Low-Fidelity Model Mesh Density and the Performance of Variable-Resolution Shape Optimization Algorithms

Surrogate based optimization (SBO) provides an interesting alternative to conventional aerodynamic shape optimization methods. By shifting the optimization burden to a cheap and yet reasonably accurate surrogate model, the design cost can be substantially reduced. SBO methods exploiting physically based surrogates can be particularly efficient because underlying low-fidelity models embed some knowledge about the system under consideration (e.g., by sharing the simulation tools with the high-fidelity models) so that good accuracy and even better generalization capability can be obtained through a correction based on a very limited number of high-fidelity model samples. The major open problem here is the proper selection of the low-fidelity model. The type of simplifications made to construct the model, as well as its level of accuracy (e.g., mesh density) may be crucial for the algorithm performance both in terms of the quality of the final design and the computational cost of the design process. Here, we investigate this trade off using space mapping (SM) as an exemplary SBO technique and two dimensional airfoil shape optimization as a representative design problem. Both lift maximization and drag minimization test cases are considered.