Bubbly flows around ships have been studied for years, mostly in relation with ship acoustic signatures. Bubbles are generated at the bow and shoulder breaking waves, at the hull/free surface contact line, the propeller and the highly turbulent stern flow. These bubbles are further transported downstream by the flow forming a two-phase mixture in the wake that can be kilometers long. The presence of bubbles in the wake of a ship significantly affects the acoustic response of the medium and can be detected by measuring acoustic attenuation and backscattering making a ship vulnerable to detection. Additionally, the bubbly wake shows at the surface as a characteristic signature of white water, and given the length of the bubbly wake, it makes a ship visible from satellites. Therefore, the bubbly wake can be used to detect and identify surface ships. Bubbly flows do not scale to model scale experiments, and experiments on full scale ships are scarce mostly due to difficult access areas and the high speeds involved. It is therefore of interest to simulate the bubbly flow around ships to provide information difficult, if not impossible, to obtain with experiments. This work presents the development of a code for the simulation of polydispersed bubbly flows with a focus on ship hydrodynamics. The mathematical model implemented is based on a two-fluid formulation coupled with a Boltzmann-like transport equation describing the bubbly phase. The tool developed attempts to include most of the relevant physics of the problem to represent better the conditions of real scenarios. The resulting code allows the simulation of polydispersed bubbly flows in situations including free surface and air entrainment, high void fraction levels and moving control surfaces and propulsors. The code is two-way coupled, with a strong coupling between the two phases and between the bubble sizes. The complexity of the problems tackled in this research required the development of novel numerical methods solving issues never identified before or simply neglected. These methods play an essential role in the accuracy, robustness and efficiency of the code and include: a two-phase projection method that not only couples pressure and velocity but also implicitly couples void fraction, a time splitting marching scheme to solve separately coupling in space and in bubble sizes, and a stable numerical method to integrate the strong coupling introduced by collision forces. The implemented code is applied to the simulation of the bubbly flow around a full scale ship using the latest available models and computational techniques. A study is performed on the influence of several mechanisms on the predicted bubbly wake and comparisons with available experimental data are presented. The influence of breakup in the boundary layer is analyzed in detail as well. In addition, this work identifies several modeling and implementations issues and attempts to provide a path for future studies. To illustrate the flexibility and robustness of the code, a final demonstration case is presented that includes rotating propellers. The computation is performed at full scale, with the fully appended geometry of the vessel and includes incoming waves, oceanic background and rectified diffusion models. Many of these features are unique to this computation and make it the first of its kind.