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Spectral solution of the breakage-coalescence population balance equation Picard and Newton iteration methods

机译：破损-凝聚总体平衡方程Picard和Newton迭代方法的频谱解

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摘要

The behavior of dispersed systems such as gas-liquids or liquid-liquid systems depends on the characteristics of the dispersed phase. The population balance (PB) equation is encountered in numerous engineering disciplines in order to describe complex processes where the accurate prediction of the dispersed phase plays a major role for the overall behavior of the system. In the present study, the orthogonal collocation, Galerkin and least-squares methods have been adopted to solve a non-linear PB equation which consists of both breakage and coalescence terms. The performance of the methods is demonstrated by comparing the numerical solution results with the (manufactured) analytical solution of the problem. For the least-squares method, the choice of linearization technique influences the numerical performance, whereas the Gaierkin and orthogonal collocation methods obtain the same numerical accuracy for both the Picard and Newton iteration techniques. The least-squares method suffers from lack of convergency using the Picard method. On the other hand, if the Newton method is employed, the least-squares method obtains the same accuracy as the Galerkin and orthogonal collocation methods.
机译：分散体系（如气液体系或液液体系）的行为取决于分散相的特性。为了描述复杂的过程，在众多的工程学科中都遇到了人口平衡（PB）方程，其中分散相的准确预测对于系统的整体性能起着重要的作用。在本研究中，采用正交搭配，Galerkin和最小二乘方法来求解由破损和合并项组成的非线性PB方程。通过将数值解结果与问题的（制造的）解析解进行比较，证明了该方法的性能。对于最小二乘法，线性化技术的选择会影响数值性能，而盖尔金法和正交搭配法对于Picard和Newton迭代技术均获得相同的数值精度。最小二乘法使用Picard方法缺乏收敛性。另一方面，如果采用牛顿法，则最小二乘法可获得与伽勒金法和正交配置法相同的精度。

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