Interfaces and Free Boundaries


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Volume 15, Issue 3, 2013, pp. 381–403
DOI: 10.4171/IFB/307

Published online: 2013-12-12

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

Raul Borsche[1], Rinaldo M. Colombo[2] and Mauro Garavello[3]

(1) Technische Universität Kaiserslautern, Germany
(2) Università degli Studi di Brescia, Italy
(3) Università di Milano-Bicocca, Italy

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.

Keywords: Mixed PDE–ODE problems, balance laws, ordinary differential equations

Borsche Raul, Colombo Rinaldo, Garavello Mauro: On the interactions between a solid body and a compressible inviscid fluid. Interfaces Free Bound. 15 (2013), 381-403. doi: 10.4171/IFB/307