While the particle-in-cell (PIC) method is quite mature, verification and validation of both newly developed methods and individual codes have largely focused on an idiosyncratic choice of a few test cases. Many of these test cases involve either 1-D or 2-D simulations. This is either due to the availability of (quasi-) analytic solutions or historical reasons. In addition, tests often focus on the investigation of particular physics problems, such as particle emission or collisions, and do not necessarily study the combined impact of the suite of algorithms necessary for a full-featured PIC code. As 3-D codes become the norm, there is a lack of benchmark tests that can establish the validity of these codes; existing papers either do not delve into the details of the numerical experiment or provide other measurable numeric metrics (such as noise) that are outcomes of the simulation. This article seeks to provide several test cases that can be used for validation and bench-marking of PIC codes in 3-D. We focus on examples that are collisionless and can be run with reasonable computational resources. Three test cases are presented in significant detail; these include basic particle motion, beam expansion, and adiabatic expansion of plasma. All presented cases are compared either against existing analytical data or other codes. We anticipate that these cases should help fill the void of bench-marking and validation problems and help the development of new PIC codes.

中文翻译：

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细胞方法中验证 3-D 粒子的一组基准测试


虽然细胞内粒子（PIC）方法相当成熟，但新开发的方法和单个代码的验证和确认主要集中在少数测试用例的特殊选择上。许多测试用例涉及一维或二维模拟。这要么是由于（准）解析解的可用性，要么是历史原因。此外，测试通常侧重于研究特定的物理问题，例如粒子发射或碰撞，而不一定研究全功能 PIC 代码所需的算法套件的综合影响。随着 3D 代码成为常态，缺乏可以确定这些代码有效性的基准测试；现有论文要么不深入研究数值实验的细节，要么提供作为模拟结果的其他可测量的数值指标（例如噪声）。本文旨在提供几个可用于 3D PIC 代码验证和基准测试的测试用例。我们专注于无碰撞且可以使用合理的计算资源运行的示例。详细介绍了三个测试用例；这些包括基本的粒子运动、束流扩展和等离子体的绝热膨胀。所有提出的案例都会与现有的分析数据或其他代码进行比较。我们预计这些案例将有助于填补基准测试和验证问题的空白，并有助于新 PIC 代码的开发。