The Bolshoi simulation tracks the evolution of the large-scale structure of the universe, including the creation of the dark matter halos from which galaxies coalesced.
Initial studies show good agreement between the simulation's predictions and astronomers' observations.
"In one sense, you might think the initial results are a little boring, because they basically show that our standard cosmological model works," said Joel Primack, distinguished professor of physics at the University of California, Santa Cruz.
"What's exciting is that we now have this highly accurate simulation that will provide the basis for lots of important new studies in the months and years to come."
The new simulation replaces the Millennium Run, which used cosmological parameters based on the first release of data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP).
This gave a detailed map of subtle variations in the cosmic microwave background radiation, the primordial radiation left over from the Big Bang.
However, its data has been superseded by subsequent releases in 2008 and 2010, and the Bolshoi simulation is based on these later results.
One main aim of the Bolshoi simulation is to model the evolution of dark matter halos - and already papers are being published based on the new data.
"We've released a lot of the data so that other astrophysicists can start to use it," says Primack.
"So far it's less than one percent of the actual output, because the total output is so huge, but there will be additional releases in the future."