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 sho...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.展开更多
基金This research was supported by the Technology Foundation STW,applied science division of NWO and the technology programme of the Ministry of Economic Affairs.
文摘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.
