This paper presents computational solutions of the unsteady viscous flows generated by the variation in time of the inflow velocities. These solutions are obtained using a specially developed time-accurate numerical method for the solution of the time-dependent Navier-Sokes equations. This method is applied to obtain solutions for the unsteady viscous flows past downstream-facing steps which are generated by harmonic variations in time of the inflow velocities. Complex flow separation patterns were found for these unsteady flows.

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