A.Litvinenko and H. G. Matthies, Numerical Methods for Uncertainty Quantification and Bayesian update in Aerodynamics. Chapter in the book Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics, pp. 267-283, Editors: B. Eisfeld, H. Barnewitz, W. Fritz, F. Thiele, Springer, 2013
In this work we research the propagation of uncertainties in parameters and airfoil geometry to the solution. Typical examples of uncertain parameters are the angle of attack and the Mach number. The discretisation techniques which we used here are the Karhunen-Loève and the polynomial chaos expansions. To integrate high-dimensional integrals in probabilistic space we used Monte Carlo simulations and collocation methods on sparse grids. To reduce storage requirement and computing time, we demonstrate an algorithm for data compression, based on a low-rank approximation of realisations of random fields. This low-rank approximation allows us an efficient postprocessing (e.g. computation of the mean value, variance, etc) with a linear complexity and with drastically reduced memory requirements. Finally, we demonstrate how to compute the Bayesian update for updating a priori probability density function of uncertain parameters. The Bayesian update is also used for incorporation of measurements into the model.