This project applies new, efficient, algorithms to computer codes that will describe the complicated details of transonic flow in engine intakes and nozzles. The emphasis is on the ability of the codes to describe unsteady effects. Great accuracy is provided by a second-order integration technique based on the concept of characteristics (lambda-scheme) and coupled with tracking of discontinuities. The viscous calculations are performed by a combination of the inviscid code and a treatment of all viscous terms on a stretched grid. Inviscid calculations based on the same concepts are successfully performed in one-dimensional problems. In Phase I the feasibility is studied by performing sample calculations on one inlet geometry. A study and discussion of computational grids is provided.