Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics

Abstract

This paper describes a point-collocation nonintrusive polynomial chaos technique used for uncertainty propagation in computational fluid dynamics simulations. The application of point-collocation nonintrusive polynomial chaos to stochastic computational fluid dynamics is demonstrated with two examples: 1) a stochastic expansion-wave problem with an uncertain deflection angle (geometric uncertainty) and 2) a stochastic transonic-wing case with uncertain freestream Mach number and angle of attack. For each problem, input uncertainties are propagated with both the nonintrusive polynomial chaos method and Monte Carlo techniques to obtain the statistics of various output quantities. Confidence intervals for Monte Carlo statistics are calculated using the bootstrap method. For the expansion-wave problem, a fourth-degree polynomial chaos expansion, which requires five deterministic computational fluid dynamics evaluations, has been sufficient to predict the statistics within the confidence interval of 10,000 crude Monte Carlo simulations. In the transonic-wing case, for various output quantities of interest, it has been shown that a fifth-degree point-collocation nonintrusive polynomial chaos expansion obtained with Hammersley sampling was capable of estimating the statistics at an accuracy level of 1000 Latin hypercube Monte Carlo simulations with a significantly lower computational cost. Overall, the examples demonstrate that the point-collocation nonintrusive polynomial chaos has a promising potential as an effective and computationally efficient uncertainty propagation technique for stochastic computational fluid dynamics simulations.