The flow around a 2-D (two dimensional) airfoil is simulated at a low speed. In this study two schemes are considered: the matrix-free LU-SGS (Lower-Upper Symmetric Gauss Siedel) implicit scheme and the explicit/implicit hybrid scheme to obtain steady or quasi-steady state solutions. Regarding turbulence model, either the Baldwin-Lomax model or no turbulence model is applied to the compressible Navier-Stokes equations. Results of these calculations are well compared with experimental data.