Hybrid numerical method for wall-resolved large-eddy simulations of compressible wall-bounded turbulence

In the present study, we propose a hybrid numerical method for wall-resolved large-eddy simulation of compressible wall-bounded turbulence. Based on the hierarchical feature of energetic structures in wall-bounded turbulence, we propose to solve the convective term in the near-wall region with the low-dissipative kinetic energy preserving scheme to resolve the small-scale structures and the upwind scheme away from the wall to avoid strong numerical oscillations generated by the spurious errors. Two parameters are introduced in this method, one related to the transition point y p + and the other the transition range α . By a series of well-designed test cases, we identify that setting y p + as the streamwise grid interval Δ x + gives the best results, whereas the effects of the variation of α are marginal. By further performing simulations at higher Reynolds numbers and Mach numbers, we prove that the presently proposed method is capable of accurately predicting the skin friction, mean velocity and temperature and velocity fluctuation intensities and, in the meantime, retaining numerical stability.