Evaluation of discontinuity treatment in intrusive polynomial chaos for uncertainty quantification of a nozzle flow in CFD

Stochastic flow simulation methods based on the polynomial chaos expansion (PCE) are developed and verified to quantify the propagation of a geometric uncertainty of a quasi-one dimensional flow in a supersonic wind tunnel. The effect of uncertainty in the area of diffuser throat, i.e. second throat, on the wind tunnel starting problem is focused on, where a slight change in the area can cause a large jump of the shock wave resulting in a breakdown of the supersonic test conditions. Two major numerical techniques in our intrusive PCE are the multi-wavelet (MW) basis and the multi-element (ME) PCE, in order to properly deal with discontinuous responses of output variables, which are caused by the shock wave and its jump at started/unstarted mode change. Single-element spectral PCE using Legendre basis and the Haar-wavelet are also included as special cases of the MW, and the methods are all compared with Monte-Carlo Simulations (MCS) executed by the deterministic code. Response surfaces of the pressure by the employed PCEs qualitatively agree with the result of MCS except the spectral PCE. Furthermore, from quantitative evaluations by the probability density function (PDF) of the output on a rather complicated response surface with several discontinuities, the ME-PCE best agrees with the MCS at much lower computation costs.