  The goal of this work is to to investigate different numerical approaches and
to introduce a new, physically-based sub-grid model for the ISM physics,
including a treatment of star formation and Type II supernovae energy feedback
(MUPPI, MUlti-Phase Particle Integrator). Our model follows the ISM physics
using a system of ordinary differential equations, describing mass and energy
flows among the different gas phases in the ISM inside each gas particle. The
model also includes the treatment of SNe energy transfer from star-forming
particles to their neighbours. We will show in this Thesis how this model is
able to reproduce observed ISM properties, while also providing an effective
thermal energy feedback and responding to variations in the local
hydrodynamical properties of the gas, e.g. crossing of a spiral density wave in
a galaxy disk. We believe the model we presented here will be particularly
useful in cosmological simulations of formation and evolution of isolated
galaxies and galaxy clusters. For this reason, the first application of the
present Ph.D. work will therefore be to apply MUPPI to cosmological
simulations, with the aim of determine how an improved treatment of star
formation and feedback astrophysical processes impacts on many open issues,
from the properties of simulated disk galaxies to the properties of cold
baryons (galaxies and diffuse stellar component) in galaxy clusters, to the
properties of the Intra-Cluster Medium in presence of an effective supernovae
thermal feedback.
