688
Views
28
CrossRef citations to date
0
Altmetric
Original Articles

The continuous adjoint approach to the k–ε turbulence model for shape optimization and optimal active control of turbulent flows

, , , &
Pages 370-389 | Received 22 Jul 2013, Accepted 22 Jan 2014, Published online: 20 Mar 2014

References

  • Anderson, W. K., and D. L. Bonhaus. 1999. “Airfoil Design on Unstructured Grids for Turbulent Flows.” AIAA Journal 37 (2): 185–191. doi: 10.2514/2.712
  • Anderson, W. K., and V. Venkatakrishnan. 1999. “Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation.” Computers & Fluids 28 (4–5): 443–480. doi: 10.1016/S0045-7930(98)00041-3
  • Bueno-Orovio, A., C. Castro, F. Palacios, and E. ZuaZua. 2012. “Continuous Adjoint Approach for the Spalart–Allmaras Model in Aerodynamic Optimization.” AIAA Journal 50 (3): 631–646. doi: 10.2514/1.J051307
  • Burgreen, G. W., and O. Baysal. 1996. “Three-Dimensional Aerodynamic Shape Optimization Using Discrete Sensitivity Analysis.” AIAA Journal 34 (9): 1761–1770. doi: 10.2514/3.13305
  • Carnarius, Angelo, Frank Thiele, Emre Özkaya, Anil Nemili, and Nicolas R. Gauger. 2013. “Optimal Control of Unsteady Flows Using a Discrete and a Continuous Adjoint Approach.” System Modeling and Optimization, IFIP Advances and Communication Technology 391: 318–327. doi: 10.1007/978-3-642-36062-6_32
  • Cathalifaud, P., and P. Luchini. 2000. “Algebraic Growth in Boundary Layers: Optimal Control by Blowing and Suction at the Wall.” European Journal of Mechanics-B/Fluids 19 (4): 469–490. doi: 10.1016/S0997-7546(00)00128-X
  • Collis, S. Scott, Ronald D. Joslin, Avi Seifert, and Vassilis Theofilis. 2004. “Issues on Active Flow Control: Theory, Control, Simulation and Experiment.” Progress in Aerospace Sciences 40 (4-5): 237–289. doi: 10.1016/j.paerosci.2004.06.001
  • Duta, M. C., M. B. Giles, and M. S. Campobasso. 2002. “The Harmonic Adjoint Approach to Unsteady Turbomachinery Design.” International Journal for Numerical Methods in Fluids 40 (3–4): 323–332. doi: 10.1002/fld.289
  • Dwight, R., J. Brézillon, and D. Vollmer. 2006. “Efficient Algorithms for Solution of the Adjoint Compressible Navier–Stokes Equations with Applications.” Paper presented at the 7th ONERA-DLR Aerospace Symposium (ODAS), Toulouse, October 4–6.
  • Elliott, J., and J. Peraire. 1996. “Aerodynamic Design Using Unstructured Meshes.” Paper presented at the 27th AIAA Fluid Dynamics Conference, New Orleans, LA, June 17–20. 10.2514/6.1996-1941.
  • Fletcher, R., and C. M. Reeves. 1964. “Function Minimization by Conjugate Gradients.” Computer Journal 7 (2): 149–154. doi: 10.1093/comjnl/7.2.149
  • Giles, M. B., and N. A. Pierce. 1997. “Adjoint Equations in CFD: Duality, Boundary Conditions and Solution Behaviour.” Paper presented at the 13th AIAA Computational Fluid Dynamics Conference, Snowmass Village, CO, June 29–July 2. 10.2514/6.1997-1850.
  • Giles, M., and N. Pierce. 2000. “An Introduction to the Adjoint Approach to Design.” Flow, Turbulence and Combustion 65: 393–415. doi: 10.1023/A:1011430410075
  • Grinfield, P. 2010. “Hadamard's Formula Inside and Out.” Journal of Optimization Theory and Applications 146 (3): 654–690. doi: 10.1007/s10957-010-9681-6
  • He, J. W., M. Chevalier, R. Glowinski, R. Metcalfe, A. Nordlander, and J. Periaux. 2000. “Drag Reduction by Active Control for Flow Past Cylinders.” Computational Mathematics Driven by Industrial Problems 1739: 287–363.
  • Jameson, A. 1988. “Aerodynamic Design Via Control Theory.” Journal of Scientific Computing 3 (3): 233–260. doi: 10.1007/BF01061285
  • Jameson, Antony, and Juan J. Alonso. 1996. “Automatic Aerodynamic Optimization on Distributed Memory Architectures.” Paper presented at the 34th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 8–12. AIAA Paper Number 96-0409. http://aero-comlab.stanford.edu/Papers/reno96.pdf.
  • Jameson, A., N. Pierce, and L. Martinelli. 1998. “Optimum Aerodynamic Design Using the Navier–Stokes equations.” Theoretical and Computational Fluid Dynamics 10: 213–237. doi: 10.1007/s001620050060
  • Joslin, R. D., M. D. Gunzburger, R. A Nicolaides, G. Erlebacher, and M. Y. Hussaini. 1997. “Self-Contained Automated Methodology for Optimal Flow Control.” AIAA Journal 35 (5): 816–824. doi: 10.2514/2.7452
  • Launder, B. E., and B. I. Sharma. 1974. “Application of the Energy-Dissipation Model of Turbulence to the Calculation of Flow near a Spinning Disc.” Letters in Heat and Mass Transfer 1 (2): 131–137. doi: 10.1016/0094-4548(74)90150-7
  • Lee, B. J., and C. Kim. 2007. “Automated Design Methodology of Turbulent Internal Flow Using Discrete Adjoint Formulation.” Aerospace Science and Technology 11 (2–3): 163–173. doi: 10.1016/j.ast.2006.12.001
