Application of Physics-Based Surrogate Models to Benchmark Aerodynamic Shape Optimization Problems

Abstract

This paper presents the results of applying direct and surrogate-based optimization (SBO) algorithms to two-dimensional aerodynamic benchmark problems, both involving transonic flow, one invisvid and the other viscous. The direct optimization methods used in this study are the adjoint-based FUN3D and Stanford University Unstructured solvers. The SBO algorithms include the SurroOpt framework, which exploits approximation-based models, the multi-level optimization (MLO) algorithm, which relies on physics-based models, as well as the adjoint-enhanced MLO algorithm. The results demonstrate that direct optimization and the approximation-based methods are able to yield designs that are comparable to those obtained with high-dimensional shape parameterization methods. Physics-based SBO shows a rapid design improvement at a low computational cost compared to the direct and the approximation-based SBO techniques, which indicates that—for certain problems—derivative-free methods may be competitive to adjoint-based algorithms when embedded in surrogate-assisted frameworks. On the other hand, global search approaches, while more expensive, exhibit the potential to produce the best quality results.