The current work is based on an extension of an approach developed by Rai and is discussed in detail in Rai (1987) and Rai, Madavan and Gavali (1993). 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 rotors and stators. The thin-layer Navier-Stokes equations are solved in the inner zones where viscous effects are important. The Euler equations are used in the outer zones where viscous effects are weak. 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 (1978) turbulence model is used to compute the turbulent eddy viscosity. Details of the turbulence model, zonal and natural boundary conditions, grid configuration, bookkeeping system, and database management systems are discussed in Gundy-Burlet et al. (1989).