Look at this
http://www.physics.lsa.umich.edu/hubble-volume/expert.htm
http://www.physics.lsa.umich.edu/hubble-volume/
==quote==
* Each simulation:
o employs one billion mass elements and 1024^3 Fourier grid cells
o generates nearly 0.5 terabytes of raw output (later compressed to about 200 Gb)
o requires roughly 70 hours of CPU on 512 processors (four years of a single processor!)
* Some details of the LCDM model :
o Wm = 0.3, WL=0.7, s8 = 0.9, power spectrum from CMBFAST
o simulated cube of comoving length 3/h gigaparsecs (3000/h Mpc)
o simulation begun at redshift z = 35
o force resolution is 0.1/h Mpc
==endquote==
Note that the formidable SIMON WHITE is involved (Cambridge, UC Berkeley, now director Max Planck Astrophysics at Garching)
kick-ass astrophysicist IMHO.
But it is just a simulation with mass points corresponding to galaxies.
It is called Hubble Volume. roughly a cube chunk of the universe on a scale of 13 billion lightyears on a side at present (earlier smaller).
I think that uses effective largescale modeling.
If you are interested in microscopic modeling of spacetime on a Planck scale using Monte Carlo simulation of a quantum gravity dynamical model, then
Renate Loll did that, with her co-worker Jan Ambjorn at Utrecht Netherlands but her computer resources were teensy compared with what she needed.
http://arxiv.org/abs/hep-th/0509010
The Universe from Scratch
R. Loll, J. Ambjorn, J. Jurkiewicz
Her universes were brief little quantum fluctuation burps. But SHE DID NOT FORCE THEM TO BE EVEN THE RIGHT DIMENSION AND THEY TURNED OUT TO BE 3 + 1 = 4 DIMENSIONAL. That was a triumph, which occurred in 2005. After many years many people being frustrated, she succeeded in having it evolve the right dimensionality of its own accord instead of being told what dimension to be. After all, Nature does this.
Dan Christensen has the use of a Beowulf cluster (supercomputer) at the Uni Western Ontario and he has been doing quantum gravity simulations but so far I think this is way too small to be what you are imagining.
Maybe it isn't possible even in 100 years. I don't know what computer resources it would take to do a really satisfying job of simulating the universe.
If all you want to do is simulate GALAXY FORMATION in a fixed spatially flat standardized spacetime. then I think that may have been done. Wallace might know.
Other people may know of other computer simulations of universe(s).