Finite‐element scheme for solution of the dynamic population balance equation

Abstract

Abstract A first‐order finite‐element scheme is proposed for solving the 1‐D dynamic population balance equation. The model includes the kinetic processes of nucleation, growth, aggregation, and breakage in a spatially uniform system with or without flow. The numerical scheme features improved stability by taking into account the convective nature of the growth term, and enhanced conservation of moments at nonuniform grids by identifying and mitigating the sources of conservation error in the evaluation of the aggregation source term. Exhaustive benchmarking is carried out against analytical solutions for size‐dependent growth and nucleation, size‐dependent aggregation with a variety of kernels, binary and multiple breakage with uniform and parabolic daughter particle distributions, and combinations of these, respectively. In all cases tested the method proves capable of producing accurate results at a reasonable CPU time, while being relatively simple and easy to implement.