Quantification of Airfoil Geometry-Induced Aerodynamic Uncertainties---Comparison of Approaches

Abstract
Uncertainty quantification in aerodynamic simulations calls for efficient numerical methods to reduce computational cost, especially for uncertainties caused by random geometry variations which involve a large number of variables. This paper compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and by point collocation, radial basis function and a gradient-enhanced version of kriging, and examines their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry which is parameterized by independent Gaussian variables. The results show that gradient-enhanced surrogate methods achieve better accuracy than direct integration methods with the same computational cost.

Citation
Liu D, Litvinenko A, Schillings C, Schulz V (2017) Quantification of Airfoil Geometry-Induced Aerodynamic Uncertainties---Comparison of Approaches. SIAM/ASA Journal on Uncertainty Quantification 5: 334–352. Available: http://dx.doi.org/10.1137/15M1050239.

Acknowledgements
This work was supported by the project MUNA under the framework of the German Luftfahrtforschungsprogramm funded by the Ministry of Economics (BMWi). A part of this work was done by A. Litvinenko during his stay at King Abdullah University of Science and Technology. We are grateful to the anonymous reviewers for their diligence and insights which have greatly helped to improve this paper. Special gratitude is extended to Dr. Stefan Gortz at Institute of Aerodynamics and Flow Technology of the German Aerospace Center (DLR) for his invaluable advice during the modifi cation. The authors also thank Bernhard Eisfeld and Normann Krimmelbein at DLR for their kind help on the CFD test case.

Publisher
Society for Industrial & Applied Mathematics (SIAM)

Journal
SIAM/ASA Journal on Uncertainty Quantification

DOI
10.1137/15M1050239

arXiv
1505.05731

Additional Links
https://arxiv.org/abs/1505.05731http://epubs.siam.org/doi/10.1137/15M1050239

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