Unsteady discrete adjoint formulation for two-dimensional flow problems with deforming meshes

AIAA Journal

Volumn 46, Issue 6, 2008, Pages 1351-1364

  Mani, Karthik ^a,b   Mavriplis, Dimitri J ^a,b  

^a UNIVERSITY OF WYOMING   (United States)

^b Department of Mechanical Engineering ^*

Author keywords

[No Author keywords available]

Indexed keywords

ADJOINT; ADJOINT FORMULATION; APPLIED (CO); ARBITRARY LAGRANGIAN-EULERIAN (ALE); DESIGN VARIABLES; FLOW PROBLEMS; FORWARD PROBLEMS; GENERAL (CO); GOVERNING EQUATIONS; INDIVIDUAL (PSS 544-7); LOAD PROFILING; NONLINEAR FLOWS; PITCHING AIRFOILS; PRESSURE PROFILES; SENSITIVITY DERIVATIVES; TIME INTEGRATION SCHEMES; TIME-DEPENDENT; TWO DIMENSIONAL FLOWS; TWO-DIMENSIONAL (2D); UNSTEADY FLOW PROBLEMS;

AERODYNAMICS; AIRFOILS; DEFORMATION; FLUID DYNAMICS; FLUID MECHANICS; LINEARIZATION; MESH GENERATION; OPTIMIZATION; TWO DIMENSIONAL; UNSTEADY FLOW;

SHAPE OPTIMIZATION;

EID: 45849083479     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.29924     Document Type: Article

References (27)

1. Jameson, A., "Aerodynamic Shape Optimization Using the Adjoint Method," VKI Lecture Series on Aerodynamic Drag Prediction and Reduction, von Karman Institute of Fluid Dynamics, Rhode St. Genese, Belgium, 2003.
2. Jameson, A., and Vassberg, J., "Computational Fluid Dynamics for Aerodynamic Design: Its Current and Future Impact," AIAA Paper 2001-0538, 2001.
3. Nadarajah, S., and Jameson, A., "A Comparison of the Continuous and Discrete Adjoint Approach to Automatic Aerodynamic Optimization," AIAA Paper 2000-0667, 2000.
4. Nielsen, E., and Anderson, W., "Recent Improvements in Aerodynamic Design Optimization on Unstructured Meshes." AIAA Journal, Vol. 40, No. 6, June 2002, pp. 1155-1163.
5. Jameson, A., Alonso, J., Reuther, J., Martinelli, L., and Vassberg, J., "Aerodynamic Shape Optimization Techniques Based on Control Theory," AIAA Paper 98-2538, 1998.
6. Giles, M., Duta, M., and Muller, J., "Adjoint Code Developments Using Exact Discrete Approach," AIAA Paper 2001-2596, 2001.
7. Mavriplis, D. J., "Multigrid Solution of the Discrete Adjoint for Optimization Problems on Unstructured Meshes," AIAA Journal, Vol. 44, No. 1, Jan. 2006, pp. 42-50. doi:10.2514/1.15696
8. Mavriplis, D. J., "Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes," AIAA Journal, Vol. 45, No. 4, April 2007, pp. 740-750. doi:10.2514/1.22743
9. Elliott, J., and Peraire, J., "Practical Three-Dimensional Aerodynamic Design and Optimization Using Unstructured Meshes," AIAA Journal, Vol. 35, No. 9, 1997, pp. 1479-1485.
10. Soto, R., and Yang, C., "An Adjoint-Based Design Methodology for CFD Optimization Problems," AIAA Paper 2003-0299, 2003.
11. Ghayour, K., and Baysal, O., "Limit-Cycle Shape Optimization using Time-Dependent Transonic Equation," AIAA Paper 99-3375, 1999.
12. Nadarajah, S., and Jameson, A., "Optimal Control of Unsteady Flows using A Time Accurate Method," AIAA Paper 2002-5436, 2002.
13. Rumpfkeil, M., and Zingg, D., "A General Framework for the Optimal Control of Unsteady Flows with Applications," AIAA Paper 2007-1128, Jan. 2007.
14. Nadarajah, S., McMullen, M., and Jameson, A., "Non-Linear Frequency Domain Based Optimum Shape Design for Unsteady Three-Dimensional Flow," AIAA Paper 2006-387, 2006.
15. Nadarajah, S., McMullen, M., and Jameson, A., "Optimal Control of Unsteady Flows Using Time Accurate and Non-Linear Frequency Domain Methods," AIAA Paper 2003-3875, June 2003.
16. Byrd, R. H., Lu, P., and Nocedal, J., "A Limited Memory Algorithm for Bound Constrained Optimization," SIAM Journal on Scientific and Statistical Computing, Vol. 16, No. 5, 1995, pp. 1190-1208. doi:10.1137/0916069
17. Yang, Z., and Mavriplis, D. J., "Higher-Order Time Integration Schemes for Aeroelastic Applications on Unstructured Meshes," AIAA Journal, Vol. 45, No. 1, Jan. 2007, pp. 138-150. doi:10.2514/1.22847
18. Mavriplis, D., "Multigrid Techniques for Unstructured Meshes," Notes Prepared for the 26th Computational Fluid Dynamics Lecture Series Program, von Karman Institute of Fluid Dynamics, Rhode St. Genese, Belgium, 1995.
19. Roe, P., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," Journal of Computational Physics, Vol. 43, No. 2, 1981, pp. 357-372. doi:10.1016/0021-9991(81)90128-5
20. Geuzaine, P., Grandmont, C., and Farhat, C., "Design and Analysis of ALE Schemes with Provable Second-Order Time-Accuracy for Inviscid and Viscous Flow Simulations," Journal of Computational Physics, Vol. 191, No. 1, 2003, pp. 206-227. doi:10.1016/S0021-9991(03)00311-5
21. Mavriplis, D., and Yang, Z., "Construction of the Discrete Geometric Conservation Law for High-Order Time Accurate Simulations on Dynamic Meshes," Journal of Computational Physics, Vol. 213, No. 2, 2006, pp. 557-573. doi:10.1016/j.jcp.2005.08.018
22. Batina, J. T., "Unsteady Euler Airfoil Solutions Using Unstructured Dynamic Meshes," AIAA Journal, Vol. 28, No. 8, Aug. 1990, pp. 1381-1388.
23. Hicks, R., and Henne, P., "Wing Design by Numerical Optimization," Journal of Aircraft, Vol. 15, No. 7, 1978, pp. 407-412.
24. Valarezo, W. O., and Mavriplis, D. J., "Navier-Stokes Applications to High-Lift Airfoil Analysis," Journal of Aircraft, Vol. 32, No. 3, 1995, pp. 618-624.
25. Dwight, R., and Brezillon, J., "Effect of Various Approximations of the Discrete Adjoint on Gradient-Based Optimization," AIAA Paper 2006-0690, 2006.
26. Nielsen, E., Lu, J., Park, M., and Darmofal, D., "An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids," AIAA Paper 2003-0272, 2003.
27. Giles, M., Duta, M., Müller, J.-D., and Pierce, N., "Algorithm Developments for Discrete Adjoint Methods." AIAA Journal, Vol. 41, No. 2, 2003, pp. 198-205.