A method is presented in this paper for calculating transonic flow field in turbomachinery cascades. With respect to non-orthogoanl curvilinear coordinates, the stream function equation governing fluid flow was established. Using the Artificial Compressibility Method, the discretization of the partial differential equation was carried out by use of the standard central difference formula. The set of linear algebraic equations obtained is solved by means of the Direct Matrix Method. In order to overcome the non-uniqueness of density in transonic flow in the stream function method, the velocities at grid nodes are first obtained by integrating the momentum equation and then the densities are determined from the energy equation.
Application of this method to some transonic cascade-flow with supersonic or subsonic inlet velocity shows that the solution obtained is in fair agreement with experimental data.