The visual and physical features of the flow forming around spherically blunted cylinder during pellet (millimeter-sized solid body) injection towards the flow with supersonic speed are considered. The structure of this time dependent flow is very complicated and new ideas are used in the study. Numerical simulation of moving bodies is made by the free boundary method (version of immersed boundary method) on multilevel Cartesian grids with local adaptation based on the wavelet analysis. Dynamics of a moving body interaction with the bow shock, formation of the reverse flow region between bodies, its deformation and disappearance, and subsequent establishment of a stationary flow are studied. Reduction of main body drag to the level of 20% of the original is obtained. In this process, several specific stages can be found. When the front part of the pellet is in the subsonic flow behind the front bow shock wave it has little effect on the outside flow. Then pellet interacts with the bow shock wave and deforms it. Recirculation zone forms between bodies. It grows to a certain size, after which, because of the pellet wake intensity lessening due to the pellet's increasing distance from the main body, it begins to decrease and is eventually blown away from the front part of the main body. Stationary flow close to the initial one (i.e., before pellet injection) is established around the main body. Flow dynamics are illustrated by a series of images and animations which show the distribution of density and pressure, stream lines and mesh structure.