Generalized Polynomial Chaos With Optimized Quadrature Applied to a Turbulent Boundary Layer Forced Plate

We explore the use of generalized polynomial chaos (GPC) expansion with stochastic collocation (SC) for modeling the uncertainty in the noise radiated by a plate subject to turbulent boundary layer (TBL) forcing. The SC form of polynomial chaos permits re-use of existing computational models, while drastically reducing the number of evaluations of the deterministic code compared to Monte Carlo (MC) sampling, for instance. Further efficiency is attained through the application of new, efficient, quadrature rules to compute the GPC expansion coefficients. We demonstrate that our approach accurately reconstructs the statistics of the radiated sound power by propagating the input uncertainty through the computational physics model. The use of optimized quadrature rules permits these results to be obtained using far fewer quadrature nodes than with traditional methods, such as tensor product quadrature and Smolyak sparse grid methods. As each quadrature node corresponds to an expensive deterministic model evaluation, the computational cost of the analysis is seen to be greatly reduced.