求解间歇结晶中种群平衡方程的高阶紧致差分法

IF 3.9 3区 工程技术 Q2 ENGINEERING, CHEMICAL
Fangkun Zhang, Zhenqu Hong, Chuan Li, Zimu Diao, Bin Lian, Baoming Shan, Yinglong Wang, Qilei Xu
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引用次数: 0

摘要

由于大多数人口平衡方程(PBEs)通常没有解析解,因此通常使用计算代价高昂的高阶或高分辨率方法来获得精确的数值解。本文提出了一种新的高阶紧致差分(HOCD)方法,在空间和时间上都具有四阶精度。该方法具有较高的计算精度,为批量冷却结晶过程中的一维种群平衡建模提供了高效的解决方案。提出了一种基于两层格式的紧凑差分格式,每个时间层包含三个网格点。采用Tomas算法直接求解三对角线性方程组。通过冯·诺依曼稳定性分析证明了其稳定性。与Upwind、Lax-Wendroff和高分辨率有限体积(HR-FVM)方法相比,HOCD方法具有更高的计算精度和效率,没有数值扩散或色散。通过多个案例研究证明了该方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

High-Order Compact Difference Method for Solving Population Balance Equations in Batch Crystallization

High-Order Compact Difference Method for Solving Population Balance Equations in Batch Crystallization
As there is typically no analytical solution to most population balance equations (PBEs) of interest, computationally expensive high-order or high-resolution methods are typically used to obtain accurate numerical solutions. In this study, a new high-order compact difference (HOCD) method is proposed to solve the PBE with fourth-order accuracy in both space and time. This method provides high computational accuracy with a computationally efficient solution for one-dimensional population balance modeling in batch cooling crystallization processes. A compact difference scheme is proposed based on a two-layer format, with three grid points involved at each time level. Tridiagonal linear equations are solved directly using Tomas’ algorithm. Stability is demonstrated through von Neumann stability analysis. Compared to the Upwind, Lax–Wendroff, and high-resolution finite volume (HR-FVM) methods, the HOCD method offers higher computational accuracy and efficiency, without numerical diffusion or dispersion. The effectiveness of this method is demonstrated through multiple case studies.
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来源期刊
Industrial & Engineering Chemistry Research
Industrial & Engineering Chemistry Research 工程技术-工程:化工
CiteScore
7.40
自引率
7.10%
发文量
1467
审稿时长
2.8 months
期刊介绍: ndustrial & Engineering Chemistry, with variations in title and format, has been published since 1909 by the American Chemical Society. Industrial & Engineering Chemistry Research is a weekly publication that reports industrial and academic research in the broad fields of applied chemistry and chemical engineering with special focus on fundamentals, processes, and products.
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