Physics-informed machine-learning solution to log-layer mismatch in wall-modeled large-eddy simulation

This study proposes a physics-informed machine learning to enable using the erroneous flow data at near-wall grid points as the input to the wall model in a wall-modeled large-eddy simulation (LES). The proposed neural network predicts the amount of numerical error in the near-wall grid-point data and inputs the physically correct flow variables into the wall model by correcting the near-wall error. The input and output features of the neural networks are selected based on the physical relations of the turbulent boundary layer for robustness against various Reynolds and Mach number conditions. The proposed neural networks allow the wall model to accurately predict the wall shear stress from the erroneous near-wall information and yields accurate predictions of the turbulence statistics. Additionally, the proposed physics-informed machine-learning approach reproduces the asymmetry in the probability density functions of the predicted wall shear stress observed in direct numerical simulations, while the conventional wall model with input away from the wall does not. The results suggest that using the near-wall information for wall modeling may increase the fidelity of the wall-modeled LES.