Abstract
The finite-element method is applied to the stream function formulation of transonic flows. Numerical dissipation, necessary for the calculation of mixed flows with shocks, is introduced via the artificial compressibility method. The classical problem of double-valuedness of the mass flux versus Mach number is resolved by direct integration of the vorticity equation. Solutions are obtained for isolated airfoils, the blade-to-blade cascade equation, as well as the radial equilibrium equation governing the hub-to-shroud through flow in turbomachinery.
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