Predictive LES wall modeling via physics-informed neural networks

While data-based approaches were found to be useful for sub-grid scale (SGS) modeling in Reynolds-averaged Navier-Stokes (RANS) simulations, there have not been many attempts of using machine learning (ML) techniques for wall modeling in large-eddy simulations (LES). LES wall modeling poses additional challenges to data-based modeling approaches. First, datasets of higher fidelity are not easily accessible. Second, wall modeling 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. We will also show the necessity of incorporating physics 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 will show that the inclusion of 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 Re_\tau=1,000, the trained networks are found to capture the law of the wall at arbitrary Reynolds numbers and outperform the conventional equilibrium model in a non-equilibrium flow.