A comparison of optimization-based approaches for a model computational aerodynamics design problem (Q1184637)

The objective of this paper is to compare three optimization-based methods for solving aerodynamic design problems. We use the Euler equations for one-dimensional duct flow as a model problem. The optimization methods are (i) the black-box method with finite difference gradients, (ii) a modification where gradients are found by an algorithm based on the implicit function theorem, and (iii) an all-at-once 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.