Scientists have managed to simulate twelve billion years of a Universe that is very similar to ours (difficult to state that it is ours, what they did was to apply the physical laws we are aware of in the simulation...).
The team was led from Cambridge (Harvard and MIT) and involved several institutions all around the world. Although there have been several simulators developed previously this is by far the one with the best resolution (12 billion 3D pixels) and accuracy.
Following the evolution of a Universe along 12 billion years in a space that is a cube having the side of 350 million light years is not a piece of cake in computation power demand. The scientists had needed 3 months of computation from a cluster of 8,000 computers for the complete simulation (based on a program totalling 100,000 instruction code). They said that running such a simulation on a computer you are using today would have required 2,000 years of processing time!
2,000 years is a lot but then it takes about 23 years to squeeze this processing capacity into 3 months. You can expect that your children will be able to simulate the universe evolution on their tablet, or on whatever form the computers may take into the future.
For the time being be contented to look at the simulation results of Illustris.