This paper describes the development and application of a parabolic finite-volume procedure for the computation of viscous rotating flows having complex geometries. A parabolic numerical scheme has been developed to include the influence of the Coriolis force on pressure corrections. Two-equation turbulence models were employed to account for the effect of turbulence on the flows. Numerical tests for 2-D flows have been conducted, and the results show that computation with the new pressure-based method gives reasonably good agreement with the experiments.