Liquid injection modeling and simulation face new challenges related to the need for predictive simulations in many fields such as combustion, chemical engineering, rocket booster propulsion and atmospheric studies. However, building up a global multi-scale model with the capability to resolve the whole injection process requires a major breakthrough in terms of both modeling and numerical methods. A new model for polydisperse sprays with coupling capabilities to the separated phases zone is proposed in (Essadki 2019, Loison 2023) and, in the present contribution, we design specific numerical methods. The key ingredient in (Loison 2023) is a good choice of variables, which can describe both the polydisperse character of a spray as well as the geometrical dynamics of non spherical droplets. The resulting system of equations is hyperbolic but has a more complex structure; realizability conditions are satisfied at the continuous level, which imply a precise framework for numerical methods. To achieve the goals of accuracy, robustness and realizability, the kinetic finite volume schemes (Bouchut 2003) and Discontinuous Galerkin methods are promising numerical approaches (Cockburn and Shu 1998). We focus here on a two-phase simulation of a polydisperse spray with oscillating droplets and assess the ability of the model and of the related numerical methods to capture the physics of such flows.