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

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. In this paper two efficient non-intrusive approaches for unsteady problems are developed based on time-independent parametrization and interpolation at constant phase. The interpolation of the samples is performed using both a global polynomial interpolation and a robust Adaptive Stochastic Finite Elements formulation with Newton-Cotes quadrature in simplex elements. Applications to an elastically mounted cylinder, a transonic airfoil flow, and an elastically mounted airfoil illustrate the efficiency, robustness, and straightforward implementation of the methodologies.