Accurate Deep Learning sub-grid scale models for large eddy simulations

In this work, sub-grid scale (SGS) turbulence models have been developed for the purpose of large-eddy simulations (LES).

To this end, robust and efficient Deep Learning (DL) algorithms have been used because of their superior capability in establishing high-order complex non-linear relations between the input features and output variables, which may be out of the scope of the state-of-the-art conventional modeling strategies.

Accuracy of the input and output features is important to formulate accurate DL models, and therefore, data from direct simulations of the canonical channel flow at friction Reynolds numbers Re_τ≈ 395 and 590 are used for training and testing.

The DNS data is filtered in all three spatial directions.

Two training strategies are adopted.

In one of these, the scalar coefficients corresponding to the five symmetric integrity basis tensors (Lund & Novikov, 1992) are the target variables.

The DL models approximate these coefficients based on the six scalar invariants as the input features computed from the filtered strain rate and rotation rate tensors, and terms computed from their higher powers.

In another strategy, all of the aforementioned variables (six scalar invariants, and the six independent components of each of the five integrity basis tensors; 36 in total) are fed to the Neural Networks (NNs) to directly predict the six target SGS stress components.

While the former strategy results in excellent agreements between the statistical distributions of the truth and the predictions for all six stress components, the latter strategy results in a significantly reduced mean-squared-error (m.s.e. obtained is at least half of that obtained with the first strategy) upon the convergence of the models in apriori testing.

The latter strategy also yields significantly higher correlation coefficients with the true SGS stresses.

The models are being implemented in LES codes for a-posteriori testing.