Supercomputers are used to simulate the universe from Big Bang to present day. The Illustris Project is the biggest virtual universe yet. It took years to program it and the system was completed in 2014. Data from the project was released in 2015. Data from the simulation is now compared to real life observations.
Link: The Illustris Project web site
Gizmag: Illustris omputer simulation creates the first realistic virtual universe
Presentation of the project at ArXiv
Presentation of the project data at ArXiv
Top 500 of supercomputers (nr 27 was used by Illustris)
More simulations: NASA Pleiades Supercomputer | About Pleiades
Cosmos Magazines: A ringside seat at the birth of stars
Wikipedia: Illustris project | Pleiades