Numerical simulations are of a tremendous help to understand the growth of non-linear cosmological structures and how they lead to the formation of galaxies. In recent years, with the goal of improving their prediction power, new hydrodynamical techniques and physical models have been developed. Beside those improvements, the community must be ready for what could be a major paradigm change, the exascale supercomputer that will allow for the simulation of higher resolution and/or larger cosmological volume. Being ready to fully benefit from those upcoming facilities requires an important effort in adapting existing codes. Among the domains that will benefit from the exascale computing are dwarf galaxies and their low mass end, the ultra faint dwarf galaxies (UFD). Since twenty years, dwarfs have become an important research topic in astrophysics due to recent observing facilities allowing a large number of unprecedented observations. Simulations of such galaxies require extremely high resolution down to the individual star level and, thus, require the adaptation of existing physical models. In the first part of my thesis, I extended a previous work performed with the code GEAR on understanding the formation of dwarf galaxies in a cosmological context. I studied the ram pressure stripping mechanism due to the hot halo of the Milky Way and how it modifies the observed properties of dwarf galaxies. I demonstrated that the thermal pressure due to the hot halo on the dwarf's gas can strongly impact the effect of ram pressure. To ensure the quality of our simulations, I have participated in the AGORA project that aims at comparing the predictions of different simulation codes and understanding the underlying differences. In the last AGORA paper, we have performed the first comparison of cosmological simulations using common models for the radiative cooling and star formation. In the second part of this thesis, an important effort has been dedicated to migrate our physical models from our code GEAR towards SWIFT. Thanks to the improved performance of SWIFT (speedup of 7.65x) and the successful migration, our code is now fast enough to simulate UFDs at the resolution of individual stars. On the physics side, our star formation and stellar feedback methods need to be further improved due to the high resolution required in UFDs. To solve this issue, I designed and started the implementation of a new star formation scheme based on a new type of particles called "sink particles". Going towards the exascale also requires a better design of the output system previously based on snapshots of the simulation saved at regular time intervals. In this purpose, I introduced the "Continuous Simulation Data Stream" (CSDS) specially designed for simulations where gravity is producing strong differences in timescale between particles or cells. The CSDS reduces the disk space used by a single simulation while improving the time resolution of the output and making the analysis easier and flexible. Finally, while the simulation code and the associated physical models have a tremendous impact on the quality of the simulations, the initial conditions need to be carefully designed as they can deeply impact the results. Using a Bayesian approach, I have developed my own code that generates constrained initial conditions that reproduce the Local Group.