Multiscale Convolutional Neural Networks for Subgrid-scale Modeling in Large-Eddy Simulation

Abstract: This study proposes a multiscale convolutional neural network subgrid-scale (MSC-SGS) model for large-eddy simulation (LES). This model incorporates multiscale representations obtained via filtering to capture turbulent vortices interactions and physical processes at different scales. Subsequently, it progressively encodes information from the largest to the smallest scale, thereby mimicking an energy-cascade process. A turbulent channel flow with $\text{Re}_{\tau} = 180$ is adopted as the training and testing dataset, whereas the rate-of-strain tensor is used as the input variable to adhere the rotational invariance. $\textit{A priori}$ test results show that the MSC-SGS model predicts the physical quantities of residual stress, SGS dissipation, backscatter, and SGS transport more accurately than two other convolutional neural network (CNN)-based monoscale and U-Net, while maintaining high temporal correlation. Based on $\textit{a posteriori}$ test, the MSC-SGS model outperforms the two other CNN models and the conventional Smagorinsky model in predicting turbulence statistics while ensuring numerical stability without resorting to ad-hoc treatments such as clipping excessive backscatters. The LES results based on the MSC-SGS model closely align with DNS data in terms of turbulence statistics, energy spectra, and the quantitative reproduction of instantaneous-flow structures. These findings suggest that incorporating multiscale representations effectively advances the development of SGS models for LES.