Commun. Comput. Phys., 6 (2009), pp. 406-432.

A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter

Jeroen A. S. Witteveen 1*, Hester Bijl 1

1 Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629HS Delft, The Netherlands.

Received 26 September 2008; Accepted (in revised version) 30 October 2008
Available online 15 December 2008


The Unsteady Adaptive Stochastic Finite Elements (UASFE) approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations. In this paper, it is shown that the underlying Adaptive Stochastic Finite Elements (ASFE) method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing (ED). It is also shown that the method is total variation diminishing (TVD) for one random parameter and for multiple random parameters for first degree Newton-Cotes quadrature. It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time. The two methods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.

AMS subject classifications: 60H35, 65C30, 65N15, 65P99, 76M35

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Key words: Total variation diminishing, extrema diminishing, error bounds, stochastic finite elements, uncertainty quantification, transonic flow, transonic flutter.

*Corresponding author.
Email: (J. A. S. Witteveen), (H. Bijl)

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