:The present work described a method for performing detailed computations of Navier-Stokes equations in turbomachinery application. The time-marching strategy developed is a modified form of the basic Beam-Warming implicit algorithm using the concept of novel “pre-processed” approach to solve the equations of the 3-D Reynolds averaged N-S equations with a mixing length turbulence model in finite volume form and in the blade-relative frame using cylindrical coordinates and with appropriate source terms to permit the solution to be obtained in a rotating cylindrical coordinate system. Time steps are not severely limited when mesh points are finely distributed. Computational efficiency and compatibility to vectorized computer processors is maintained by use of approximate factorization techniques. An outline of the scheme is addressed and the present capabilities of the solver are assessed. Numerical results are reported for a high speed low-pressure modern gas turbine blade and show good agreement with other workers measurements. The overall accuracy of the predictions is most severely limited by turbulence model, particularly transition modelling.