Abstract Particle tracking, that is, the repeated localization of particles within a grid by means of tracking the particles’ trajectories, is routinely applied in particle-based schemes where the domain is described by an unstructured polyhedral grid. A range of tracking algorithms are available in the literature, which are inherently similar to algorithmic approaches common both in event-driven particle dynamics (EDPD) and ray-tracing methods. We propose a reformulation of existing particle tracking algorithms in the context of EDPD. On the one hand, this resolves inconsistencies in the mapping between particle positions and grid cells triggered, e.g., by imperfect grids. More importantly, it allows the specification of solid objects via constructive solid geometry (CSG), a standard technique for the modeling of solids in computer-aided design. While usually considered contrary approaches, our description of the computational domain as the combination of a bounding volume defined by an unstructured grid and solids modeled via CSG embedded into this volume can be highly advantageous. The two different approaches of modeling the computational domain complement each other perfectly, as the CSG representation is not only efficient in terms of memory and computing time, but also avoids the challenges of generating finely resolved unstructured grids in the presence of complicated boundaries. These benefits, as well as the positive impact of several algorithmic optimizations of the extended tracking algorithm, are exemplified via a particle-based simulation of a gas flow through a highly porous medium.

中文翻译：

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复杂几何中的稳健事件驱动粒子跟踪

摘要 粒子跟踪，即通过跟踪粒子的轨迹在网格内重复定位粒子，通常应用于基于粒子的方案，其中域由非结构化多面体网格描述。文献中提供了一系列跟踪算法，它们本质上类似于事件驱动粒子动力学 (EDPD) 和光线跟踪方法中常见的算法方法。我们建议在 EDPD 的背景下重新制定现有的粒子跟踪算法。一方面，这解决了粒子位置和网格单元之间映射的不一致性，例如由不完美的网格触发。更重要的是，它允许通过构造实体几何 (CSG) 来指定实体对象，CSG 是计算机辅助设计中实体建模的标准技术。虽然通常被认为是相反的方法，但我们将计算域描述为由非结构化网格定义的边界体积和通过嵌入该体积的 CSG 建模的实体的组合可能是非常有利的。两种不同的计算域建模方法完美互补，因为 CSG 表示不仅在内存和计算时间方面高效，而且避免了在存在复杂边界的情况下生成精细解析的非结构化网格的挑战。这些好处，以及扩展跟踪算法的几种算法优化的积极影响，通过基于粒子的气体流过高度多孔介质的模拟得到了例证。我们将计算域描述为由非结构化网格定义的边界体积和通过嵌入该体积的 CSG 建模的实体的组合可能非常有利。两种不同的计算域建模方法完美互补，因为 CSG 表示不仅在内存和计算时间方面高效，而且避免了在存在复杂边界的情况下生成精细解析的非结构化网格的挑战。这些好处，以及扩展跟踪算法的几种算法优化的积极影响，通过基于粒子的气体流过高度多孔介质的模拟得到了例证。我们将计算域描述为由非结构化网格定义的边界体积和通过嵌入该体积的 CSG 建模的实体的组合可能非常有利。两种不同的计算域建模方法完美互补，因为 CSG 表示不仅在内存和计算时间方面高效，而且避免了在存在复杂边界的情况下生成精细解析的非结构化网格的挑战。这些好处，以及扩展跟踪算法的几种算法优化的积极影响，通过基于粒子的气体流过高度多孔介质的模拟得到了例证。