on an Axisymmetric Body," Experimental Data Rase for Computer Program Assessment, AGARD-R-138 B8, May 1979.
44. Brown, J., Yates, L., Bogdanoff, D., Chapman, G., Loomis, M., and Tam, T., "Free Flight Testing in Support of the Mars Smart Lander Aerodynamics Database," AIAA Paper 2002-4410 (Rev. JSR), 2002.