Empirical Assessment of Non-Intrusive Polynomial Chaos Expansions for High-Dimensional Stochastic CFD Problems

Abstract

Uncertainties in the atmosphere and flight conditions can drastically impact the performance of an aircraft and result in certification delays. However, uncertainty propagation in high-fidelity simulations, which have become integral to the design process, can pose intractably high computational costs. This study presents a non-intrusive, parametric reduced order modeling (ROM) method to enable the prediction of uncertain fields with thousands of random variables and nonlinear features under limited sampling budgets. The methodology combines linear dimensionality reduction with sparse polynomial chaos expansions and is assessed in a variety of CFD-based test cases, including 3D supersonic flow over a passenger aircraft with uncertain flight conditions. Each problem has strong nonlinearities, such as shocks, to investigate the effectiveness of models in real-world aerodynamic simulations that may arise during conceptual or preliminary design. The performance is assessed by comparing the uncertain mean, variance, point predictions, and integrated quantities of interest obtained using the ROMs to Monte Carlo simulations. It is observed that if the flow is entirely supersonic or subsonic, then the method can predict the pressure field accurately and rapidly. Moreover, it is also seen that statistical moments can be efficiently obtained using closed-form analytical expressions and closely match Monte Carlo results.