GENGA. II. GPU Planetary N-body Simulations with Non-Newtonian Forces and High Number of Particles

Abstract

We present recent updates and improvements of the graphical processing unit (GPU) N-body code GENGA. Modern state-of-the-art simulations of planet formation require the use of a very high number of particles to accurately resolve planetary growth and to quantify the effect of dynamical friction. At present the practical upper limit is in the range of 30,000–60,000 fully interactive particles; possibly a little more on the latest GPU devices. While the original hybrid symplectic integration method has difficulties to scale up to these numbers, we have improved the integration method by (i) introducing higher level changeover functions and (ii) code improvements to better use the most recent GPU hardware efficiently for such large simulations. We added treatments of non-Newtonian forces such as general relativity, tidal interaction, rotational deformation, the Yarkovsky effect, and Poynting–Robertson drag, as well as a new model to treat virtual collisions of small bodies in the solar system. We added new tools to GENGA, such as semi-active test particles that feel more massive bodies but not each other, a more accurate collision handling and a real-time openGL visualization. We present example simulations, including a 1.5 billion year terrestrial planet formation simulation that initially started with 65,536 particles, a 3.5 billion year simulation without gas giants starting with 32,768 particles, the evolution of asteroid fragments in the solar system, and the planetesimal accretion of a growing Jupiter simulation. GENGA runs on modern NVIDIA and AMD GPUs.

Forming rocky exoplanets around K-dwarf stars

“…For the N-body simulations we employed the GENGA software (Grimm & Stadel 2014;Grimm et al 2022). GENGA is a GPU implementation of a hybrid symplectic N-body integrator, developed based on another N-body code MERCURY (Chambers 1999), for simulating planet and planetesimal dynamics in the final stages of planet formation, and the evolution of planetary systems.…”

“…The planetesimal number was chosen based on a series of simulations testing the speed of the code. Since more bodies result in more calculations and longer computational time scaling roughly as N 2 (Grimm et al 2022), using 12 000 particles achieves a high-enough resolution, but still within a reasonable time limit of around 2 months and available computation time. The fact that simulations with higher initial disk masses start with larger bodies should not affect the Fig.…”

GANBISS: A new GPU accelerated N-body code for Binary Star Systems

“…With the results R m you are able to calculate a polynomial of order q recursively. Equation (6) shows the recursive scheme:…”

“…To greatly increase the performance of such simulations and reduce the time needed for a single simulation one can make use of the parallelization possibilities of graphical processing units (GPU). The first GPU code with an application to planet formation is the GENGA code, which is in its current state able to simulate up to ∼ 60000 interacting bodies [6]. Yet, these simulations are limited to single star systems due to the chosen symplectic integration method.…”

Swiftest: An N-body Integrator for Gravitational Systems

“…The SyMBA integrator included in Swiftest is most similar to the hybrid symplectic integrator MERCURY6 (Chambers, 1999), the MERCURIUS integrator of REBOUND (Rein & Liu, 2012;Rein & Tamayo, 2015), and the GPU-enabled hybrid symplectic integrators such as QYMSYM (Moore & Quillen, 2011) and GENGA II (Grimm et al, 2022), with some important distinctions. The hybrid symplectic integrators typically employ a symplectic method, such as the original WHM method in Jacobi coordinates or the modified method that uses the Democratic Heliocentric coordinates, only when bodies are far from each other relative to their gravitational spheres of influence (some multiple of a Hill's sphere).…”