Deep learning of the spanwise-averaged Navier-Stokes equations

TL;DR

This paper introduces the spanwise-averaged Navier-Stokes (SANS) equations combined with a deep learning closure model, enabling efficient 3D turbulence simulation with high accuracy and significantly reduced computational cost.

Contribution

The paper presents a novel flow decomposition (SANS) and a deep learning closure model, improving turbulence simulation efficiency and accuracy over traditional 2D methods.

Findings

Achieved up to 92% correlation in closure term predictions.

SANS with ML closure predicts wake metrics with 1-10% error.

Reduces 3D simulation costs by 99.5% compared to full 3D models.

Abstract

Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier-Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.