Packing3D.jl: An open-source analytical framework for computing packing density and mixing indices using partial spherical volumes

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-09-16 DOI:10.1016/j.cpc.2025.109863

Freddie J. Barter , Christopher R.K. Windows-Yule

{"title":"Packing3D.jl: An open-source analytical framework for computing packing density and mixing indices using partial spherical volumes","authors":"Freddie J. Barter , Christopher R.K. Windows-Yule","doi":"10.1016/j.cpc.2025.109863","DOIUrl":null,"url":null,"abstract":"<div><div>Accurate quantification of local packing density and mixing in simulations of particulate systems is essential for many industrial applications. Traditional methods which simply count the number of particle centres within a given volume of space (cell) introduce discontinuities at cell boundaries, leading to unreliable measurements of packing density. We introduce Packing3D.jl, an open-source Julia package providing analytic partial-volume calculations for spheres intersecting Cartesian and cylindrical meshes. We derive closed-form solutions for single, double and triple spherical-cap intersections, plus sphere-cylinder overlaps. We implement efficient mesh-generation routines, principal-cell indexing, and data-splitting functions for time-series analyses. Performance and accuracy were validated against simple cubic and face-centred cubic lattices and via boundary-shift continuity tests. Packing3D.jl converges exactly to theoretical lattice densities, eliminates discontinuities at sub-particle resolution, and scales linearly with particle count. Memory usage remains modest (40 B per particle, 48 B per cell). Packing3D.jl provides researchers with continuous, reproducible volume-fraction fields and robust mixing indices at high performance, facilitating sensitivity analyses and optimisation in granular process engineering.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> Packing3D.jl</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/srdxk6f77w.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link:</em> <span><span>https://github.com/fjbarter/Packing3D.jl</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> MIT</div><div><em>Programming language:</em> <span>Julia</span></div><div><em>Nature of problem:</em> Inaccuracy and discontinuity of packing density calculation by counting centres</div><div><em>Solution method:</em> Derive and implement a fast algorithm for analytically calculating particle volumes intersected by planes, providing a continuous and much more accurate measurement of packing density</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"317 ","pages":"Article 109863"},"PeriodicalIF":3.4000,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465525003650","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

Accurate quantification of local packing density and mixing in simulations of particulate systems is essential for many industrial applications. Traditional methods which simply count the number of particle centres within a given volume of space (cell) introduce discontinuities at cell boundaries, leading to unreliable measurements of packing density. We introduce Packing3D.jl, an open-source Julia package providing analytic partial-volume calculations for spheres intersecting Cartesian and cylindrical meshes. We derive closed-form solutions for single, double and triple spherical-cap intersections, plus sphere-cylinder overlaps. We implement efficient mesh-generation routines, principal-cell indexing, and data-splitting functions for time-series analyses. Performance and accuracy were validated against simple cubic and face-centred cubic lattices and via boundary-shift continuity tests. Packing3D.jl converges exactly to theoretical lattice densities, eliminates discontinuities at sub-particle resolution, and scales linearly with particle count. Memory usage remains modest (40 B per particle, 48 B per cell). Packing3D.jl provides researchers with continuous, reproducible volume-fraction fields and robust mixing indices at high performance, facilitating sensitivity analyses and optimisation in granular process engineering.

Program summary

Program Title: Packing3D.jl

CPC Library link to program files: https://doi.org/10.17632/srdxk6f77w.1

Developer's repository link: https://github.com/fjbarter/Packing3D.jl

Licensing provisions: MIT

Programming language: Julia

Nature of problem: Inaccuracy and discontinuity of packing density calculation by counting centres

Solution method: Derive and implement a fast algorithm for analytically calculating particle volumes intersected by planes, providing a continuous and much more accurate measurement of packing density

查看原文本刊更多论文

Packing3D。一个开源的分析框架，用于计算使用部分球形体积的堆积密度和混合指数

在颗粒系统模拟中，精确量化局部堆积密度和混合对许多工业应用至关重要。传统的方法是在给定的空间（细胞）体积内简单地计算粒子中心的数量，在细胞边界引入不连续，导致不可靠的堆积密度测量。我们引入Packing3D。jl，一个开源的Julia包，为球体与笛卡尔网格和圆柱网格相交提供解析的部分体积计算。我们得到了单、双、三重球帽交点以及球柱交点的闭合解。我们实现了高效的网格生成例程，主单元索引和数据分割功能，用于时间序列分析。通过简单立方和面心立方晶格以及边界位移连续性测试验证了性能和准确性。Packing3D。Jl精确收敛于理论晶格密度，消除了亚粒子分辨率的不连续，并与粒子数线性缩放。内存使用保持适度（每个粒子40 B，每个单元48 B）。Packing3D。Jl为研究人员提供连续，可重复的体积分数场和高性能的强大混合指数，促进颗粒工艺工程的敏感性分析和优化。节目简介节目标题：Packing3D。jlCPC库链接到程序文件：https://doi.org/10.17632/srdxk6f77w.1Developer's存储库链接：https://github.com/fjbarter/Packing3D.jlLicensing条款：mit编程语言：juliananproblem的性质：不准确和不连续的填料密度计算通过计数中心解决方法：推导和实现一个快速算法解析计算粒子体积相交的平面，提供一个连续的和更准确的测量填料密度

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.