A TVD Uncertainty Quantification Method with Bounded Error Applied to Transonic Airfoil Flutter (Communications in Computational Physics, 2018)
The Unsteady Adaptive Stochastic Finite Elements (UASFE) approach is arobust and efficient uncertainty quantification method for resolving the effect of randomparameters in unsteady simulations. In this paper, it is shown that the underlyingAdaptive Stochastic Finite Elements (ASFE) method for steady problems based onNewton-Cotes quadrature in simplex elements is extrema diminishing (ED). It is alsoshown that the method is total variation diminishing (TVD) for one random parameterand for multiple random parameters for first degree Newton-Cotes quadrature. It isproven that the interpolation of oscillatory samples at constant phase in the UASFEmethod for unsteady problems results in a bounded error as function of the phase forperiodic responses and under certain conditions also in a bounded error in time. Thetwo methods are applied to a steady transonic airfoil flow and a transonic airfoil flutterproblem.