  This paper highlights how unstructured space-time meshes can be used in
production engineering applications with moving domains. Unstructured
space-time elements can connect different spatial meshes at the bottom and top
level of the space-time domain and deal with complicated domain
movements/rotations that the standard arbitrary Lagrangian-Eulerian techniques
can not resolve without remeshing. We use a space-time finite element
discretization, by means of 4D simplex space-time elements, referred to as
pentatopes by Behr [2008], which leads to entirely unstructured grids with
varying levels of refinement both in space and in time. Furthermore, we use
stabilization techniques, and the stabilization parameter is defined based on
the contravariant metric tensor, as shown in the work of Pauli and Behr [2017].
Its definition was extended in 4D by von Danwitz et al. [2019], allowing us to
deal with complex anisotropic simplex meshes in the space-time domain.
