  In this paper we introduce a numerical scheme for fluid-structure interaction
problems in two or three space dimensions: A flexible elastic plate is
interacting with a viscous, compressible barotropic fluid. Hence the physical
domain of definition (the domain of Eulerian coordinates) is changing in time.
We introduce a fully discrete scheme that is stable, satisfies geometric
conservation, mass conservation and the positivity of the density. We also
prove that the scheme is consistent with the definition of continuous weak
solutions.
