Application of symmetry lters on a DNS database to build euclidean invariant data-driven turbulence models :a comparison between neural network and random forest machine learning techniques

Abstract

In industrial applications, great part of the ows occurs in the turbulent regime. Highly accurate numerical solutions, such as Direct Numerical Simulation (DNS), have prohibitive computational costs so most numerical problems are solved using Reynolds Average Navier-Stokes (RANS) models, which feature low computational cost and not often satisfactory accuracy. The use of Machine Learning (ML) techniques for turbulence models has already been used in the literature, setting DNS data as a target in ML models, based on data from the mean velocity eld, or the Reynolds stress tensor, R. In recent studies, however, it was observed that the DNS data for R does not show satisfactory convergence, when compared to data for the mean velocity and pressure elds. In order to get around this problem, a methodology was developed to correct the modi ed divergent of R, using only data related to the mean velocity eld, called t, which presented promising results when compared to R corrections. In this work, the use of a database with Euclidean invariance and the in uence of the quality of the DNS database, used in Neural Networks (NN) and Random Forests (RF), to predict the turbulent properties R and t, are investigated in a turbulent ow in a square duct. A treatment of the DNS database is carried out in order to emulate longer DNS averaging simulation times and, consequently, better convergence of related elds. The results obtained by all models built, show that there is a direct relation between the convergence of DNS data, the symmetry present in this ow pattern and the performance of data-driven turbulence models.