This paper describes a computational study undertaken as part of a grand challenge project to determine the aerodynamic effect of flow control in the afterbody regions at subsonic and supersonic speeds using an advanced scalable unstructured flow solver. High parallel efficiency is achieved for both steady and time-accurate unsteady flow field simulations using advanced scalable Navier-Stokes computational techniques on SGI Origin 3000, IBM SP3 and Linux Cluster. Numerical simulations with the unsteady synthetic jet show the jets to substantially alter the flow field both near the jet and the base region of the projectile that in turn affects the forces and moments even at zero degree angle of attack. The results have shown the potential of high performance computing computational fluid dynamics simulations on parallel machines to provide insight into the jet interaction flow fields leading to improved projectile designs and accurate prediction of flight trajectories.