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- Title
Euler's First-Order Explicit Method--Peridynamic Differential Operator for Solving Population Balance Equations of the Crystallization Process.
- Authors
Chunlei Ruan; Cengceng Dong; Kunfeng Liang; Zhijun Liu; Xinru Bao
- Abstract
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.
- Subjects
DIFFERENTIAL operators; CRYSTALLIZATION; DISCONTINUOUS precipitation; BATCH processing; CONTINUOUS processing
- Publication
CMES-Computer Modeling in Engineering & Sciences, 2024, Vol 138, Issue 3, p3033
- ISSN
1526-1492
- Publication type
Article
- DOI
10.32604/cmes.2023.030607