An accurate and robust Navier-Stokes procedure to predict the complex flow about an aerofoil has been developed. Much improvement over existing methods is achieved in various aspects of the solution procedure. The computational grid generated by conformal mapping, which is not only orthogonal but aligned with the inviscid streamlines, keeps the equations simple and minimizes the error due to false diffusion. Formal second-order accuracy is ensured by employing the QUICK scheme for the convective derivatives in the full Navier-Stokes and turbulence transport equations. To treat the separated region properly and to better resolve the flow field in the wake, the two-layer k-epsilon turbulence model is incorporated. The onset of transition is triggered in a unique fashion to warrant the smooth transition to turbulent flow. Sample calculations for various aerofoil sections show that the prediction is improved substantially over those by existing methods. The details of the flow extending to the wake, such as the surface pressure distribution, C-Lmax, the velocity fields and the Reynolds stress profiles, are found to be in excellent agreement with the data. (C) 1997 by John Wiley & Sons, Ltd.