An Uncertainty-Quantification Framework for Assessing Accuracy, Sensitivity, and Robustness in Computational Fluid Dynamics

Abstract

A framework is developed based on different uncertainty quantification (UQ) techniques in order to assess validation and verification (V&V) 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 computational parameters. These parameters are divided into two groups: based on the variation of the first group, a computer experiment is designed, the data of which may become uncertain due to the parameters of the second group. To construct a surrogate model based on uncertain data, Gaussian process regression (GPR) with observation-dependent (heteroscedastic) noise structure is used. To estimate the propagated uncertainties in the simulator's outputs from first and also the combination of first and second groups of parameters, standard and probabilistic polynomial chaos expansions (PCE) are employed, respectively. Global sensitivity analysis based on Sobol decomposition is performed in connection with the computer experiment to rank the parameters based on their influence on the simulator's output. To illustrate its capabilities, the framework is applied to the scale-resolving simulations of turbulent channel flow using the open-source CFD solver Nek5000. Due to the high-order nature of Nek5000 a thorough assessment of the results' accuracy and reliability is crucial, as the code is aimed at high-fidelity simulations. 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 wall-bounded turbulence.

Applying Bayesian Optimization with Gaussian Process Regression to Computational Fluid Dynamics Problems

“…In this derivation, the noise samples are assumed to be independent and identically distributed (iid) as ε ∼ N (0, σ 2 ). A more general case in which the noise is allowed to be observation-dependent has been developed by Goldberg et al [23], and recently applied for the purpose of uncertainty quantification in CFD by Rezaeiravesh et al [50].…”

“…Refs. [4,43,72,49,50]. In fact, most of those studies are classified as UQ forward problems, the outcomes of which can be nicely employed in BO, which is, in fact, an inverse UQ problem.…”