Large eddy simulation of a separated turbulent boundary layer using the multi-timescale wall model

The multi-timescale (MTS) wall model for large eddy simulation (WMLES) has been shown to make accurate wall-stress predictions over a wide range of non-equilibrium conditions (Fowler et al. JFM 2022, 2023). So far, MTS applications have been limited to non-stationary flows with streamwise homogeneity such as steady channel flow with a suddenly applied spanwise pressure gradient, linearly accelerating channel flow, and pulsating channel flow. Here, the MTS wall model is tested for flows with streamwise heterogeneity such as a zero-pressure-gradient flat-plate developing boundary layer over a wide range of Reynolds numbers and a separated boundary layer induced by suction and blowing on the top surface of the domain. A hybrid pseudo-spectral finite difference LES code has been modified to handle developing boundary layers through the use of a modified rescaling-recycling inflow generation method and streamwise periodicity is achieved with the use a fringe region at the end of the domain. Wall-modeled LES results with the MTS model show good agreement with the DNS results of Coleman et al. JFM 2018 and detailed comparisons are made to the standard equilibrium wall model (which also performs well), with particular attention to pressure gradient effects in the separation region.