The averaged conservation laws are numerically solved for unsteady turbulent flows of compressible fluids using implicit iterative schemes. To investigate the effects of upstream vortices on the flow filed in the stator blade passages of an axial compressor, upstream vortices are modeled by a vortex shedding flow behind a circular cylinder, which moves in the transverse direction at the entrance of the stator blade row. The interface problem arising due to the relative motion of two different reference systems is handled by a novel technique, which allows the evaluation of the numerical flux at the interface also in the same way as at interior points. To validate the interface technique and to exhibit the temporal behaviour of vortices in the blade passages, some results are presented.