Simulation of Primordial Star Formation with Parallel Processing
Summary by Feng Zhou, 9/4/2002
The numerical simulation of star formation is a very important and popular problems in modern cosmology. If solved successfully, it can add a lot to our knowledge of the evolution of all kinds of cosmic structures and the universe as a whole. The star formation is composed of complex chemical, dynamical and thermodynamic processes, each of which plays important role during some or all parts of the whole process. The objective of the simulation is to show the dynamic process of star formation and the influence of different parameters on the process.
As stars are formed by the gravitational amplification of initially very small density fluctuations in the early universe, the spatial range and resolution we have to deal with is tremendous. To solve a simulation of a structure as large as the Milky Way galaxy, we will need a total spatial dynamic range SDR = 1020 - a seemingly unreachable goal. Even simulation of a single cosmic structure requires excessive spatial dynamic range, which translates into enormous memory and processing power requirement.
Star formation is an ideal candidate to solve
with massive parallel processing because of the sheer size and inherent
parallelism of the problem. However, to solve the star formation problem
using a traditional static, uniform mesh is simply not feasible in the
foreseeable
future. In [1], Greg L. Bryan et al.[2]
proposes using structured adaptive mesh refinement (SAMR: [3]) to solve the
problem. Basically, the idea behind SAMR is simple. Dynamically add
and modify several levels of finer meshes onto the basic coarse mesh. Do
computation in higher resolution only when needed. The finer (child) mesh
obtains its boundary conditions from the coarser (parent) grid or from other
neighboring (sibling) grids with the same mesh spacing.
By using SAMR, Greg L. Bryan et al. were able to achieve an unprecedented temporal dynamic range of 1022, with more than 8000 subgrids at 34 levels of refinement, which are generated automatically. Their system, named Enzo [4], combines an Euler solver for gas, an N-body solver for dark matter, a Poisson solver for the gravitational field, and a stiff reaction flow solver for the chemistry simulation. It successfully simulated the formation process of a primordial star within a volume that is 256 comoving kiloparsec (kpc) on a side (1 parsec is 3.26 light years).
The platform Enzo runs on is the Blue Horizon SP2 system at the San Diego Supercomputer Center. It now ranks number 25 in Top500 list as of June, 2002. The brief specifications are:
The reported sustained performance of the application on Blue Horizon is 13 Gflop/s on 64 of the 1,152 processors. The peak performance of the 64 processors should be 929.0 / 1152 * 64 = 51.6 Gflop/s. Thus the sustained performance is about 25% of the peak performance, which shows that the application has good efficiency. It is also reported that the application has a memory usage which often reaches up to 20 GB.
Numerical Cosmology is a very promising application area of massive parallel processing, because of the enormous problem size and inherent high parallelism. Greg L. Bryan et al. successfully built a parallel simulator based on the SAMR method and did a simulation. However, the primordial star formation simulation problem should only be regarded as an "entry-level" problem in this field because of the simpler environment of the event (only millions of years after the Big Bang) than current universe. That makes primordial star formation an easier "clean initial value" problem. There are many other much more complex problems out there that are awaiting to be solved by massive parallel processing.
[1] Greg L. Bryan et al., Achieving Extreme Resolution in Numerical Cosmology Using Adaptive Mesh Refinement: Resolving Primordial Star Formation, Super Computing 2001, Denver, Colorado, November 10-16, 2001
[2] Ab initio Simulations of the Formation of the First Star in the Universe, at http://www.tomabel.com/GB
[3] M.J.Berger and P. Colella, Local Adaptive Mesh Refinement for Shock Hydrodynamics, J. Computational Physics, vol. 82, 1989, pp. 64-84
[4] AMR (enzo) User's Guide, http://www.mit.edu/~gbryan/amr_guide/