Neural network-based closure models for large-eddy simulations with explicit filtering

TL;DR

This paper introduces a neural network-based closure model for large-eddy simulations that uses explicit filtering to improve the correlation between a priori accuracy and a posteriori performance, leading to more reliable turbulence modeling.

Contribution

The paper proposes an explicit filtering approach in neural network-based LES models to address dataset shift issues and improve predictive reliability.

Findings

Explicit filtering controls aliasing errors effectively.

The model achieves accurate and stable simulations at Re_τ=180.

A priori accuracy correlates well with a posteriori performance in the proposed method.

Abstract

Data from direct numerical simulations of turbulent flows are commonly used to train neural network-based models as subgrid closures for large-eddy simulations; however, models with low a priori accuracy have been observed to fortuitously provide better a posteriori results than models with high a priori accuracy. This anomaly can be traced to a dataset shift in the learning problem, arising from inconsistent filtering in the training and testing stages. We propose a resolution to this issue that uses explicit filtering of the nonlinear advection term in the large-eddy simulation momentum equations to control aliasing errors. Within the context of explicitly-filtered large-eddy simulations, we develop neural network-based models for which a priori accuracy is a good predictor of a posteriori performance. We evaluate the proposed method in a large-eddy simulation of a turbulent flow in a plane channel at $Re_{\tau} = 180$. Our findings show that an explicitly-filtered large-eddy simulation with a filter-to-grid ratio of 2 sufficiently controls the numerical errors so as to allow for accurate and stable simulations.