A universal wall-function method for RANS turbulence modelling is presented, which is designed by consistency between the global turbulence model and the near-wall model. This ensures solutions independent of the wall-distance of the first grid node above the wall provided it is located in the logarithmic part of the boundary layer or below. The near-wall RANS solutions of the Spalart-Allmaras and SST k-omega turbulence model are investigated in regions of strong adverse pressure gradient leading to separation, and suggestions for the design of wall-function methods for non-equilibrium flows are given. New universal wall-functions in closed-form are proposed, which give almost grid-independent predictions for equilibrium boundary layers for all variants of the Spalart-Allmaras and the k-omega model resp. The method is then applied successfully to aerodynamic flows with separation including a transonic flow with shock induced separation and a subsonic highlift airfoil close to stall.