Mathematics – Logic
Scientific paper
Jan 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997aas...18912218p&link_type=abstract
American Astronomical Society, 189th AAS Meeting, late abstracts, #122.18; Bulletin of the American Astronomical, Vol. 29, p. 73
Mathematics
Logic
1
Scientific paper
Cosmological N-body and hydrodynamic simulations start with a realization of a random density fluctuation field representing a cosmological model at an early epoch. The density field is often replaced by a set of particles whose positions and velocities are set to conform to the desired density field. Each particle represents a cloud of huge number of real particles. Positions and velocities of particles are subsequently integrated by various numerical codes. We have simulated a set of collisionless collapses of Gaussian density peaks by using the PM and P(3) M codes. We find that in cosmological simulations the physics at scales below the mean particle separation(MPS) is dominated by inaccuracies in describing the initial density field, and cannot be studied even by the high force-resolution codes. Since density fluctuations are ill-defined at scales smaller than MPS, it is desirable not to amplify this problem during the evolution. The P(3) M code is shown to divergently amplify the inaccuracies of particle representation of initial density fluctuations below MPS scale. Consequently, all high force resolution codes including the hierarchical tree and the direct N-body codes whose two-body force continues to rise down to the scales 10 ~ 1000 times shorter than MPS, should share this problem. On the other hand, numerical codes like the PM code whose force law turns down at scales near MPS or the pixel size, significantly slow down the amplification of errors in the initial conditions.
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