Modeling of crystallization systems via generalized orthogonal polynomials method
Modeling of crystallization systems via generalized orthogonal polynomials method
复制标题
通过广义正交多项式方法对结晶系统进行建模
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
R. Chang
中科院分区：
文献类型：
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作者：
Maw‐Ling Wang;H. Horng;R. Chang
摘要采用广义正交多项式（GOP）对描述结晶过程动力学的粒子数平衡方程进行了模拟。建模的实例包括MSMPR结晶过程的常微分方程、瞬态间歇结晶过程的偏微分方程和结晶器内晶体破裂的泛函微分方程。其关键思想是将人口密度函数表示为。广义正交多项式级数然后通过积分运算矩阵将常（或偏、或泛函）微分方程变换为一组展开系数的代数（或常微分、或代数）方程。使用GOP近似的优点是几乎任何类型的正交多项式都可以用于近似系统，并且具有非常精确的结果。此外，它是非常容易计算的膨胀系数，通过使用…
Abstract The population balance equation which is used to describe the dynamic of crystallization processes is simulated by the proposed generalized orthogonal polynomials (GOP). Examples of modeling include the ordinary differential equation for MSMPR crystallization processes, the partial differential equation for transient batch crystallization processes and the functional differential equation for breakage of crystals within the crystallizer. The key idea is to express the population density function by. a generalized orthogonal polynomials series. The ordinary (or partial, or functional) differential equation is then transformed into a set of algebraic (or ordinary differential, or algebraic) equations of expansion coefficients through the integration operation matrix. The advantage of using GOP approximation is that almost any kind of orthogonal polynomials can be used to approximate the system with very accurate results. Furthermore, it is very easy to calculate the expansion coefficients by using ...