The numerical modeling of the supersonic flow over the annular step body formed by two coaxial cylinders is performed within the ideal gas model framework through Godunov's method. The numerical simulation has shown that for the cylinder-cylinder configuration without cavity there exist two characteristic flow regimes, which follow one after the other periodically. The flow over the cup-cylinder configuration (without jet injection) has unsteady character also. Numerical calculations indicate that bow shock oscillations remain the same or decrease in amplitude to a cavity with annular injection depending on the injection intensity. The domain of the steady flow existence is established.
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