Direct Numerical Simulation of Turbulent Separated Flow over the Periodic Hill Geometry at Re_h = 19000

We present results from direct numerical simulation (DNS) of incompressible flow over the periodic hill geometry that has, over the years, come to be regarded as a canonical case for turbulent separated flow. In our DNS, the computational domain consisted of 3.2x10⁶ hexahedral elements, with the elements clustered in the near wall region to ensure that the maximum distance of the first grid point from the wall was around 0.1 (in wall units). The incompressible Navier-Stokes equations were evolved using the high-order, spectral element codes, Nek5000, and nekRS, on the IBM Blue Gene/Q (Mira) and on the IBM Power9+NVIDIA (Summit) platforms, respectively. Time advancement was carried out via third-order BDF/extrapolation, with explicit treatment of the nonlinear term and independent system solves for the viscous and pressure updates. In our DNS we represent the flow variables with polymial basis functions of polynomial order p = 7 and p = 9, to demonstrate exponential convergence in p. The DNS mean velocity profiles, velocity correlations, and the locations of the separation/reattachment points,  compare well with data from the ERCOFTAC database. We also present comparisons of DNS and large eddy simulation (LES) at the same Reynolds numbers, to shed light on the sub-grid modeling.