We develop an all-hex meshing strategy for the interstitial space in beds of densely packed spheres that is tailored to turbulent flow simulations based on the spectral element method (SEM). The SEM achieves resolution through elevated polynomial order N and requires two to three orders of magnitude fewer elements than standard finite element approaches do. These reduced element counts place stringent requirements on mesh quality and conformity. Our meshing algorithm is based on a Voronoi decomposition of the sphere centers. Facets of the Voronoi cells are tessellated into quads that are swept to the sphere surface to generate a high-quality base mesh. Refinements to the algorithm include edge collapse to remove slivers, node insertion to balance resolution, localized refinement in the radial direction about each sphere, and mesh optimization. We demonstrate geometries with 10^2-10^5 spheres using approximately 300 elements per sphere (for three radial layers), along with mesh quality metrics, timings, flow simulations, and solver performance.

中文翻译：

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密堆积球体的全六角网格划分策略

我们为密集球体床中的间隙空间开发了一种全六角网格划分策略，该策略适用于基于光谱元素方法 (SEM) 的湍流模拟。SEM 通过提高多项式阶数 N 实现分辨率，并且需要的元素比标准有限元方法少两到三个数量级。这些减少的元素数量对网格质量和一致性提出了严格的要求。我们的网格划分算法基于球体中心的 Voronoi 分解。Voronoi 单元的面被细分为四边形，这些四边形被扫掠到球体表面以生成高质量的基础网格。对算法的改进包括边缘折叠以移除细长条、节点插入以平衡分辨率、在每个球体的径向局部改进以及网格优化。