Probabilistic Collocation: An Efficient Non-Intrusive Approach for Arbitrarily Distributed Parametric Uncertainties

TLDR: The ProbabilisticCollocation method is introduced, which combines the non-intrusiveness of the Stochastic Collocation method with the exponential convergence for arbitrary probability distributions of the Galerkin Polynomial Chaos method.

Abstract: Complex o w and uid-structure interaction simulations require ecien t uncertainty quantication methods. In addition, a good property of an uncertainty quantication method is non-intrusiveness, meaning that existing deterministic solvers can be used for uncertainty quantication. In this paper the Probabilistic Collocation method is introduced, which combines the non-intrusiveness of the Stochastic Collocation method with the exponential convergence for arbitrary probability distributions of the Galerkin Polynomial Chaos method. Due to the non-intrusiveness and exponential convergence, the Probabilistic Collocation method requires only a few collocation points for a high accuracy. For the one dimensional piston problem the eciency of the Probabilistic Collocation method is compared with the Galerkin Polynomial Chaos method, the Non-Intrusive Polynomial Chaos method and the Stochastic Collocation method. The strength of the Probabilistic Collocation method is demonstrated by solving steady o w around a NACA0012 airfoil with an uncertain free stream velocity using a commercial o w solver. Dieren t possibilities of representing the stochastic solution are demonstrated to show the potential use of uncertainty quantication.