Abstract: The Navier-Stokes equations are solved with the second-order LU-SGS-τTS implicit time-stepping method. The sixth-order symmetric TVD scheme with fifth-order WENO interpolation based on Roe is applied to the convection terms. A boundary layer flow around a flat plate, a low speed flow around the Aerospatial A-profile at high incidence and a transonic flow with shock/boundary interaction around RAE2822 airfoil are computed by Baldwin-Lomax and Spalart-Allmaras models with the transition criterion, respectively. The results show that the approaches capture the transition automatically.

Key words: LU-SGS-τTS time-stepping method, sixth-order symmetric TVD scheme, transition criterion