A Comparison of OptimizationBased Approaches for a Model Computational Aerodynamics Design Problem
Abstract
The objective of this paper is to compare three optimizationbased methods for solving aerodynamic design problems. We use the Euler equations for onedimensional duct flow as a model problem. The optimization methods are (i) the blackbox method with finite difference gradients, (ii) a modification where gradients are found by an algorithm based on the implicit function theorem, and (iii) an allatonce method where the flow and design variables are simultaneously altered. The three methods are applied to the model problem and compared for efficiency, robustness, and implementation difficulty. We also show that the blackbox (implicit gradient) method is equivalent to applying the "variational" or "optimal control" approach to design optimization directly to the discretized analysis problem, rather than to the continuous problem as is usually done. The blackbox method with implicit gradients seems to provide a good compromise of features, and can be retrofitted to most existing analysis codes to turn them into design codes. Although the allatonce method was found to be less robust than the blackbox methods, when it succeeded it was considerably more efficient.
 Publication:

Journal of Computational Physics
 Pub Date:
 January 1992
 DOI:
 10.1016/00219991(92)90174W
 Bibcode:
 1992JCoPh..98...74F