Hydrodynamic methods and sub-resolution models for cosmological simulations

Cosmological simulations are powerful tools in the context of structure formation. They allow us to explore the assembly and clustering of dark matter halos, to validate or reject possible scenarios of structure formation, and to investigate the physical properties of evolving galaxies across time. Cosmological hydrodynamical simulations are especially key to study how the complex interstellar medium of forming galaxies responds to the most energetic processes during galaxy evolution, such as stellar feedback ensuing supernova explosions and feedback from AGN. Given the huge dynamical range of physical scales spanned by the astrophysical processes involved in cosmic structure formation and evolution, cosmological simulations resort to sub-resolution models to capture processes occurring below their resolution limit. The impact of different sub-grid prescriptions accounting for the same process is striking, though often overlooked. Some among the main aforementioned processes include: hot gas cooling, star formation and stellar feedback, stellar evolution and chemical enrichment, black hole growth and feedback. Producing simulations of cosmic structure formation and galaxy evolution in large computational volumes is key to shed light on what drives the formation of the first structures in the Universe, and their subsequent evolution. Not only are predictions from simulations crucial to compare with data from ongoing observational instruments, but they can also guide future observational campaigns. Besides, since we have entered the era of high-performance computing, it is fundamental to have numerical codes which are very efficient from the computational point of view. In this chapter, we review the main hydrodynamic methods used in cosmological simulations and the most common techniques adopted to include the astrophysical processes which drive galaxy formation and evolution (abridged).