High Reynolds number viscous flows around airfoils are computed by solving the Reynolds-averaged Navier-Stokes equations using a block-structured Cartesian mesh approach named Building-Cube Method. Airfoil surface boundaries are represented by very fine staircase and the Spalart-Allmaras turbulence model is employed. The main objective is to investigate whether fine isotropic mesh and staircase representation of surface can accurately predict aerodynamic coefficients of airfoils or not. The computed results show unsteady flow features even with turbulence model. Very fine and isotropic mesh resolves the small scale vortices that may cause unsteadiness. The time-averaged pressure distributions show good agreement with the experiments.