This work is motivated by the numerical simulation of the generation and break-up of droplets after the impact of a rigid body on a tank filled with a compressible fluid. This paper splits into two very different parts. The first part deals with the modeling and the numerical resolution of a spray of liquid droplets in a compressible medium like air. Phenomena taken into account are the breakup effects due to the velocity and pressure waves in the compressible ambient fluid. The second part is concerned with the transport of a rigid body in a compressible liquid, involving reciprocal effects between the two components. A new one-dimensional algorithm working on a fixed Eulerian mesh is proposed.