Moving Finite Elements Method Applied to Dynamic Population Balance Equations

摘要

A moving finite elements scheme is developed and used for solving 1-D dynamic population balance equations (PBE). The method stands on the weighted finite-elements based approach, and the local solutions are represented by cubic Hermite polynomials. The weighting function is the gradient of residuals with respect to time derivatives of the solution at the nodes and nodal velocities. The general PBE considered includes nucleation, growth, aggregation and breakage terms. The accuracy of the moving finite elements method (MFEM) is evaluated by comparing the results to the analytical solution in problems involving combinations of the first three phenomena considered. The formulation addressed was successful when used for solving a two-phase system representing a semibatch precipitation reactor. The MFEM enables one to achieve accurate results at reasonable CPU times, thus, showing to be adequate for these kind of problems.