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.

翻译：本文重点介绍在移动域的工程生产应用中如何使用非结构化的时空介质。无结构化的时空元素可以在时空域的底层和顶层将不同空间介质连接起来,并处理标准任意的Lagrangian-Eulelian 技术若不重新显示就无法解决的复杂领域移动/轮换。我们使用4D简单时空元素,称为Behr [2008] 的五角形时空时空元素,从而导致完全没有结构化的网格,空间和时间的精细程度不一。此外,我们使用稳定技术,稳定参数是根据Pauli和Behr [2017] 的工作所显示的反动强力来确定的。其定义在4D由Von Danwitz 等人 ([2019] 等人)在4D中扩展,允许我们处理空间时域内复杂的一向式简单介质介质的网格。