液滴破碎方程的三种数值解法及分析比较  

Comparison and Analysis of Three Methods for Numerical Solution of Droplet Breakage Equation

作　　者：王日腾[1] 李春晖[1] 矫彩山[1] 

机构地区：[1]哈尔滨工程大学,黑龙江哈尔滨150001

出　　处：《核化学与放射化学》2014年第B12期90-97,共8页Journal of Nuclear and Radiochemistry

摘　　要：介绍了求解群体平衡模型液滴破碎方程的三种数值方法：固定点法（fixedpivottechnique，FPT），Attarakih2004法和单元平均法（cellaveragedtechnique，CAT）。针对固定点法在第一区间数密度突变（值过低）的问题作了适当的修正，得到的结果与整体分布曲线及另两种方法的计算值很好地吻合。三种方法得到的常微分方程组均采用定步长的四阶龙格一库塔法求解，由C语言编写计算程序。计算结果表明，固定点法和Attarakih2004法在区间宽度相同的情况下计算结果几乎完全吻合，单元平均法比上述两种方法有更高的精度和计算效率。Three methods for numerical solution of droplet breakage equation（PBE） under the population balance concept in batch system are introduced： fixed pivot technique（FPT）, method developed by Attarakih （MDA）, cell averaged technique （CAT）. Differences and accuracies are also discussed. For overcoming the significant deviation of number density in the left boundary of FPT, a slight modification is recommended, and the numerical results show good agreement with analytical solution. All of numerical solutions for differential equations set are approached by fourth-order Runge-Kutta method, and the algorithms are programmed by C programming language. The numerical results show that the FPT and MDA have almost the same accuracy under large interval width, while the CAT is of better accuracy and efficiency, which show a prosperous future in solving the simultaneous breakage and aggregation equations. However, all of the three methods show steady and solid results even after a relatively long processing time.

关 键 词：群体平衡模型 液滴破碎 数值方法 

分 类 号：TL941.19[核科学技术—辐射防护及环境保护]