TY  - EJOU
AU  - Ruan, Chunlei 
AU  - Dong, Cengceng 
AU  - Liang, Kunfeng 
AU  - Liu, Zhijun 
AU  - Bao, Xinru 

TI  - Euler’s First-Order Explicit Method–Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2024
VL  - 138
IS  - 3
SN  - 1526-1506

AB  - Using Euler’s first-order explicit (EE) method and the peridynamic differential operator (PDDO) to discretize the time and internal crystal-size derivatives, respectively, the Euler’s first-order explicit method–peridynamic differential operator (EE–PDDO) was obtained for solving the one-dimensional population balance equation in crystallization. Four different conditions during crystallization were studied: size-independent growth, size-dependent growth in a batch process, nucleation and size-independent growth, and nucleation and size-dependent growth in a continuous process. The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods. The method is characterized by non-oscillation and high accuracy, especially in the discontinuous and sharp crystal size distribution. The stability of the EE–PDDO method, choice of weight function in the PDDO method, and optimal time step are also discussed.
KW  - Population balance equation; crystallization; peridynamic differential operator; Euler’s first-order explicit method

DO  - 10.32604/cmes.2023.030607