A new highly efficient and stable population array (PA) algorithm to solve multi-dimension population balance equation - Wu, Yuanyi; Rohani, Sohrab (Chemical engineering science, 2021)
•Fast and accurate numerical solver of a crystallization population balance model.•Efficient computation for multi-dimensional crystal growth problems.•Modelling complex mechanisms including breakage and agglomeration of crystals. Solving the population balance equation (PBE) requires a robust and efficient numerical method. The widely used discretization techniques are prone to numerical diffusion caused by over-prediction of the crystal size. The multi-dimensional solution is highly inefficient due to the computations performed on the unused grids. We present an efficient numerical solver using the population array (PA) method, which employs an array to store the size and counts information as a sparse grid. The two-dimensional pure-growth case using the proposed technique could achieve ten times speedup compared to the high-resolution discretization method. A row compression algorithm is proposed to reduce the computational cost by grouping the crystals with similar internal coordinates. Various numerical cases including crystal growth, continuous crystallization, polymorphic transformation, agglomeration, and breakage were simulated and compared with the analytical solutions and the established high-resolution discretization schemes to confirm the accuracy and computational efficiency of the proposed PA algorithm.