An uncertainty-quantification framework for assessing accuracy, sensitivity, and robustness in computational fluid dynamics

Combining different existing uncertainty quantification (UQ) techniques, a framework is obtained to assess a set of metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in particular. The metrics include accuracy, sensitivity and robustness of the simulator's outputs with respect to uncertain inputs and parameters. These inputs and parameters are divided into two groups: based on the variation of the first group (e.g. numerical/computational parameters such as grid resolution), a computer experiment is designed, the data of which may become uncertain due to the parameters of the second group (e.g. finite time-averaging). To construct a surrogate model based on uncertain data, Gaussian process regression (GPR) with observation-dependent (heteroscedastic) noise is used. To estimate the propagated uncertainties in the simulator's outputs from the first group of parameters, a probabilistic version of the polynomial chaos expansion (PCE) is employed Global sensitivity analysis is performed using probabilistic Sobol indices. To illustrate its capabilities, the framework is applied to the scale-resolving simulations of turbulent channel and lid-driven cavity flows using the open-source CFD solver Nek5000. It is shown that at wall distances where the time-averaging uncertainty is high, the quantities of interest are also more sensitive to numerical/computational parameters. In particular for high-fidelity codes such as Nek5000, a thorough assessment of the results' accuracy and reliability is crucial. The detailed analyses and the resulting conclusions can enhance our insight into the influence of different factors on physics simulations, in particular the simulations of high-Reynolds-number turbulent flows including wall turbulence.