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.

中文翻译：

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时变拓扑域的四维弹性变形单纯形时空网格

以通过生物或工程阀门的流量为例，有多种应用，其中流体域的拓扑结构随时间变化。这种拓扑变化是物理行为的特征，但对计算机模拟提出了特殊挑战。克服这一挑战的一种方法是将特定于应用程序的时空几何视为一个连续的计算域。在这项工作中，我们获得了具有四维单纯形元素（五角星）的时空域的符合边界的离散化。为了便于构建复杂几何的五面体网格，广泛使用的弹性网格更新方法扩展到四维网格。在由此产生的工作流程中，拓扑变化优雅地包含在五面体网格中，并且在模拟过程中不需要任何额外的处理。在瓣膜模拟和受夹紧动脉启发的流动模拟中，证明了具有时变拓扑结构的域的单纯形时空网格的潜力。