The current work is an extension of an algorithm developed by Rai and is discussed in detail in Rai and Chakra-varthy (1986). The algorithm is discussed in brief here. The flow field is divided into two basic types of zones. The thin-layer Navier-Stokes equations are solved in inner zones near the airfoil where viscous effects are important. The Euler equations are used in outer zones where viscous effects are weak. These equations are cast in the strong conservative form. A fully implicit finite difference method is used to advance the solution of the nonlinear equations in time. At each time step, four Newton-Raphson iterations are used to reduce the factorization and linearization errors by an order of magnitude. The convective terms are evaluated using a third-order-accurate upwind-biased Osher scheme, and the viscous terms are evaluated using second-order 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).