On the interactions between a solid body and a compressible inviscid fluid

This paper presents a model describing the interaction between a solid body and a compressible inviscid fluid in a pipe. The resulting system consists in a 1D hyperbolic balance law coupled with an ordinary differential equation and is proved to be well posed. Simple explicit solutions and numerical integrations show qualitative features of this model. In particular, we consider a ball falling in a vertical tube closed at the bottom. This system results in the ball bouncing on the shocks reflected between the ball and the bottom.