This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier–Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier–Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space–time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

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