The compressible hybrid RANS/LES formulation using an additive operator

In this work, the compressible governing equations for the hybrid Reynolds-averaged/large-eddy simulations are formally derived by applying a hybrid filter to the Navier-Stokes equations. This filter is constructed by linearly combining the Reynolds-average (RANS) and large-eddy simulation (LES) operators with a continuous blending function. The derived hybrid equations include additional terms that represent the interactions between RANS and LES formulations. The relevance of these terms is investigated in flat-plate turbulent boundary layer simulations and indicate that these additional terms play a fundamental role in compensating for the turbulence that is neither modeled nor resolved in the transition region between RANS and LES. Results also show that when the additional terms are included, the calculations are not very sensitive to the blending function implemented in the hybrid filter. In the contrary, when these terms are neglected and a step function is implemented in the hybrid filter, nonphysical discontinuities are predicted in the flow statistics.