  • Li, Zhijin, I. M. Navo, M. Y. Hussaini, and F. X. Le Dimet. 2003. “Optimal Control of Cylinder Wakes Via Suction and Blowing.” Computers & Fluids 32 (2): 149–171. doi: 10.1016/S0045-7930(02)00007-5
  • Mishra, A., K. Mani, D. Mavriplis, and J. Sitaraman. 2013. “Time Dependent Adjoint-Based Optimization for Coupled Aeroelastic Problems.” Presented at the 31st AIAA Applied Aerodynamics Conference, San Diego, CA. 10.2514/6.2013-2906.
  • Nadarajah, Siva, and Antony Jameson. 2001. “Studies of the Continuous and Discrete Adjoint Approaches to Viscous Automatic Aerodynamic Shape Optimization.” Paper presented at the 15th AIAA Computational Fluid Dynamics Conference, Anaheim, June 11–14. 10.2514/6.2001-2530.
  • Nadarajah, S., and A. Jameson. 2002. “Optimal Control Theory of Unsteady Flows Using a Time Accurate Method.” Presented at the 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA, September 4–6. 10.2514/6.2002-5436.
  • Naumann, Uwe. 2012. The Art of Differentiating Computer Programs: An Introduction to Algorithmic Differentiaion. Philadelphia, PA: SIAM.
  • Nemili, A., E. Özkaya, N. R. Gauger, F. Kramer, A. Carnarius, and F. Thiele. 2013. “Discrete Adjoint Based Sensitivity Analysis for Optimal Flow Control of a 3D High-Lift Configuration.” Presented at the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, June 24–27. 10.2514/6.2013-2585.
  • Nielsen, E. J., J. Lu, M. A. Park, and D. L. Darmofal. 2004. “An Implicit Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids.” Computers & Fluids 33 (9): 1131–1155. doi: 10.1016/j.compfluid.2003.09.005
  • Othmer, C. 2008. “A Continuous Adjoint Formulation for the Computation of Topological and Surface Sensitivities of Ducted Flows.” International Journal for Numerical Methods in Fluids 58 (8): 861–877. doi: 10.1002/fld.1770
  • Papadimitriou, D. I., and K. C. Giannakoglou. 2007. “A Continuous Adjoint Method with Objective Function Derivatives Based on Boundary Integrals for Inviscid and Viscous Flows.” Journal of Computers & Fluids 36 (2): 325–341. doi: 10.1016/j.compfluid.2005.11.006
  • Papadimitriou, D. I., and K. C. Giannakoglou. 2012. “Aerodynamic Design Using the Truncated Newton Algorithm and the Continuous Adjoint Approach.” International Journal for Numerical Methods in Fluids 68 (6): 724–739. doi: 10.1002/fld.2530
  • Patankar, S. V., and D. B. Spalding. 1972. “Calculation Procedure for Heat, Mass and Momentum Transfer in Three-dimensional Parabolic Flows.” International Journal of Heat and Mass Transfer 15 (10): 1787–1806. doi: 10.1016/0017-9310(72)90054-3
  • Pironneau, O. 1984. Optimal Shape Design for Elliptic Systems. New York: Springer-Verlag.
  • Pralits, J. O., A. Hanifi, and D. S. Henningson. 2002. “Adjoint-Based Optimization of Steady Suction for Disturbance Control in Incompressible Flows.” Journal of Fluid Mechanics 467: 129–161. doi: 10.1017/S0022112002001301
  • Prandtl, L. 1904. “Über Flüssigkeitsbeweung bei sehr kleiner Reibung.” In Proceedings of the 3rd International Mathematical Congress, Heidelberg, 484–491. Teuber Verlag, Leipzig.
  • Reuther, J., J. J. Alonso, M. J. Rimlinger, and A. Jameson. 1996. “Aerodynamic Shape Optimization of Supersonic Aircraft Configurations Via an Adjoint Formulation on Distributed Memory Parallel Computers.” Presented at the 6th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, September 4–6. 10.2514/6.1996-4045.
  • Taylor, T. W. R., F. Palacios, K. Duraisami, and J. J. Alonso. 2013. “A Hybrid Adjoint Approach Applied to Turbulent Flow Simulations.” Presented at the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, June 24–27. 10.2514/6.2013-2452.
  • Zhang, Z., P. C. Chen, S. Yang, Z. Wang, and Q. Wang. 2013. “Unsteady Aero-Structure Coupled Adjoint Method for Flutter Suppression.” Presented at the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, June 24–27. 10.2514/6.2013-2849.
  • Zymaris, A. S., D. I. Papadimitriou, K. C. Giannakoglou, and C. Othmer. 2009. “Continuous Adjoint Approach to the Spalart–Allmaras Turbulence Model for Incompressible Flows.” Computers & Fluids 38 (8): 1528–1538. doi: 10.1016/j.compfluid.2008.12.006
  • Zymaris, A. S., D. I. Papadimitriou, K. C. Giannakoglou, and C. Othmer. 2010. “Adjoint Wall Functions: A New Concept for Use in Aerodynamic Shape Optimization.” Journal of Computational Physics 229 (13): 5228–5245. doi: 10.1016/j.jcp.2010.03.037
  • Zymaris, A. S., D. I. Papadimitriou, E. M. Papoutsis-Kiachagias, K. C. Giannakoglou, and C. Othmer. 2013. “The Continuous Adjoint Method as a Guide for the Design of Flow Control Systems Based on Jets.” Engineering Computations 30 (4): 494–520. doi: 10.1108/02644401311329343

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.