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Optimization and Computational Fluid Dynamics - Department of ...

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144 Nicolas R. Gauger<br />

optimization is about 68% <strong>and</strong> the shock completely vanished (Fig. 5.18) as<br />

expected for inviscid cases. Figure 5.18 presents the comparison <strong>of</strong> the initial<br />

<strong>and</strong> final surface pressure distributions achieved with the one-shot approach<br />

(present) <strong>and</strong> with the conventional gradient based adjoint approach (steepest<br />

descent).<br />

Altogether, the numerical cost <strong>of</strong> the one-shot optimization is <strong>of</strong> the magnitude<br />

<strong>of</strong> just 4 flow simulations, which is a dramatic reduction in computation<br />

time compared to the conventional approach.<br />

Acknowledgements The author thanks his colleagues at DLR, in particular A. Fazzolari,<br />

J. Brezillon <strong>and</strong> M. Widhalm, as well as the MEGADESIGN partners V. Schulz <strong>and</strong> S.<br />

Hazra from University <strong>of</strong> Trier for their contributions to this chapter. Furthermore, the<br />

author thanks A. Walther <strong>and</strong> C. Moldenhauer from TU Dresden for their support <strong>and</strong><br />

contributions w.r.t. algorithmic differentiation.<br />

References<br />

1. Brezillon, J., Dwight, R.: Discrete adjoint <strong>of</strong> the Navier-Stokes equations for aerodynamic<br />

shape optimization. In: Proceedings <strong>of</strong> EUROGEN05 (2005)<br />

2. Brezillon, J., Gauger, N.R.: 2D <strong>and</strong> 3D aerodynamic shape optimization using the<br />

adjoint approach. Aerospace Science <strong>and</strong> Technology 8(8), 715–727 (2004)<br />

3. Dwight, R.: Efficiency improvments <strong>of</strong> RANS-based analysis <strong>and</strong> optimization using<br />

implicit <strong>and</strong> adjoint methods on unstructured grids. Ph.D. thesis, DLR-Report No.<br />

DLR-FB–2006-11 (ISSN 1434-8454) (2006)<br />

4. Fazzolari, A.: An aero-structure adjoint formulation for efficient multidisciplinary wing<br />

optimization. Ph.D. thesis, TU Braunschweig, Germany (2006)<br />

5. Fazzolari, A., Gauger, N.R., Brezillon, J.: An aero-structure adjoint formulation for<br />

efficient multidisciplinary wing optimization. In: Proceedings <strong>of</strong> EUROGEN05 (2005)<br />

6. Fazzolari, A., Gauger, N.R., Brezillon, J.: Efficient aerodynamic shape optimization<br />

in mdo context. Journal <strong>of</strong> <strong>Computational</strong> <strong>and</strong> Applied Mathematics 203, 548–560<br />

(2007)<br />

7. Gauger, N.R.: Aerodynamic shape optimization using the adjoint Euler equations. In:<br />

Proceedings <strong>of</strong> the GAMM Workshop on Discrete Modelling <strong>and</strong> Discrete Algorithms<br />

in Continuum Mechanics, pp. 87–96. Logos Verlag, Berlin (2001)<br />

8. Gauger, N.R.: Das Adjungiertenverfahren in der aerodynamischen Formoptimierung.<br />

Ph.D. thesis, DLR-Report No. DLR-FB–2003-05 (ISSN 1434-8454) (2003)<br />

9. Gauger, N.R., Brezillon, J.: Aerodynamic shape optimization using adjoint method.<br />

Journal <strong>of</strong> the Aeronautical Society <strong>of</strong> India 54(3), 247–254 (2002)<br />

10. Gauger, N.R., Walther, A., Moldenhauer, C., Widhalm, M.: Automatic differentiation<br />

<strong>of</strong> an entire design chain for aerodynamic shape optimization. In: Notes on Numerical<br />

<strong>Fluid</strong> Mechanics <strong>and</strong> Multidisciplinary Design (to appear), vol. 96. Springer Verlag<br />

(2007)<br />

11. Giering, R., Kaminski, T., Slawig, T.: Applying TAF to a Navier-Stokes solver that<br />

simulates an Euler flow around an airfoil. Future Generation Computer Systems 21(8)<br />

(2005)<br />

12. Giles, M.B., Duta, M.C., Müller, J.D., Pierce, N.A.: Algorithm developments for discrete<br />

adjoint methods. AIAA Journal 41(2), 198–205 (2003)

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