This paper describes a generalized wall function for threedimensional turbulent boundary layer flows. Since the formulation is valid for various pressure gradients including those associated with zero skin friction, it can be applied to wall bounded complex flows with acceleration, deceleration and recirculation. This generalized wall function is extended to the whole surface layer (or inner layer), covering the viscous sublayer, buffer layer and inertial sublayer; therefore, it is a unified

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... l function. This 'unified' feature is particularly useful for computational fluid dynamics (CFD) to deal with flows with complex geometries, because it allows a flexible grid resolution near the wall to provide accurate wall boundary conditions. This paper also describes a systematic procedure for implementing the wall function in a general CFD code. Finally, a few examples of complex turbulent flows are presented to show the performance of the generalized wall function.