The continuous adjoint approach to the k–ω SST turbulence model with applications in shape optimization

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
   Web of Science ®Google Scholar
• Anderson, W. K., and V. Venkatakrishnan. 1997. “Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation.” In Proceedings of the 35th AIAA Aerospace Sciences Meeting & Exhibit, 6–9 January 1997, Reno, NV, AIAA Paper No. 97-0643. doi:10.2514/6.1997-643.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• Gauger, N. R., A. Walther, C. Moldanhauer, and M. Wildhalm. 2008. “Automatic Differentiation of an Entire Design Chain for Aerodynamic Shape Optimization.” New Results in Numerical and Experimental Fluid Mechanics VI, Contributions to the 15th STAB/DGLR Symposium, Darmstadt, Germany, 2006, Vol. 96 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), 454–461. Berlin: Springer.
   Google Scholar
• Giles, M. B., and N. A. Pierce. 1997. “Adjoint Equations in CFD: Duality, Boundary Conditions and Solution Behaviour.” In Proceedings of the 13th Computational Fluid Dynamics Conference, Snowmass Village, CO, AIAA Paper No. 97-1850. doi:10.2514/6.1997-1850.
   Google Scholar
• Griewank, A., and A. Walther. 2000. “Algorithm 799: Revolve: An Implementation of Checkpointing for the Reverse or Adjoint Mode of Computational Differentiation.” ACM Transactions on Mathematical Software (TOMS) 26 (1): 19–45. doi: 10.1145/347837.347846
   Web of Science ®Google Scholar
• Hartmann, R., J. Held, and T. Leicht. 2011. “Adjoint-Based Error Estimation and Adaptive Mesh Refinement for the RANS and k–ω Turbulence Model Equations.” Journal of Computational Physics 230: 4268–4284. doi: 10.1016/j.jcp.2010.10.026
   Web of Science ®Google Scholar
• Jameson, A. 1988. “Aerodynamic Design via Control Theory.” Journal of Scientific Computing 3 (3): 233–260. doi: 10.1007/BF01061285
   Google Scholar
• Jameson, A., N. Pierce, and L. Martinelli. 1998. “Optimum Aerodynamic Design Using the Navier–Stokes Equations.” Theoretical and Computational Fluid Dynamics 10 (1): 213–237. doi: 10.1007/s001620050060
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Menter, F. R. 1994. “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications.” AIAA Journal 32 (8): 269–289. doi: 10.2514/3.12149
   Web of Science ®Google Scholar
• Menter, F. R., M. Kuntz, and R. Langtry. 2003. “Ten Years of Industrial Experience with the SST Turbulence Model.” Turbulence, Heat and Mass Transfer 4: 625–632.
   Google Scholar
• Naumann, U. 2012. U.N.: The Art of Differentiating Computer Programs. SIAM.
   Google Scholar
• Nemili, A., E. Ozkaya, 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.” In Proceedings of the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA. AIAA Paper No. 13-2585. doi:10.2514/6.2013-2585.
   Google Scholar
• 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: 1131–1155. doi: 10.1016/j.compfluid.2003.09.005
   Web of Science ®Google Scholar
• Nocedal, J., and S. J. Wright. 1999. Numerical Optimization. New York: Springer.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Papoutsis-Kiachagias, E. M., A. S. Zymaris, I. S. Kavvadias, D. I. Papadimitriou, and K. C. Giannakoglou. 2014. “The Continuous Adjoint Approach to the k–ε Turbulence Model for Shape Optimization and Optimal Active Control of Turbulent Flows.” Engineering Optimization doi:10.1080/0305215X.2014.892595.
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Pironneau, O. 1984. Optimal Shape Design for Elliptic Systems. New York: Springer-Verlag.
   Google Scholar
• Steward, J. L., I. M. Navon, M. Zupanski, and N. Karmitsa. 2012. “Impact of Non-Smooth Observation Operators on Variational and Sequential Data Assimilation for a Limited-Area Shallow Water Equations Model.” Quarterly Journal of the Royal Meteorological Society 138 (663): 323–339. doi: 10.1002/qj.935
   Web of Science ®Google Scholar
• Taylor, T. W. R., F. Palacios, K. Duraisami, and J. J. Alonso. 2013. “A Hybrid Adjoint Approach Applied to Turbulent Flow Simulations.” In Proceedings of the 21st AIAA Computational Fluid Dynamics Conference, San Diego, CA, AIAA Paper No. 13-2452. doi:10.2514/6.2013-2452
   Google Scholar
• Towara, M., and U. Naumann. 2013. “A Discrete Adjoint Model for OpenFOAM.” Procedia Computer Science 18 (2013): 429–438. doi: 10.1016/j.procs.2013.05.206
   Google Scholar
• Vieser, W., T. Esch, and F. R. Menter. 2002. “Heat Transfer Predictions Using Advanced Two-Equation Turbulence Models.” CFX Technical Memorandum CFX-VAL10/0602, AEA Technology, Otterfing, Germany.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar