Abstract: A pseudo-compressibility method developed by Rogers is used to solve the incompressible Navier-Stokes equation. Numerical flux is scattered through 3rd order Roe scheme and the 2nd order Harten-Yee TVD scheme separately. In order to accelerate convergence, several implicit methods(ADI-LU, LGS, LU-SGS) are accepted. Efficiency of different methods are shown as a classical flowfield around a cylinder in low Re(Re=200). Roe scheme is used to simulate two low speed unsteady problems:Low Re flowfield around a rotational cylinder(ω=1) and flowfield around a pitching NACA0015 airfoil with identical pitching rate.