Large-eddy simulation enhanced by machine learning: space-time correlations, wall models, and shape optimization

This article reviews our research progress on developing machine-learning-enhanced large-eddy simulation (LES) methods, with a focus on neural-network-based (NN-based) subgrid-scale (SGS) modeling, wall modeling, and LES-enabled shape optimization. We first identify the limitations of the eddy viscosity (EV) SGS models, which over-predict the space-time correlations due to the absence of random forcing (RF). Therefore, an NN-based SGS model is proposed to represent the coupled effects of the EV model and RF for the correct prediction of space-time correlations in turbulent channel flows. Furthermore, we introduce the knowledge-integrated additive (KIA) learning wall model, a physics-based modeling architecture built upon the simplified boundary-layer equations with NN-based forcing terms. The KIA model is designed to respect the law of the wall and enable continual learning without catastrophic forgetting. Finally, a self-adaptive ensemble Kalman method is proposed for LES-based shape optimization with the aim of aeroacoustic shape optimization. The ensemble-based sensitivity analysis is shown to effectively provide accurate sensitivity for chaotic Lorenz systems and demonstrates its utility in optimizing the trailing-edge shape of an airfoil. The synergy of these NN-based SGS and wall models is expected to enable time-accurate LES and LES-based shape optimization for complex turbulent flows.