GPU enabled parallel logarithmic Hamiltonian leapfrog for the stability analysis of circumbinary systems
Vemuri, Sivasai Pavan
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Permalink
https://hdl.handle.net/2142/121376
Description
Title
GPU enabled parallel logarithmic Hamiltonian leapfrog for the stability analysis of circumbinary systems
Author(s)
Vemuri, Sivasai Pavan
Issue Date
2023-07-19
Director of Research (if dissertation) or Advisor (if thesis)
Eggl, Siegfried
Department of Study
Aerospace Engineering
Discipline
Aerospace Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Logarithmic Hamiltonian Leapfrog algorithm, parallel processing, circumbinary systems
Abstract
The discovery of exoplanets orbiting multiple star systems as well as recent NASA missions to binary asteroids has sparked renewed interest in the study of orbital dynamics with a focus on both orbital evolution and the chaotic behavior of the N-body problem (N$>$2). With analytical studies falling short of effectively describing the transition from regular to chaotic motion in such systems, the need to use numerical methods arises. There has been extensive research in terms of numerical methods with applications in astrodynamics. Many studies have delved deep into the phenomena that perturb stable orbits inducing chaotic nature. Numerical methods have reached a stage where they can give accurate and reliable results over a wide range of parameters on reasonable timescales.
This research is focused on using parallel computing capabilities to run accurate simulations of circumbinary orbits involving 3 bodies. With an emphasis on using robust solvers for planetary motion predictions, this thesis circumnavigates problems involved in most of the currently used numerical methods and instead uses the Logarithmic Hamiltonian leapfrog formulation. A comparative study of the LHLA method and conventional numerical methods clearly shows the superior performance of the LHLA integrator even with larger timesteps. An important goal of this work is to prove the usability of the time-transformed leapfrog integrator for the classical general N-body problem with Graphic Processing Units (GPUs). It also provides a validated methodology to conduct stability analysis of circumbinary orbits which can easily be extended to other problems.
A Python library, `CuPy' is used to leverage parallel computing capabilities enabling us to simulate thousands of trajectories simultaneously. With this, we investigate the orbital dynamics of multiple co-planar circumbinary orbits. The binary eccentricity, star and planet masses, semi-major axis and mean anomaly of the planet are varied to understand the role of these orbital elements in determining the long-term stability of the planet. It was observed that the stability of the system greatly depends on the semi-major axis of the planet which is in conformation with previous research. We describe regions of P-type stability and regions of certain instability.
Moreover, we determine that the elliptic restricted three body problem approximation starts to break down when the outer companion mass exceeds 0.1\% of the binary star's mass. With reduced computational time and the option of running accurate, massively parallel simulations simultaneously, this work enables the study of the general N-body problem and the effect of various orbital elements in the evolution of orbits of interest.
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