ABSTRACT
One of the most important problems of modern Cosmology is to understand how the Universe evolved from an initial homogeneous and isotropic distribution of mass and energy to the complex structures we observe today: stars, galaxies, clusters of galaxies, and large-scale structures. This chapter reviews the past, the present and the future of numerical simulations in Cosmology. It summarises the basic ideas behind the N-body methods to simulate gravitational evolution of density fluctuations and the numerical techniques that have been developed during the last 20 years. The chapter presents the formulation of gas dynamics in Cosmology and reviews the two major numerical techniques used to solve the fluid equations: Eulerian methods and smoothed particle hydrodynamics (SPH). One of the major drawbacks of Eulerian methods as compared with SPH is that resolution is determined by the cell separation in a fixed, uniform mesh. The chapter discusses the attempts to introduce the short-scale non-adiabatic processes related to star formation and star-gas interactions.
