Prediction of the bubble size distribution in the wake of a ship is important to analyze its acoustic signature. To achieve CFD simulation of dynamic ships with moving control surfaces and rotating propellers in waves, a robust implementation is paramount. In this work a mass conserving multigroup discretization strategy of the Boltzmann transport equation for polydispersed bubbly flows is presented, as well as an analysis of available breakup and coalescence models. Modifications of the discrete equations for the fixed pivot method at the boundaries are introduced that guarantee exact bubble mass conservation. The role of the time stepping scheme in the conservation of mass and number of bubbles is discussed. Though the conservation properties of the discrete system of equations are satisfied provided they are solved exactly, in practice an iterative procedure must be used since the ODE's are non-linear. Three iterative schemes are proposed and they are analyzed in terms of robustness and efficiency. Breakup, coalescence and dissolution models are analyzed from the numerical point of view. Available models of breakup and coalescence are studied finding appropriate choices for ship applications. Other models are appropriate as well, but are more costly numerically. As appropriate for ship applications, an extension to the model of Prince and Blanch for salt water is proposed and analyzed. The final model is tested against experimental data and computations by other researchers, and convergence properties in bubble size discretization is studied. It is found that for salt water the final steady state is dependent on the initial condition since there is a range of sizes for which coalescence and breakup are both negligible. (C) 2013 Elsevier Ltd. All rights reserved.