A lattice Boltzmann method (LBM) is introduced for accurate simulation of crystallization processes modelled using one-dimensional population balance equations (PBEs) with growth and nucleation phenomena. LBM for PBEs with size independent growth is developed by identifying their similarity with the advection equation. To obtain an efficient method for PBEs with size dependent growth, a coordinate transformation scheme is introduced, which can handle processes with size independent and size dependent growth rates in the same framework. The performance of the proposed scheme is verified using benchmark examples drawn from literature, which shows that LBM provides at least the same level of accuracy, while requiring lower computation time than the well-established high resolution finite volume method.
Majumder, A., Kariwala, V., Ansumali, S., & Rajendran, A. (2010). Entropic lattice Boltzmann method for crystallization processes. Chemical Engineering Science, 65(13), 3928–3936. https://doi.org/10.1016/j.ces.2010.03.030