We have performed spectral/spectral-element simulations of a single oblate spheroid with small geometrical aspect ratio settling in an unbounded ambient fluid, for a range of Galileo numbers covering the various regimes of motion (steady vertical, steady oblique, vertical periodic and chaotic). The high-fidelity data provided includes particle quantities (statistics in the chaotic case), as well as flow profiles and pressure maps. The reference data can be used as an additional benchmark for other numerical approaches, where a careful grid convergence study for a specific target parameter point is often useful. We further describe an extension of a specific immersed boundary method (Uhlmann, J. Comput. Phys, 209(2):448--476, 2005) to enable the tracking of non-spherical particles. Finally, the reference cases are computed with this immersed boundary method at various spatial and temporal resolutions, and grid convergence is discussed over the various regimes of spheroidal particle motion. The cross-validation results can serve as a guideline for the design of simulations with the aid of similar non-conforming methods, involving spheroidal particles with Galileo numbers of ${\cal O}(100)$.

中文翻译：

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在无界环境流体中沉降的单个扁球体：稳态和非稳态尾流状态下的模拟基准

我们已经对在无界环境流体中具有小几何纵横比的单个扁球体进行了光谱/光谱元素模拟，适用于涵盖各种运动状态（稳定垂直、稳定倾斜、垂直周期和混沌）的一系列伽利略数. 提供的高保真数据包括粒子数量（混沌情况下的统计数据），以及流动剖面和压力图。参考数据可用作其他数值方法的附加基准，其中针对特定目标参数点的仔细网格收敛研究通常很有用。我们进一步描述了特定浸入边界方法的扩展（Uhlmann, J. Comput. Phys, 209(2):448--476, 2005）以实现对非球形粒子的跟踪。最后，参考案例是用这种浸入边界方法在各种空间和时间分辨率下计算的，并讨论了在各种球体粒子运动机制上的网格收敛。交叉验证结果可以作为模拟设计的指导方针，借助类似的非一致性方法，涉及伽利略数为 ${\cal O}(100)$ 的球体粒子。