A least squares method for the solution of population balance problems

A general framework is developed, using the least squares method (LSM), for the solution of a generalized population balance equation. The basic idea in the LSM is to minimize the integral of the square of the residual over the computational domain. The capability of the method for solving the PBE is evaluated by using case problems involving coalescence and breakage kernels having analytical solutions which allow the analysis of the method to be performed in a general way. By using the LSM to solve the PBE, the error in the properties of the distribution function depends on the order of the expansion, thus avoiding the introduction of heuristic rules to obtain sufficient accuracy in the values of a few of the physical moments. An interesting characteristic of the LSM applied to PBE is that a low number of equations are required to solve the problem.