In a standard theory of the formation of the planets in our Solar System, terrestrial planets and cores of gas giants are formed through accretion of kilometer-sized objects (planetesimals) in a protoplanetary disk. Gravitational N-body simulations of a disk system made up of numerous planetesimals are the most direct way to study the accretion process. However, the use of N-body simulations has been limited to idealized models (e.g., perfect accretion) and/or narrow spatial ranges in the radial direction, due to the limited number of simulation runs and particles available. We have developed new N-body simulation code equipped with a particle–particle particle–tree (P3T) scheme for studying the planetary system formation process: GPLUM. For each particle, GPLUM uses the fourth-order Hermite scheme to calculate gravitational interactions with particles within cut-off radii and the Barnes–Hut tree scheme for particles outside the cut-off radii. In existing implementations, P3T schemes use the same cut-off radius for all particles, making a simulation become slower when the mass range of the planetesimal population becomes wider. We have solved this problem by allowing each particle to have an appropriate cut-off radius depending on its mass, its distance from the central star, and the local velocity dispersion of planetesimals. In addition to achieving a significant speed-up, we have also improved the scalability of the code to reach a good strong-scaling performance up to 1024 cores in the case of N = 106.

中文翻译：

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具有单独截止方法的行星系统形成的粒子-粒子-粒子-树代码：GPLUM

在我们太阳系中行星形成的标准理论中，类地行星和气态巨行星的核心是通过原行星盘中千米大小的物体（小行星）的吸积形成的。由众多小行星组成的盘系统的引力 N 体模拟是研究吸积过程的最直接方法。然而，由于模拟运行和可用粒子的数量有限，N 体模拟的使用仅限于理想化模型（例如，完美吸积）和/或径向上的狭窄空间范围。我们开发了配备粒子-粒子-粒子-树 (P3T) 方案的新 N 体模拟代码，用于研究行星系统形成过程：GPLUM。对于每个粒子，GPLUM 使用四阶 Hermite 方案计算与截止半径内的粒子的引力相互作用，并使用 Barnes-Hut 树方案计算截止半径外的粒子。在现有的实现中，P3T 方案对所有粒子使用相同的截止半径，当小行星种群的质量范围变宽时，模拟会变慢。我们已经解决了这个问题，方法是允许每个粒子根据其质量、与中心恒星的距离以及小行星的局部速度分散具有适当的截止半径。除了实现显着的加速之外，我们还改进了代码的可扩展性，在 N = 106 的情况下达到了高达 1024 个内核的良好的强扩展性能。