Numerical solutions are obtained for two-dimensional incompressible turbulent viscous flow over airfoils of arbitrary geometry. A body-fitted coordinate system is numerically transformed to a rectangular grid in the computational plane. The unsteady Reynolds-averaged Navier-Stokes equations in the primitive variables of velocity and pressure are used. Turbulence is modeled with an algebraic eddy viscosity technique modified for separated adverse pressure gradient flows. The set of transformed partial differential equations is solved with an implicit finite-difference method. Numerical solutions for a NACA 0012 airfoil near stall at a chord Reynolds number of 170,000 are favorably compared with surface pressure and velocity field measurements. A small laminar separation bubble near the leading edge is observed. Computed lift and drag coefficients agree well with experimental values.