Open Access

ARTICLE

Probabilistic Collocation used in a Two-Step approach for \\efficient uncertainty quantification in computational fluid dynamics.

G.J.A. Loeven^1,2, H. Bijl³

1 Ph. D. researcher, Faculty of Aerospace Engineering, P.O. Box 5058, 2600 GB Delft, The Netherlands.
2 Corresponding author: G. J. A. Loeven@TUDelft.nl.
3 Full Professor, Faculty of Aerospace Engineering, P. O. Box 5058, 2600 GB Delft, The Netherlands.

Computer Modeling in Engineering & Sciences 2008, 36(3), 193-212. https://doi.org/10.3970/cmes.2008.036.193

Abstract

In this paper a Two-Step approach is presented for uncertainty quantification for expensive problems with multiple uncertain parameters. Both steps are performed using the Probabilistic Collocation method. The first step consists of a sensitivity analysis to identify the most important parameters of the problem. The sensitivity derivatives are obtained using a first or second order Probabilistic Collocation approximation. For the most important parameters the probability distribution functions are propagated using the Probabilistic Collocation method using higher order approximations. The Two-Step approach is demonstrated for flow around a NACA0012 airfoil with eight uncertain parameters in the free stream conditions and geometry. The first step identified the freestream velocity, angle of attack, and the camber of the airfoil as the three most important parameters. In the second step the probability distributions of all three parameters are propagated using higher order Probabilistic Collocation approximations. Statistical properties of the lift and drag are obtained, as well as uncertainty bounds for the pressure and skinfriction on the surface of the airfoil.

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Keywords

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