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

摘要

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