SST(shear stress transport) and TNT (turbulent/non-turbulent) turbulence models were solved by implicit fully coupled with the transport and mean flow control equations. Techniques of local time step and implicit treatment of turbulence source term were used to accelerate and stabilize the calculation. Test cases of hypersonic compression corner flow

conical cylinder flare flow and supersonic asymmetric shock wave/boundary layer interaction were simulated by the AUSMPW+ (AUSM by pressure-based weight functions) scheme and LU-SGS (lower-upper symmetric Gauss-Seidel) implicit fully coupled method. The results show that:SST and TNT turbulence models used can predict the wall pressure and heat flux of the wall at the 15 degree compression corner flows well. Discrepancies between calculated and experimental results increase with the increase of compression corner. Compressibility correction has a great effect on the pressure and heat flux of compression corner flows and has little effect on supersonic asymmetric shock wave/boundary layer interaction. The implicit fully coupled method shows better convergence characteristic than explicit coupled method.