Solving The Compressible Euler Equations In Timedependent Geometries

. In this paper we shall present a numerical algorithm to solve the compressible Euler equations in three dimensional geometries with a moving boundary. The numerical algorithm consists of a new cell--centered upwind finite volume scheme of higher order on a grid of simplices and the possibility to refine and coarse the grid locally appropriate to the approximated solution. We will describe a new criterion to control the refinement and coarsening process. Furthermore we will describe briefly the idea to model the moving boundary without lack of conservation in the flux quantities. 1. Flow Problem We want to solve the compressible Euler equations in geometries with inlets and outlets (cylinder model of a two--stroke--engine). This work is supported by the Deutsche Forschungsgemeinschaft 2 MONIKA WIERSE In this geometry consisting of tetrahedra a piston is moving up and down. The piston motion will cause very high jumps e. g. in the pressure, if an inlet or outlet opens. This motivat..