In this work, lattice Boltzmann method (LBM) is developed for efficient and accurate solution of multi-dimensional population balance equations (PBEs) used to model crystallization processes with growth and nucleation. Detailed derivation of LBM for multi-dimensional advection equation is presented, where the velocity is a function of space coordinates. The developed scheme is subsequently applied to solve multi-dimensional PBEs with size-dependent growth rate by drawing an analogy between the advection equation and the PBE. The computational advantage of LBM is shown by solving several benchmark examples taken from the literature and comparing the results with those obtained using well-established high resolution (HR) method. It is found that LBM provides at least as accurate solution as HR method, while requiring lower computation time.
Majumder, A., Kariwala, V., Ansumali, S., & Rajendran, A. (2012). Lattice Boltzmann method for multi-dimensional population balance models in crystallization. Chemical Engineering Science, 70, 121-134. https://doi.org/10.1016/j.ces.2011.04.041