Predicting unresolved scales interactions with 3D neural networks in homogeneous isotropic turbulence

¹ Aix-Marseille Université, CNRS, PIIM, UMR 7345 - Marseille, France
² Univ. Lille, CNRS, ONERA, Arts et Metiers ParisTech, Centrale Lille, FRE 2017- LMFL - Laboratoire de Mécanigue des Fluids de Lille-Kampé de Fériet - F-59000 Lille, France
³ ICAM Engineering School, Grand Paris Sud Campus - Lieusaint, France
⁴ CNRS, Insitut Jean le Rond d'Alembert, Sorbonne Université - Paris, France

^(a) E-mail: nathaniel.saura@univ-amu.fr (corresponding author)

Received: 3 February 2023
Accepted: 7 June 2023

Abstract

Interactions between the different scales of motion featured by any turbulent flow are currently mathematically and numerically intractable. Instead, numerical reduced models, such as Large Eddy Simulations (LES), have been proposed: large-scale motions are resolved using the large eddy equations whereas small-scale influence is modeled through the subgrid stress tensor and injected into the large-scale dynamics. In this paper, we develop the learning of this tensor from the raw 3D filtered velocity field diced into sub-cubes whose length is turbulence-induced. We used the U-net convolutional neural network architecture. The performance is assessed using component-wise correlations, PDF and contours comparisons. We extended our a priori analyses to monitor the impacts of such predictions on momentum and kinetic energy evolution. Our model is shown to perform well considering velocity fields extracted from 150% more turbulent simulations.