A variety of modeling techniques for the population balances resulting from particle coagulation were examined. The simplified models using the non-uniform discretization scheme were compared to uniform discrete models. Further, new algorithms that incorporate a non-uniform discretization were developed. The uniform discrete population balance was used as the basis of comparison as it considers a continuous distribution of size classes of particles. Comparisons included the particle collision mechanisms of perikinetic, orthokinetic, and differential sedimentation with the inclusion of flow-induced break-up. Initial particle populations considered were both monodisperse and polydisperse. The analysis focused on the resulting population distribution and a statistical comparison to the uniform discrete model. In the course of the investigation, new algorithms were found to be substantial improvements in terms of computational time over the other models and compared favorably to the discrete/continuous model with respect to accuracy. New probability distribution functions for aggregates produced in non-uniform discrete coagulation modeling were derived and incorporated into the population balance equations. These new algorithms made it possible to simulate fractal aggregate coagulation with high accuracy, perfect mass conservation and exceptional computational efficiency. Parameter sensitivity analysis showed that a break-up kernel does not influence total particle concentration within the limited range of having the break-up coefficient less than collision efficiency, but does influence the particle size distribution and coagulation patterns. An aggregate break-up study with various kernel parameters indicated that break-up rate is more influenced by particle volume and not size class or diameter as previously suspected. The new probability distribution functions are found to be useful in fractal aggregation modeling via the higher numerical stability and accuracy. The new particle population model (Eq. (17)) is shown in the investigation to be superior to all of the other models, having mass conservation factor of over 0.99 and computation time of 3.125 × 10 −2 s, thus the new model of Eq. (17) can be used to develop predictive simulations for coagulation in computational fluid dynamics and reaction modeling.