Invariant Data-Driven Subgrid Stress Modeling in the Strain-Rate Eigenframe for Large Eddy Simulation

TL;DR

This paper introduces a novel data-driven subgrid stress model for large eddy simulation that leverages the strain rate eigenframe to ensure physical invariances, trained on DNS data, and validated across various flow conditions.

Contribution

The paper proposes a new invariant tensor representation in the strain-rate eigenframe for subgrid modeling, enabling efficient neural network training and improved generalization in LES.

Findings

Model achieves high accuracy in a priori tests.

Model generalizes well to unseen filter widths and Reynolds numbers.

Neural network trained on minimal data performs robustly in simulations.

Abstract

We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows. The key to our approach is representation of model input and output tensors in the filtered strain rate eigenframe. Provided inputs and outputs are selected and non-dimensionalized in a suitable manner, this yields a model form that is symmetric, Galilean invariant, rotationally invariant, reflectionally invariant, and unit invariant. We use this model form to train a simple and efficient neural network model using only one time step of filtered direct numerical simulation data from a forced homogeneous isotropic turbulence simulation. We demonstrate the accuracy of this model as well as the model's ability to generalize to previously unseen filter widths, Reynolds numbers, and flow physics using a priori and a posteriori tests.