Our Universe in a Supercomputer

Cosmological simulations of galaxy and structure formation have undergone rapid development over the last decade and this progress is currently accelerating. The methodology evolved from purely gravitational computations of large scale structure to full hydrodynamical simulations which include a plethora of complex baryonic physical processes. Recent successes of these simulations have been impressive, obtaining models of present day galaxies with a morphological mix in broad accord with observation, which has been a long standing goal for more than 20 years.

In this talk I will review the state-of-the-art of cosmological simulations, and future prospects of moving towards ab-initio simulations. Specifically, I will discuss our development of novel algorithms that can extend the dynamical range of simulations at a modest computational cost, not only to track the currently implemented physics of galaxy formation more accurately, but also to incorporate crucial physical processes that have been so far neglected due to their complexity. I will highlight several examples of such processes ranging from the smallest to the largest scales in the Universe and present an outlook towards the next generation of simulation models with the aim to tackle some of the most pressing astrophysical questions.