Enabling a flow agnostic LES approach using deep learning

Despite the sustained growth in computing power, direct numerical simulations (DNS) of turbulence--where the entire range of scales are resolved--remain prohibitively expensive for natural and engineering flows. An attractive alternative is large eddy simulation (LES), where the large scales are resolved, while the entire spectrum of small scales is modeled, significantly boosting computational performance by nominally sacrificing on accuracy. Recent advancements in machine learning techniques have further bolstered LES closures. Nevertheless, considerable variability and deficiencies persists in LES models, particularly in applications such as scalar mixing, particle transport, and combustion, where small scales play a pivotal role. Here, we present a novel modeling approach for LES, where instead of modeling the entire range of small scales, a multilevel approach is adapted. Using tensor representation theory, a general function closure is obtained at each level in terms of filtered velocity gradients. A reduced order generalization is then obtained by employing autoencoders and training based on DNS data from a variety of turbulent flows. The approach outlined here results in a versatile, flow-agnostic LES closure that can be trained and applied to progressively more complex turbulent flows using deep neural networks.