Simulations of laminar and turbulent flows over periodic hills with immersed boundary method

Laminar and turbulent flows over periodic hills are investigated with an immersed boundary method to mimic the curved geometry of the hill within the Cartesian framework. Here, turbulence is modeled through large eddy simulation with and without wall models. For laminar flows examined, flow over periodic hill separates earlier and reattaches later with the increase of Reynolds number. For turbulent flow simulations, Reynolds numbers from 2800 to 10595 are investigated. Predictions without wall models, i.e. assuming linear velocity profile at the wall, return better results both in mean and turbulence quantities, especially for the axial velocity at Reynolds number being 2800 and 5600. The good performance may lay in the fact that at these lower Reynolds numbers, the adopted grid resolves partly the near wall region. Predictions with wall models show a faster recovery of the recirculation zone and excessive diffusive transport across the shear layer. Among the wall models, turbulent boundary layer equation performs marginally better.