Compact differencing and filtering schemes for large-eddy simulation of compressible transitional boundary layer

Compressible large-eddy simulation is applied to a transitional compressible boundary layer using a compact differencing scheme with spatial filtering. Simulated properties of the transitional boundary layer show reasonable agreement with experiment. The nature of the unsteady flowfield reasonably demonstrates that the interactions between the relatively large-scale coherent structures, such as low-speed streaks, pairs of longitudinal vortices, and hairpin vortices, observed in the transitional region play an important role in determining the behavior of transition. Therefore, these key coherent structures need to be directly resolved with adequate grid resolution and appropriate numerical scheme to properly simulate the physics of transition. Once the hairpin vortices appear, transition is promoted and the coherent structures break down to finer scales. Computational results show that the under-resolution of the finer scale structures has little influence on the overall results if the key coherent structures are adequately resolved. The filtering parameter sensitively delays transition when the key coherent structures are influenced by the filtering even a little. Once the flow develops into a fully turbulent state, spatial filtering has little influence on the flowfield. The present results reasonably illustrate the guidelines regarding how to properly simulate compressible transitional boundary layers using compact spatial differencing and filtering schemes.