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On numerical simulations in astrophysics
Numerical simulations are useful tools for understanding astrophysical phenomena
(as well as in many other fields). Important examples include:
- the formation of stars (including binariy and multiple stars),
- the dynamics of planetesimals and the formation of planets and the solar
system,
- the dynamics of star clusters, gaseous nebulae, and galaxies,
- the formation of galaxies of the various types that are observed,
- the formation of galaxy clusters and the large scale structures of the
universe.
From the view of the code (which can be realized in every numerically capable
language such as Fortran, C, C++, and others), two main types of dynamics have
been developed:
- N-Body Dynamics
- Smoothed Particle Hydrodynamics (SPH)
N-Body code is best suited to study the dynamics of systems consisted of a
certain number of discrete bodies, e.g. stars or planets, which are in (usually
gravitational) interaction. On the other hand, SPH is appropriate to simulate
gasses or fluids, such as gaseous nebulae, stellar or planetary interiors, etc.,
by studying them in an approximation of smoothened interacting particles.
Combinations of both are also commonly used, e.g. for model galaxies consisting
of both stars and nebulae (dust and gas).
Traditionally, the interaction of mutually each pair of bodies is considered for
calculations, leading to an increase of the CPU time required by N^2, if N is the
number of particles.
In 1986, however, this situation could be significantly improved when
Joshua Barnes
and Piet Hut introduced their
TREE method (TREECODE).
Here, the volume under consideration is devided in smaller and smaller cells,
until each cell contains only zero or one particles.
Then, the force on each particle is calculated by considering the interaction
with the cells, taking into account large cells only for the remote
(and thus weaker) interactions.
This method has improved the increase of CPU time to a N*log N behaviour, so
that larger particle numbers can be treated with this scheme, which has become
quite common in the meantime.
Some useful links to numerical simulation code:
Some of the hottest papers in this field are available from here
(xxx.lanl.gov, astro-ph preprint archive):
Very preliminary collection of further links:
Hartmut Frommert
[contact]
[SEDS]