Four-Dimensional Elastically Deformed Simplex Space-Time Meshes for Domains with Time Variant Topology

TL;DR

This paper introduces a novel four-dimensional simplex mesh method for simulating fluid domains with changing topology over time, enabling seamless integration of topology changes in computational models.

Contribution

It extends elastic mesh update methods to 4D, allowing boundary conforming discretizations of complex, time-varying topologies without additional simulation handling.

Findings

Successfully applied to valve and artery flow simulations.

Enables accurate modeling of topology changes over time.

Simplifies the computational treatment of dynamic geometries.

Abstract

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.