Unsupervised and supervised machine learning pipeline for super-resolution-based subgrid scale modelling in coarse-grid large-eddy simulations

This study proposes a machine-learning-based subgrid scale (SGS) model for very coarse-grid large-eddy simulations (vLES). An issue with SGS modelling for vLES is that, because the energy-containing eddies are not accurately resolved by the computational grid, the resolved turbulence deviates from the physically accurate turbulence. This limits the use of supervised machine-learning models commonly trained using pairs of direct numerical simulation (DNS) and filtered DNS data. The proposed methodology utilises both unsupervised learning (cycle-consistency generative adversarial network (GAN)) and supervised learning (conditional GAN) to construct a machine-learning pipeline. The unsupervised learning part of the proposed method first transforms the non-physical vLES flow field to resemble a physically accurate flow field. The second supervised learning part employs super-resolution of turbulence to predict the SGS stresses. The proposed pipeline is trained using a fully developed turbulent channel at the friction Reynolds number of approximately 1000. The a priori validation shows that the proposed unsupervised–supervised pipeline successfully learns to predict the accurate SGS stresses, while a typical supervised-only model shows significant discrepancies. In the a posteriori test, the proposed unsupervised–supervised-pipeline SGS model for vLES using a progressively coarse grid yields good agreement of the mean velocity and Reynolds shear stress with the reference data at both the trained Reynolds number 1000 and the untrained higher Reynolds number 2000, showing robustness against varying Reynolds numbers. A budget analysis of the Reynolds stresses reveals that the proposed unsupervised–supervised-pipeline SGS model predicts a significant amount of SGS backscatter, which results in the strengthened near-wall Reynolds shear stress and the accurate prediction of mean velocity.