Data-driven wall modeling for turbulent separated flows

The large-eddy simulation of wall-bounded turbulent flows at high Reynolds numbers is made more efficient by the use of wall models that predict the wall shear stress, allowing coarser cell sizes at the wall. In this paper, a data-driven approach for the modeling of the wall shear stress is examined using filtered high-fidelity numerical data from two fully developed turbulent channel flows and two turbulent flows with separated regions: a three-dimensional diffuser and a backward-facing step. The model is a multilayer perceptron based on the flow information in the vicinity, given by the distance to the wall and the velocity components at a given number of grid points above the wall. The model is Mach number equivariant at the quasi-incompressible limit, Galilean invariant, statistically rotational invariant and can extrapolate to flow conditions unseen in the training dataset. The relevance of the machine-learning procedure is verified a priori using the filtered numerical data and a posteriori by performing wall-modeled large-eddy simulations implementing the model. The results show that the model is able to leverage the local spatial information to discriminate developed wall turbulence and separated regions in flow configurations not included in the training dataset.