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Introduction

This is a 3D simulation of a dynamical system of particles, under the influence of gravity.

Consider n point masses m_1, ... ,m_n in three-dimensional space. Suppose that the force of attraction experienced between each pair of particles is Newtonian. Then, if the initial positions in space and initial velocities are specified for every particle at some present instant t_0, determine the position of each particle at every future (or past) moment of time.

Configuration

N particles are generated randomly within a sphere. For each particle generated, its coordinate P(p_x, p_y, p_z) $$p_x^2 + p_y^2 + p_z^2 < 1 m$$, it mass m $$10^5 kg < m < 10^6 kg $$. The elapse time interval is set to $$0.1 s$$. Also Opengl is employed to visualize the simulation result.

Algorithms

Integration Algorithm

Using classic Runge-Kutta method.

http://math.fullerton.edu/mathews/n2003/RungeKuttaMod.html

Simulation Algorithm

Barnes-Hut simulation

J. Barnes and P. Hut (December 1986). "A hierarchical O(N log N) force-calculation algorithm". Nature 324 (4): 446-449. doi:10.1038/324446a0.

The volume is divided up into cubic cells in an octree, so that only particles from nearby cells need to be treated individually, and particles in distant cells can be treated as a single large particle centered at its center of mass.

Parallel

Using c++0x thread provided by pthread.

Simulation Result

  • N = 3 ------- file video/nbody_3.mkv
  • N = 30 ------- file video/nbody_30.mkv
  • N = 300 ------- file video/nbody_300.mkv
  • N = 1000 ------- file video/nbody_3000.mkv

Discussion

Author

Wang Feng [email protected]

License

Licensed under the GPLv3.