While the ability to solve for multiphase flows that contain of a distribution of properties is crucial to the accurate prediction of physical system, there is currently a lack of numerical solution methods to solve for these types of flows. In this work, three new numerical procedures are developed in order to accurately solve for systems containing polydisperse multiphase flows, and flows with velocity distributions. The ability to correctly solve these flows allows for the local segregation of size that is generally not possibly due to the limitations of the standard solution techniques. First, a numerical algorithm is presented to solve bubbly flows using the standard two fluid model coupled to the moment transport equations of a monokinetic number density function (NDF). This provides the stability of a two-fluid solver, while adding additional accuracy that comes from the inclusions of a range of sizes, and corresponding velocities. The algorithm is first tested to ensure numerical stability, and then validated against against experimental data, as well as the two-fluid and multi-fluid models. Next, a semi-implicit solution method for the handling of the particle pressure flux for polydisperse granular systems is presented in the multifluid framework, and is based on the work of Syamlal et al. (1993). The method is first verified by examining the segregation of sizes in a settling bed, then is validated against existing implementations of polydisperse kinetic theory, as well as experimental results in a bidisperse fluidised bed and a cyclic vertical riser. Finally, a solution method to the transport of the joint size-velocity NDF is presented using QBMM. The presented method makes no assumptions on the size or velocity distribution. Additionally, the relevant source terms to describe change in size are presented using a volume fraction formulation which is important for numerical stability when small particles are under consideration. The solution procedure is first validated using simple 0-D cases for both population balance equations and collision models, then using an axisymmetric 1-D spray cases in which both the size and velocity evolution are important, and finally using 2-D crossing jet cases. All work has been implemented in the open-source framework OpenFOAM.