Physics Based & Machine Learning Methods For Uncertainty Estimation In Turbulence Modeling

Turbulent flows play an important role in many scientific and technological design problems. Both Sub-Grid Scale (SGS) models in Large Eddy Simulations (LES) and Reynolds Averaged Navier Stokes (RANS) based modeling will require turbulence models for computational research of turbulent flows in the future. Turbulence model-based simulations suffer from a multitude of causes of forecast uncertainty. For example, the simplifications and assumptions employed to make these turbulence models computationally tractable and economical lead to predictive uncertainty. For safety-critical engineering design applications, we need reliable estimates of this uncertainty. This article focuses on Uncertainty Quantification (UQ) for Computational Fluid Dynamics (CFD) simulations. We review recent advances in the estimate of many types of uncertainty components, including numerical, aleatoric, and epistemic. We go into further depth on the possible use of Machine Learning (ML) methods to quantify these uncertainties. Above all, we elaborate further on significant limitations in these techniques. These range from realizability constraints on the Eigenspace Perturbation Method (EPM) to the requirement for Monte Carlo (MC) approaches for mixed uncertainty. Based on this study, we pinpoint important problems that need to be addressed and offer focused solutions to move beyond these obstacles.