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

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 themethod is total variation diminishing (TVD) for one randomparameter 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 twomethods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem.