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Volume 6, Issue 2
A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter

Jeroen A. S. Witteveen & Hester Bijl

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

Published online: 2009-06

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  • Abstract

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.

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@Article{CiCP-6-406, author = {Jeroen A. S. Witteveen and Hester Bijl}, title = {A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {2}, pages = {406--432}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7687.html} }
TY - JOUR T1 - A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter AU - Jeroen A. S. Witteveen & Hester Bijl JO - Communications in Computational Physics VL - 2 SP - 406 EP - 432 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7687.html KW - AB -

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.

Jeroen A. S. Witteveen and Hester Bijl. (2009). A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter. Communications in Computational Physics. 6 (2). 406-432. doi:
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