Four-dimensional elastically deformed simplex space-time meshes for domains with time-variant topology

Abstract

Considering the flow through biological or engineered valves as an example, 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 behavior, but poses a particular challenge in computer simulations. A way to overcome this challenge is to consider the application-specific space-time geometry 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.