Abstract
Because detailed aerodynamic shape optimizations still suffer from high computational costs, efficient optimization strategies are required. Regarding the deterministic optimization methods, the adjoint approach is seen as a promising alternative to the classical finite difference approach. With the adjoint approach, the sensitivities needed for the aerodynamic shape optimization can be efficiently obtained using the adjoint flow equations. Here, one is independent of the number of design variables with respect to the numerical costs for determining the sensitivities. Another advantage of the adjoint approach is that one obtains accurate sensitivities and gets rid of the laborious tuning of the denominator step sizes for the finite differences.
Differentiation between continuous and discrete adjoint approaches is noted. In the continuous case, one formulates the optimality condition first, then derives the adjoint problem and finally does the discretization of the so obtained adjoint flow equations. In the discrete case, one takes the discretized flow equations for the derivation of the discrete adjoint problem. This can be automated by so-called algorithmic differentiation (AD) tools.
The different adjoint approaches will be explained for single disciplinary aerodynamic shape optimization first and then their extension to multidisciplinary design optimization (MDO) problems will be discussed for aerostructure cases. Finally, we will discuss the so-called one-shot methods. Here, one breaks open the simulation loop for optimization.
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References
Brezillon, J., Dwight, R.: Discrete adjoint of the Navier-Stokes equations for aerodynamic shape optimization. In: Proceedings of EUROGEN05 (2005)
Brezillon, J., Gauger, N.R.: 2D and 3D aerodynamic shape optimization using the adjoint approach. Aerospace Science and Technology 8(8), 715–727 (2004)
Dwight, R.: Efficiency improvments of RANS-based analysis and optimization using implicit and adjoint methods on unstructured grids. Ph.D. thesis, DLR-Report No. DLR-FB-2006-11 (ISSN 1434-8454) (2006)
Fazzolari, A.: An aero-structure adjoint formulation for efficient multidisciplinary wing optimization. Ph.D. thesis, TU Braunschweig, Germany (2006)
Fazzolari, A., Gauger, N.R., Brezillon, J.: An aero-structure adjoint formulation for efficient multidisciplinary wing optimization. In: Proceedings of EUROGEN05 (2005)
Fazzolari, A., Gauger, N.R., Brezillon, J.: Efficient aerodynamic shape optimization in mdo context. Journal of Computational and Applied Mathematics 203, 548–560 (2007)
Gauger, N.R.: Aerodynamic shape optimization using the adjoint Euler equations. In: Proceedings of the GAMM Workshop on Discrete Modelling and Discrete Algorithms in Continuum Mechanics, pp. 87–96. Logos Verlag, Berlin (2001)
Gauger, N.R.: Das Adjungiertenverfahren in der aerodynamischen Formoptimierung. Ph.D. thesis, DLR-Report No. DLR-FB-2003-05 (ISSN 1434-8454) (2003)
Gauger, N.R., Brezillon, J.: Aerodynamic shape optimization using adjoint method. Journal of the Aeronautical Society of India 54(3), 247–254 (2002)
Gauger, N.R., Walther, A., Moldenhauer, C., Widhalm, M.: Automatic differentiation of an entire design chain for aerodynamic shape optimization. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design (to appear), vol. 96. Springer Verlag (2007)
Giering, R., Kaminski, T., Slawig, T.: Applying TAF to a Navier-Stokes solver that simulates an Euler flow around an airfoil. Future Generation Computer Systems 21(8) (2005)
Giles, M.B., Duta, M.C., Müller, J.D., Pierce, N.A.: Algorithm developments for discrete adjoint methods. AIAA Journal 41(2), 198–205 (2003)
Griewank, A.: Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation. Society for Industrial and Applied Mathematics, Philadelphia (2000)
Griewank, A., Juedes, D., Mitev, H., Utke, J., Vogel, O., Walther, A.: ADOL-C: A package for the automatic differentiation of algorithms written in C/C++. Tech. rep., Technical University of Dresden, Institute of Scientific Computing and Institute of Geometry (1999)
Hazra, S.B., Schulz, V.: Simultaneous pseudo-timestepping for PDE-model based optimization problems. Bit Numerical Mathematics 44(3), 457–472 (2004)
Hazra, S.B., Schulz, V., Brezillon, J., Gauger, N.R.: Aerodynamic shape optimization using simultaneous pseudo-timestepping. Journal of Computational Physics 204(1), 46–64 (2005)
Heinrich, R.: Implementation and usage of structured algorithms within an unstructured CFD-code. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 92. Springer Verlag (2006)
Hounjet, M.H.L., Prananta, B.B., Zwaan, R.: A thin layer Navier Stokes solver and its application for aeroelastic analysis of an airfoil in transonic flow. Netherlands, DLR-Publication (1995)
Jameson, A.: Aerodynamic design via control theory. Journal of Scientific Computing 3, 233–260 (1988)
Jameson, A., Martinelli, L., Pierce, N.A.: Optimum aerodynamic design using the navier-stokes equations. Theoretical and Computational Fluid Dynamics 10, 213–237 (1998)
Jameson, A., Reuther, J.: Control theory based on airfoil design using the Euler equations. AIAA Proceedings 94-4272-CP (1994)
Kroll, N., Rossow, C.C., Schwamborn, D., Becker, K., Heller, G.: MEGAFLOW-A numerical flow simulation tool for transport aircraft design (2002)
Martins, J.R., Alonso, J.J., Reuther, J.J.: Complete configuration aero-structural optimization using a coupled sensitivity analysis method. AIAA Paper 2002-5402 (2002)
Martins, J.R., Alonso, J.J., Reuther, J.J.: High-fidelity aero-structural design optimization of a supersonic business jet. AIAA Paper 2002-1483 (2002)
Nocedal, J., Wright, S.J.: Numerical Optimization. Springer Series in Operations Research. Springer (1999)
Rossow, C.C.: A flux splitting scheme for compressible and incompressible flows. Journal of Computational Physics 164, 104–122 (2000)
Schlenkrich, S., Walther, A., Gauger, N.R., Heinrich, R.: Differentiating fixed point iterations with ADOL-C: Gradient calculation for fluid dynamics. In: Proceedings of the International Conference on High Performance Scientific Computing (2006)
Widhalm, M., Gauger, N.R., Brezillon, J.: Implementation of a continuous adjoint solver in TAU. DLR-Report (in press) (2007)
Widhalm, M., Rossow, C.C.: Improvement of upwind schemes with the least square method in the DLR TAU code. In: Notes on Numerical Fluid Mechanics, vol. 87, pp. 398–406. Springer Verlag (2004)
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Gauger, N.R. (2008). Efficient Deterministic Approaches for Aerodynamic Shape Optimization. In: Thévenin, D., Janiga, G. (eds) Optimization and Computational Fluid Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72153-6_5
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DOI: https://doi.org/10.1007/978-3-540-72153-6_5
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