Modeling and simulation of population balances for particulate processes This work focuses on the modeling and numerical approximations of population balance equations (PBEs) for the simulation of different phenomena occurring in process engineering. The population balance equation (PBE) is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born die grow or leave a given control volume. In the population balance models the one independent variable represents the time the other(s) are property coordinate(s) e.g. the particle volume (size) in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes such as granulation crystallization polymerization emulsion and cell dynamics. The semi discrete high resolution schemes are proposed for solving PBEs modeling one and two dimensional batch crystallization models. The schemes are discrete in property coordinates but continuous in time. The resulting ordinary differential equations can be solved by any standard ODE solver. To improve the numerical accuracy of the schemes a moving mesh technique is introduced in both one and two dimensional cases ...