PENTACLE: Parallelized Particle-Particle Particle-Tree Code for Planet Formation

Abstract

We have newly developed a Parallelized Particle-Particle Particle-tree code for Planet formation, PENTACLE, which is a parallelized hybrid $N$-body integrator executed on a CPU-based (super)computer. PENTACLE uses a 4th-order Hermite algorithm to calculate gravitational interactions between particles within a cutoff radius and a Barnes-Hut tree method for gravity from particles beyond. It also implements an open-source library designed for full automatic parallelization of particle simulations, FDPS (Framework for Developing Particle Simulator) to parallelize a Barnes-Hut tree algorithm for a memory-distributed supercomputer. These allow us to handle $1-10$ million particles in a high-resolution $N$-body simulation on CPU clusters for collisional dynamics, including physical collisions in a planetesimal disc. In this paper, we show the performance and the accuracy of PENTACLE in terms of ${\tilde{R}}_{\mathrm{cut}}$ and a time-step $\Delta t$. It turns out that the accuracy of a hybrid $N$-body simulation is controlled through $\Delta t/{\tilde{R}}_{\mathrm{cut}}$ and $\Delta t/{\tilde{R}}_{\mathrm{cut}}\sim 0.1$ is necessary to simulate accurately accretion process of a planet for $\ge 10^6$ years. For all those who interested in large-scale particle simulations, PENTACLE customized for planet formation will be freely available from https://github.com/PENTACLE-Team/PENTACLE under the MIT lisence.

arXiv comment12 pages, 14 figures, published in PASJ

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• Non-intrusive hierarchical coupling strategies for multi-scale simulations in gravitational dynamics
• Formation and evolution of binary black holes in $N$-body simulations of star clusters with up to two million stars
• Particle-particle Particle-tree Code for Planetary System Formation with Individual Cut-off Method: GPLUM