Benchmarking Uncertainty Quantification Methods Using the NACA 2412 Airfoil with Geometrical and Operational Uncertainties Domenico Quagliarella ∗ CIRA, Italian Aerospace Research Centre, Capua, Italy Andrea Serani † and Matteo Diez ‡ CNR-INM, National Research Council-Institute of Marine Engineering, Rome, Italy Michele Pisaroni § and Pénélope Leyland ¶ EPFL, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Luca Montagliani ‖ and Umberto Iemma ∗∗ Roma Tre University, Rome, Italy Nicholas J. Gaul †† and Jaekwan Shin ‡‡ RAMDO Solutions LLC, Iowa City, IA, USA Dirk Wunsch §§ and Charles Hirsch ¶¶ NUMECA International SA, Brussels, Belgium KK Choi ∗∗∗ and Frederick Stern ††† IIHR–Hydroscience & Engineering, University of Iowa, Iowa City, IA, USA This paper presents uncertainty quantification (UQ) benchmarking activities within the NATO AVT-252 Task Group on “Stochastic Design Optimization for Naval and Aero Mili- tary Vehicles.” UQ methods are assessed and compared as an essential part of stochastic optimization procedures. Several metamodel (dynamic radial basis functions, dynamic Krig- ing, Gaussian process), Monte Carlo (multi-level Monte Carlo) and collocation (non-intrusive stochastic collocation) methods are applied to 2D and 15D UQ problems (that is with 2 or 15 uncertainties) of a NACA 2412 airfoil subject to operational (Mach number) and geometrical (design variables) uncertainties, both in the subsonic and transonic regimes. The flow is solved by MSES, XFoil, and the FINE TM /Open suite. A pure Monte Carlo simulation based on more than 300,000 samples is used as a benchmark to assess the accuracy and efficiency of UQ meth- ods. These can provide satisfactory results with errors for the expected value and standard deviation of C D smaller than 0.5 and 5% respectively. ∗ Senior Researcher † Postdoctoral Research Fellow ‡ Research Scientist, corresponding author: matteo.diez@cnr.it § Ph.D. ¶ Research Scientist ‖ M.Sc. Student ∗∗ Professor, Dept. of Engineering †† Chief Technical Officer ‡‡ Research Engineer §§ Head of Robust Design Group ¶¶ President ∗∗∗ Professor, Dept. of Mechanical Engineering ††† Professor, Dept. of Mechanical Engineering 1