A study,in steady state and two phase-flow condition, of a proton exchange membrane fuel cell is analyzed taking into account all the physical aspects and considering the cell as a whole. Particular attention is given to the water management inside it, and how it improves or limits its performance. The model also considers the transport of gaseous species, dissolved water, liquid water and the intensity of the generated current. Finally, we tried to improve the fuel cell perfomaces through topological optimization, varying the degree of vacuum in the catalyst and observing how the current production varies at a certain voltage.