Modi ed method of characteristics for solving population balance equations

This paper presents a new numerical method for solving the population balance equation using the modi ed method of characteristics. Aggregation and break-up are neglected but the density function variations in the three-dimensional space and its dependence on the external elds are accounted for. The method is an interpretation of the Lagrangian approach. Based on a pre-speci ed grid, it follows the particles backward in time as opposed to forward in the case of traditional method of characteristics. Unlike the direct marching method, the inverse marching method uses a xed grid thus, making it compatible with other numerical schemes (e.g. nite-volume, nite elements) that may be used to solve other coupled equations such as the mass, momentum, and energy conservation equations. The numerical solutions are compared with the exact analytical solutions for simple one-dimensional ow cases. Very good agreement between the numerical and the theoretical solutions has been obtained con rming the validity of the numerical procedure and the associated computer program. Copyright ? 2003 John Wiley & Sons, Ltd.