Abstract
This paper deals with the task of generating a discrete adjoint solver from a given primal Unsteady Reynolds Averaged Navier-Stokes (URANS) solver for incompressible flows. This adjoint solver is to be employed in active flow control problems to enhance the performance of aerodynamic configurations. We discuss on how the development of such a code can be eased through the use of the reverse mode of Automatic/Algorithmic Differentiation (AD). If AD is applied in a black-box fashion then the resulting adjoint URANS solver will have prohibitively expensive memory requirements. We present several strategies to circumvent the excessive memory demands. We also address the parallelization of the adjoint code and the adjoint counterparts of the MPI directives that are used in the primal solver. The adjoint code is validated by applying it to the standard test case of a rotating cylinder by active flow control. The sensitivities based on the adjoint code are compared with the values obtained from finite differences and forward mode AD code.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Caretto, L., Gosman, A., Patankar, S., Spalding, D.: Two calculation procedures for steady, three-dimensional flows with recirculation. In: Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Lecture Notes in Physics, vol. 19, pp. 60–68. Springer Berlin / Heidelberg (1973)
Carnarius, A., Thiele, F., Özkaya, E., Gauger, N.: Adjoint approaches for optimal flow control. AIAA Paper 2010–5088 (2010)
Christianson, B.: Reverse accumulation and attractive fixed points. Optimization Methods and Software 3, 311–326 (1994)
Courty, F., Dervieux, A., Koobus, B., Hascoët, L.: Reverse automatic differentiation for optimum design: from adjoint state assembly to gradient computation. Optimization Methods and Software 18(5), 615–627 (2003)
E. Özkaya, E., Gauger, N.: Automatic transition from simulation to one-shot shape optimization with Navier-Stokes equations. GAMM-Mitteilungen 33(2), 133–147 (2010). DOI 10.1002/gamm.201010011. URL http://dx.doi.org/10.1002/gamm.201010011
Elliot, J., Peraire, J.: Practical 3D aerodynamic design and optimization using unstructured meshes. AIAA Journal 35(9), 1479–1485 (1997)
Ferziger, J.H., Peric, M.: Computational Methods for Fluid Dynamics. Springer, Berlin; Heidelberg (2008)
Gauger, N., Walther, A., Moldenhauer, C., Widhalm, M.: Automatic differentiation of an entire design chain for aerodynamic shape optimization. Notes on Numerical Fluid Mechanics and Multidisciplinary Design 96, 454–461 (2007)
Giles, M., Duta, M., Müller, J., Pierce, N.: Algorithm developments for discrete adjoint methods. AIAA Journal 41(2), 198–205 (2003)
Griewank, A., Faure, C.: Reduced functions, gradients and hessians from fixed point iteration for state equations. Numerical Algorithms 30(2), 113–139 (2002)
Griewank, A., Walther, A.: Algorithm 799:revolve: An implementation of checkpointing for the reverse or adjoint mode of computational differentiation. ACM Trans. Math. Software 26(1), 19–45 (2000)
Griewank, A., Walther, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, 2nd edn. No. 105 in Other Titles in Applied Mathematics. SIAM, Philadelphia, PA (2008). URL http://www.ec-securehost.com/SIAM/OT105.html
Hascoët, L., Pascual, V.: TAPENADE 2.1 user’s guide. Rapport technique 300, INRIA, Sophia Antipolis (2004). URL http://www.inria.fr/rrrt/rt-0300.html
Heimbach, P., Hill, C., Giering, R.: An efficient exact adjoint of the parallel MIT general circulation model, generated via automatic differentiation. Future Generation Computer Systems 21(8), 1356–1371 (2004)
Jameson, A.: Aerodynamic design via control theory. J. Sci. Comput. 3, 233–260 (1988)
Jameson, A., Pierce, N., Martinelli, L.: Optimum aerodynamic design using the Navier–Stokes equations. J. Theor. Comp. Fluid Mech. 10, 213–237 (1998)
Nielsen, E., Anderson, W.: Aerodynamic design optimization on unstructured meshes using the Navier-Stokes equations. AIAA Journal 37(11), 957–964 (1999)
Pironneau, O.: On optimum design in fluid mechanics. J. Fluid Mech. 64, 97–110 (1974)
Utke, J., Hascoet, L., Heimbach, P., Hill, C., Hovland, P., Naumann, U.: Toward adjoinable MPI. In: Parallel Distributed Processing, 2009. IPDPS 2009. IEEE International Symposium on, pp. 1–8 (2009). DOI 10.1109/ IPDPS.2009.5161165
Wilcox, D.: Re-assessment of the scale-determining equation for advanced turbulence models. AIAA Journal 26(11), 1299–1310 (1988)
Xue, L.: Entwicklung eines effizienten parallelen Lösungsalgorithmus zur dreidimensionalen Simulation komplexer turbulenter Strömungen. Ph.D. thesis, Technical University Berlin (1998)
Zymaris, A., Papadimitriou, D., Giannakoglou, K., Othmer, C.: Continuous adjoint approach to the Spalart-Allmaras turbulence model for incompressible flows. Computers & Fluids 38, 1528–1538 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Özkaya, E., Nemili, A., Gauger, N.R. (2012). Application of Automatic Differentiation to an Incompressible URANS Solver. In: Forth, S., Hovland, P., Phipps, E., Utke, J., Walther, A. (eds) Recent Advances in Algorithmic Differentiation. Lecture Notes in Computational Science and Engineering, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30023-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-30023-3_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30022-6
Online ISBN: 978-3-642-30023-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)