The current algorithm is based on an extension of the approach developed by Rai and is discussed in detail in Rai. The approach is reviewed in brief here. The flow field is divided into two basic types of zones. Inner "O" grids are used to resolve the flowfield near the airfoils. These "O" grids are overlaid on outer " H" grids which are used to resolve the flowfield in the passages between airfoils. The "H" grids are allowed to slip relative to one another to simulate the relative motion between rotor and stator airfoils. The thin-layer Navier-Stokes equations are solved throughout the flow domain. The governing equations are cast in the strong conservation form. A fully implicit, finite-difference method is used to advance the solution of the governing equations in time. A Newton-Raphson subiteration scheme is used to reduce the linearization and factorization errors at each time step. The convective terms are evaluated using a third-order-accurate upwind-biased Roe scheme. The viscous terms are evaluated using second-order accurate central differences. The Baldwin-Lomax turbulence model is used to compute the turbulent eddy viscosity. As suggested by Dorney and Davis, edge length-scales are computed based on the Vatsa and Wedan blending function.