A calculation scheme to predict incompressible turbulent flows in arbitrary shapes is presented. The procedure is based on the solution of the primitive-variable formulation of the time-dependent Reynolds-averaged Navier-Stokes equations in general curvilinear coordinates. An ordinary computational cell is used for continuity and transport balances, and all the physical properties are stored at the center of this element. The scheme uses an overlapping mesh along with forward and backward differencing for mass and pressure gradients, respectively. In a manner different from the staggered-grid approach, this procedure prevents the oscillatory behavior of the pressure field. The k-ϵ model is used to describe the turbulent flow process with particular attention to the boundary conditions. Computed results are compared with numerical and experimental data.