We developed a new numerical algorithm to solve the non-stationary com
pressible Euler equations in three dimensional geometries with a movin
g boundary. The numerical algorithm consists of a new cell-centered up
wind finite volume scheme of higher order on a grid of simplices and t
he possibility to refine and to coarse the grid locally according to t
he approximated solution. Furthermore a new criterion based on local r
esiduals to control the refinement and coarsening process is used. In
this paper we will concentrate on the new technique we used to model t
he boundary (piston) motion in a conservative way. More details of the
higher order scheme, the local adaption and the modelling of the pist
on motion can be found in the author's PhD thesis.