The modelling of baryonic physics in numerical simulations of disc galaxies allows to study the evolution of the diff erent components, the physical state of the gas and the star formation. The present work aims at investigating in particular the role of the cold and dense molecular phase, which could play a role of gas reservoir in the outer galaxy discs, with low star formation e fficiency. After a presentation of galaxies with a focus on spiral galaxies, their interstellar medium and dynamical evolution, we review the current state of hydro dynamical numerical simulations and the implementation of baryonic physics. We then present the simulations we performed. These include cooling to low temperatures, and a molecular hydrogen component. We especially test the impact of the presence of molecular hydrogen in simulations with several feedback e fficiencies, and fi nd that the molecular hydrogen allows in all cases some slow stellar formation to occur in the outer disc, with an e ffect on the vertical structure of the disc that is sensitive to the feedback e fficiency. Molecular hydrogen is therefore able to play the role of gas reservoir in external parts of spiral galaxies, which accrete gas from cosmic filaments all along their lives.
