Numerical analysis of finite volume schemes for population balance equations

This work describes the numerical analysis of finite volume schemes for population balance equations in particulate processes, incorporating aggregation, breakage, growth and source terms.
These equations are a type of partial integro-differential equations. Such equations can be solved analytically only for some specific aggregation and breakage kernels. This motivates us to study numerical schemes and the numerical analysis for these equations.

The convergence analysis of a finite volume method for the aggregation and multiple breakage equations on five different types of uniform and non-uniform meshes is investigated. The criteria for the preservation of different moments is discussed. Based on this criteria, one moment and two moments preserving finite volume schemes are proposed for solving all the coupled processes.

Finally we state some applications of aggregation-breakage equations in nano-technology.