Abstract
As an entry for the 2001 Gordon Bell Award in the "special" category, we describe our 3-d, hybrid, adaptive mesh refinement (AMR) codeEnzodesigned for high-resolution, multiphysics, cosmological structure formation simulations. Our parallel implementation places no limit on the depth or complexity of the adaptive grid hierarchy, allowing us to achieve unprecedented spatial and temporal dynamic range. We report on a simulation of primordial star formation which develops over 8000 subgrids at 34 levels of refinement to achieve a local refinement of a factor of 1012in space and time. This allows us to resolve the properties of the first stars which form in the universe assuming standard physics and a standard cosmological model. Achievingextreme resolutionrequires the use of 128-bit extended precision arithmetic (EPA) to accurately specify the subgrid positions. We describe our EPA AMR implementation on the IBM SP2 Blue Horizon system at the San Diego Supercomputer Center.
Highlights
Cosmic structure is formed by the gravitational amplification of initially small density fluctuations present in the early universe
N-body tree codes are widely used in numerical cosmology to achieve high spatial dynamic ranges in gen
The highest dynamic range N-body simulation achieved SDR = 2×105 with substantially fewer particles [18]. These calculations simulate only the collisionless cold dark matter (CDM) which dominates the gravitational dynamics of structure formation
Summary
Cosmic structure is formed by the gravitational amplification of initially small density fluctuations present in the early universe. The highest dynamic range N-body simulation achieved SDR = 2×105 with substantially fewer particles [18] These calculations simulate only the collisionless cold dark matter (CDM) which dominates the gravitational dynamics of structure formation. More than 8000 subgrids at 34 levels of refinement are generated automatically to achieve a final spatial and temporal dynamic range of 1012 (for comparison, 1012 is roughly the ratio of the diameter of the earth to the size of a human cell) It is the highest dynamic range 3-d simulation ever carried out in astrophysics. Enzo combines an Euler solver for the primordial gas [8], an N-body solver for the collisionless dark matter [9], a Poisson solver for the gravitational field [14], and a 12-species stiff reaction flow solver for the primordial gas chemistry [4] The latter is needed to determine the nonequilibrium abundance of molecular hydrogen which dominates the radiative cooling of the gas. As we will see, achieving extreme resolution is more a matter of high performance data structures and extended precision arithmetic than raw gigaflops, the latter is certainly needed
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