Kriging-model-based uncertainty quantification in computational fluid dynamics

Abstract

This paper proposes an efficient and accurate non-intrusive uncertainty quantification (UQ) method in computational fluid dynamics (CFD). Emphasis is placed on developing an UQ method that can accurately predict stochastic behaviors of output solution with small number of sampling simulations, and is also accurate for non-smooth output uncertainty responses. The proposed method is based on Kriging surrogate model, and the Kriging function values are used to evaluate output uncertainties robustly even with non-smooth responses, while using both the fit uncertainty and the gradient information of the Kriging predictors for dynamic adaptive sampling. The proposed Kriging-model-based UQ method shows a superior performance in estimating the non-smooth responses of output solution in terms of accuracy and robustness compared to the existing polynomial chaos expansion and the adaptive sampling method based on only the Kriging predictor fit uncertainty. The proposed method is first tested on analytical non-smooth functions under uniform uncertainties, and then applied to the transonic RAE 2822 airfoil flow under normal uncertainties in freestream Mach number by coupling the proposed UQ method with CFD.