Data-driven learning of Reynolds stress tensor using nonlocal models

The Reynolds-averaged Navier-Stokes (RANS) equations are well-known for their efficiency in simulating turbulent flows but require a  model for the nonlinear Reynolds stress tensor to close the system of equations. While closures are traditionally obtained via introduction of transport models involving local differential operators, recent work has suggested that nonlocal interactions are important to correctly treat turbulent statistics. To this end, a machine learning framework is pursued to discover nonlocal closures from data. This work presents a data-driven approach to learn a nonlocal model for the Reynolds stress tensor from high-fidelity direct numerical simulation datasets. In this approach, the Reynolds stress tensor is modeled as an integral operator acting over a finite range of lengthscales, and therefore is capable of capturing important aspects of the small-scale anisotropic behavior in turbulent flows. To obtain a nonlocal stress tensor that efficiently and accurately captures turbulent behavior, we propose an optimization-based operator regression approach where the residual of the RANS equations is minimized to calibrate the RANS closure to direct numerical simulation (DNS) data. Different nonlocal kernels are investigated and the resulting accuracy of optimal Reynolds stress closures are demonstrated for fully-developed internal flows.

This work was supported by the National Science Foundation under grant awards 1805692 and 1846852.