UPWIND FINITE-VOLUME SCHEMES IN TIMEDEPENDENT GEOMETRIES

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.