A comparative study of three different centered schemes (Beam-Warming, SIAF and LU-SGS) and an upwind scheme in computing the shock-wave/turbulent-boundary-layer interaction phenomena is made over a two-dimensional compression corner. The Baldwin-Lomax mixing length model is adopted to dosed the turbulent shear stress in the mass-averaged, two-dimensional compressible Navier-Stokes equations. Computations are performed for a Mach number of 2.90 with the Reynolds number Reδ (based on the incoming boundary layer thickness) of 1.6×106 for α=16 ramp. The upwind scheme is found to yield oscillation-free solutions around the shock while all of the centered schemes give oscillatory solutions. The present study leads us to believe that any centered difference scheme using scalar artificial dissipation should be suspect in predicting the shock-wave/turbulent-boundary-layer interaction problem.