This paper presents an efficient approach for simulation-based inverse design of airfoil shapes using variable-fidelity computational fluid dynamics models and manifold mapping (MM). Inverse design involves determining an airfoil shape fulfilling a given target performance characteristic. In particular, the pressure coefficient distribution is typically used in aerodynamic inverse design. Such a task can be challenging when using computationally expensive simulations. In the context of local optimization, the MM technique searches for a new design in the vicinity of the current design by constructing a fast multi-fidelity model, which is setup by the available evaluations of each of the high- and low-fidelity models at the current design. The MM-based multi-fidelity model predicts the high-fidelity model response at the new design by evaluating the low-fidelity model at the new design and applying the MM mapping. The MM-based multi-fidelity model is embedded within the trust-region algorithm and terminates based on the convergence of the argument, objective, and trust-region radius to yield the optimal design. The MM-based multi-fidelity algorithm only needs one high-fidelity model evaluation per design iteration. The proposed approach is illustrated on the inverse design of airfoils in transonic inviscid flow with the NACA 2412 airfoil as baseline and the pressure distribution of the RAE 2822 airfoil at Mach 0.734 and lift coefficient 0.824 as the target. Using eight B-spline design variables, the results indicate the MM technique is able to reach the target distribution at a low computational cost when compared to derivative-free local search.
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