Informing Turbulence Closures With Computational and Experimental Data

Abstract

Data from high fidelity computational simulations and experimental measurements is used to quantify errors in the functional form of turbulence closure models. A Bayesian formalism is adopted to infer a full-field of discrepancy that provides otherwise inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) is used, the accuracy of the inferred solution is improved over the entire computational domain. By directly addressing the connection between physical data and model discrepancies, the field inversion approach enhances the value of computational and experimental data for model improvement. Based on the results, it could be argued that some of the criticism of eddy viscosity models that is usually attributed to the isotropic stress-strain relationship is partially a result of poor functional forms within the model rather than the limiting nature of the Boussinesq assumption itself. Models should rather be assessed by evaluating the type and variability of corrections that will be required in a diverse set of problems. The information from the inversion procedure can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.

Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence

“…The field inversion (FI) approach has been pursued in the context of augmentation of eddy viscosity [10], transport equation terms [61][62][63], Reynolds stresses [64,65], and in the mean flow momentum equation [66]. Given a dataset Y i , the FI approach yields δ i m , which is a spatiotemporal field, and is thus problem-specific.…”