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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 16

Unsteady Adaptive Stochastic Finite Elements for Quantification of Uncertainty in Time-Dependent Simulations

J.A.S. Witteveen and H. Bijl

Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands

Full Bibliographic Reference for this paper
J.A.S. Witteveen, H. Bijl, "Unsteady Adaptive Stochastic Finite Elements for Quantification of Uncertainty in Time-Dependent Simulations", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 16, 2008. doi:10.4203/ccp.89.16
Keywords: uncertainty quantification, stochastic finite elements, fluid dynamics, fluid-structure interaction, unsteady problems, shock waves, asymptotic behaviour, limit cycle oscillations, random parameters.

Due to recent advances in the development of efficient uncertainty quantification methods, the propagation of physical randomness in practical applications has become feasible for smooth and steady computational problems. The current challenges in modeling physical variability include problems with unsteadiness and discontinuous solutions. Modeling physical variability in these problems is vital for making reliable flow and fluid-structure interaction predictions, since it can lead to the onset of unstable behavior.

In this paper, two methodologies for unsteady problems with discontinuities are developed based on interpolation of a time-independent parametrization of the samples and interpolation of the samples at constant phase. These two ideas result both in a constant accuracy in time with a constant number of samples, in contrast with the usually fast increasing number of samples for other methods.

The interpolation of the samples is performed using both a global and a piecewise polynomial approximation. For a robust interpolation in the unsteady adaptive stochastic finite element (UASFE) approach an alternative adaptive stochastic finite element (ASFE) formulation is developed based on Newton-Cotes quadrature in simplex elements.

Results for the asymptotic stochastic behavior of an elastically mounted cylinder in random uniform flow show the efficiency of the approach. The steady random transonic Mach number flow around a NACA0012 airfoil shows the robust interpolation of discontinuous response surfaces. The application of the unsteady adaptive stochastic finite element approach to an elastically mounted airfoil illustrates that the implementation of the non-intrusive approach is straightforward by reusing an existing deterministic solver.

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