Predictive large-eddy-simulation wall modeling via physics-informed neural networks

While data-based approaches were found to be useful for subgrid scale (SGS) modeling in Reynolds-averaged Navier-Stokes (RANS) simulations, there have not been many attempts at using machine learning techniques for wall modeling in large-eddy simulations (LESs). Large-eddy simulation differs from RANS simulation in many aspects. For one thing, LES is scale resolving. For another, LES is in and of itself a high-fidelity tool. Because data sets of higher fidelity are in general not frequently accessible or available, this poses additional challenges to data-based modeling in LES. Further, SGS modeling usually needs flow information at only large scales, in contrast with wall modeling, which needs to account for both near-wall small scales and large scales above the wall. In this work we discuss how the above-noted challenges may be addressed when taking a data-based approach for wall modeling. We also show the necessity of incorporating physical insights in model inputs, i.e., using inputs that are inspired by the vertically integrated thin-boundary-layer equations and the eddy population density scalings. We show that the inclusion of the above physics-based considerations would enhance extrapolation capabilities of a neural network to flow conditions that are not within the train data. Being cheap to evaluate and using only channel flow data at Reτ=1000, the trained networks are found to capture the law of the wall at arbitrary Reynolds numbers and outperform the conventional equilibrium model in a nonequilibrium flow.