Mathematics

Turbulence is of paramount interest for both fundamental research and practical applications. On one hand, it is a complex, multiscale phenomenon that remains far from fully understood; on the other hand, turbulent flows play a crucial role in many areas of engineering. Directly discretizing the Navier-Stokes equations is typically computationally prohibitive due to the resolution required to capture the smallest scales. A common strategy to address this challenge is to solve the Reynolds-averaged Navier–Stokes (RANS) equations instead, which aim to predict the averaged flow fields only. These equations are formally obtained by applying a Reynolds operator to the Navier-Stokes equations and contain an additional term involving the so-called Reynolds Stress Tensor. The latter is an unknown term for the RANS equations. Over the past decades, a huge variety of turbulence models based have been proposed in literature to predict it. In this talk, I will present my main research line during my PhD, which focuses on closing RANS equations through Machine Learning techniques. In particular, I will discuss the Vector Basis Neural Network (VBNN) paradigm that, by construction, preserves important physical properties of the RANS system.Finally, I will comment on how this framework is particularly suited for parametric settings and how can be naturally coupled to classic Reduced Order Modeling techniques to provide high-fidelity snapshots in a computationally efficient manner.