Surrogate-based Airfoil Design with Space Mapping and Adjoint Sensitivity

This paper presents a space mapping algorithm for airfoil shape optimization enhanced with adjoint sensitivities. The surrogate-based algorithm utilizes low-cost derivative information obtained through adjoint sensitivities to improve the space mapping matching between a high-fidelity airfoil model, evaluated through expensive CFD simulations, and its fast surrogate. Here, the airfoil surrogate model is constructed though low-fidelity CFD simulations. As a result, the design process can be performed at a low computational cost in terms of the number of high-fidelity CFD simulations. The adjoint sensitivities are also exploited to speed up the surrogate optimization process. Our method is applied to a constrained drag minimization problem in two-dimensional inviscid transonic flow. The problem is solved for several low-fidelity model termination criteria. The results show that when compared with direct gradient-based optimization with adjoint sensitivities, the proposed approach requires 49-78% less computational cost while still obtaining a comparable airfoil design.