Numerical simulation of transonic viscous flows around RAE2822 2-D airfoil in Gao-Yong compressible turbulence model is presented. Convection terms and diffusion terms are calculated with ROE (flux difference splitting) scheme and CD (center difference) scheme, respectively. Runge-Kutta time marching method is employed to solve space discrete control equations. It predicts accurately pressure coefficients on airfoil surface, mean velocity, location of shock wave and Macb number contours. Shock-wave/boundary layer interaction and translation from laminar flow to turbulence flow on airfoil surface are analyzed. Numerical results agree well with experimental data. It is demonstrated that Gao-Yong compressible turbulence model can be used to simulate transonic viscous flow around an airfoil. A method for location of translation based on theory of orthotropic turbulence viscosity in Gao-Yong compressible turbulence model is presented.