  In this thesis, we aim to further elucidate the phenomenon of galaxy
evolution in the environment of galaxy clusters using the methodology of
numerical simulations. For that, we have developed hydrodynamic models in which
idealized gas-rich galaxies move within the ICM of idealized galaxy clusters,
allowing us to probe in a detailed and controlled manner their evolution in
this extreme environment. The main code used in our simulations is RAMSES, and
our results concern the changes in gas composition, star formation rate,
luminosity and color of infalling galaxies. Additionally to processes taking
place inside the galaxies themselves, we have also described the dynamics of
the gas that is stripped from those galaxies with unprecedented resolution for
simulations of this nature (122 pc in a box including an entire $10^{14}$
M$_\odot$ cluster), finding that clumps of molecular gas are formed within the
tails of ram pressure stripped galaxies, which proceed to live in isolation
within the ICM of a galaxy cluster for up to 300 Myr. Those molecular clumps
possibly represent a new class of objects; similar objects have been observed
in both galaxy clusters and groups, but no comprehensive description of them
has been given until now. We additionally create a hydrodynamic model for the
A901/2 multi-cluster system, and correlate the gas conditions in this model to
the locations of a sample of candidate jellyfish galaxies in the system; this
has allowed us to infer a possible mechanism for the generation of jellyfish
morphologies in galaxy cluster collisions in general.
