Uncertainty Quantification of Transonic Nozzle Flow by Polynomial Chaos Expansion

Abstract

This study investigates the performance of an intrusive polynomial chaos expansion (PCE) method in the uncertainty quantification (UQ) of CFD. Quasi one-dimensional flow of a transonic nozzle with an uncertainty in the exit-pressure condition is discussed. Two major numerical techniques in our intrusive PCE are Roe-variable transformation and the multi-element (ME) PCE for clear implementations and improved accuracies of the UQ code for the case with a discontinuity (shock wave). The Roe's flux difference splitting scheme for the augmented equations has a clear advantage in resolutions against a simpler scheme while the discontinuity in the stochastic space is not properly treated by the polynomial approximation. The ME-PCE has been shown quite effective to simulate a complex stochastic response. The results are compared with Monte Carlo simulations and the reliability of the developed method is verified.