粒子破碎过程的新解析解和数值解

A. Hasseine, M. Hlawitschka, Waid Omar, H. Bart
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引用次数: 2

摘要

目的:利用Adomian分解法和分段连续基函数分别得到了涉及间歇和连续流分解过程的种群平衡方程的解析解和近似解。方法先进数值方法的关键是用正交切比雪夫基多项式表示分散相的数分布函数。该方法具有同时给出分布和不同所需矩的优点,是一种简单有效的方法。因此,它不需要从初始问题和丢失信息的变换得到的矩量计算中构造分布。结果:通过求解破裂方程并与Adomian分解方法得到的解析解进行比较,对该数值方法的性能进行了评价,Adomian分解方法通常允许对该方法进行分析。结论:本文数值方法得到的数值结果与新的PBE解析解进行了比较。结果表明,分段连续基函数与解析解具有可比性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
New Analytical and Numerical Solutions of the Particle Breakup Process
Objective: In this work, we obtained the analytical and approximate solutions of the population balance equations (PBEs) involving the breakup process in batch and continuous flow by applying the Adomian decomposition method and piecewise continuous basis functions, respectively. Methods: The key to the advanced numerical method is to represent the number distribution function of the dispersed phase through the orthogonal Chebyshev basis polynomials. It is a straightforward and effective method that has the advantage of simultaneously giving the distribution and the different required moments. Therefore, it does not require the construction of the distribution from moments computations obtained by the transformation of the initial problem and the lost information. Results: The performance of this numerical approach is evaluated by solving breakup equation and comparison against analytical solutions obtained from the Adomian decomposition method, which generally allows the analysis of this approach. Conclusion: The numerical results obtained by the present numerical method were compared with the new analytical solutions of the PBE. It was found that both piecewise continuous basis functions and analytical solutions have comparable results.
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