  Employing simplex space-time meshes enlarges the scope of compressible flow
simulations. The simultaneous discretization of space and time with simplex
elements extends the flexibility of unstructured meshes from space to time. In
this work, we adopt a finite element formulation for compressible flows to
simplex space-time meshes. The method obtained allows, e.g., flow simulations
on spatial domains that change topology with time. We demonstrate this with the
two-dimensional simulation of compressible flow in a valve that fully closes
and opens again. Furthermore, simplex space-time meshes facilitate local
temporal refinement. A three-dimensional transient simulation of blow-by past
piston rings is run in parallel on 120 cores. The timings point out savings of
computation time gained from local temporal refinement in space-time meshes.
