Paola Cinnella (Laboratoire de Dynamique des Fluides, Arts et Métiers Paristech). Uncertainty quantification and data-driven discovery of turbulence models.

Computational Fluid Dynamics (CFD) models have become a fundamental tool for preliminary and advanced aerodynamic design and optimization. So-called high-fidelity CFD models like DNS (Direct Numerical Simulation) or LES (Large Eddy Simulation) remain very costly for complex high-Reynolds flows, and lower fidelity methods, relying on the Reynolds-Averaged Navier-Stokes (RANS) equations supplemented by a turbulence model, represent the workhorse for engineering flow simulations. Unfortunately, RANS models are characterized by numerous flaws, intrinsic to the simplified description of turbulence they rely on. Additionally, despite much theoretical effort for developing turbulence models on a physically sound basis, these still rely on a significant amount of empiricism and expert judgement both for defining the model mathematical structure and for calibrating the associated closure coefficients.

In recent years, an exponentially growing mess of literature has attempted to develop data-driven RANS models. Specifically, the use of machine learning techniques for generating turbulence models seem attractive, but are also risky due the the scarcity of data and the very large dimensionality of fluid flow problems. In both cases, obtaining reliable estimates of uncertainty bounds of the model outcomes appears even more compelling than the accuracy of the prediction itself.

In this talk we present recent advances on the quantification and reduction of model uncertainties by using Bayesian statistical inference techniques and about the data-driven discovery of improved turbulence models with quantified uncertainties, as well as applications to some flow configurations of interest in internal and external aerodynamics. Such approaches are quite general and can be used for quantifying and reducing model uncertainties in other fields of Science and Engineering.