  Thinking of the flow through biological or technical valves, there is a
variety of applications in which the topology of a fluid domain changes over
time. This topology change is characteristic for the physical behaviour, but
poses a particular challenge in computer simulations. A way to overcome this
challenge is to consider the space-time extent of the application as a
contiguous computational domain. In this work, we obtain a boundary conforming
discretization of the space-time domain with four-dimensional simplex elements
(pentatopes). To facilitate the construction of pentatope meshes for complex
geometries, the widely used elastic mesh update method is extended to
four-dimensional meshes. In the resulting workflow, the topology change is
elegantly included in the pentatope mesh and does not require any additional
treatment during the simulation. The potential of simplex space-time meshes for
domains with time variant topology is demonstrated in a valve simulation and a
flow simulation inspired by a clamped artery.
