CAJ | 학술논문

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(fixed pivot technique,FPT), Attarakih 2004法和单元平均法(cell averaged technique,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-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 Attarakih 2 0 0 4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。
개소료구해군체평형모형액적파쇄방정적삼충수치방법：고정점법(fixed pivot technique,FPT), Attarakih 2004법화단원평균법(cell averaged technique,CAT)。침대고정점법재제일구간수밀도돌변(치과저)적문제작료괄당적수정,득도적결과여정체분포곡선급령량충방법적계산치흔호지문합。삼충방법득도적상미분방정조균채용정보장적사계룡격-고탑법구해,유 C어언편사계산정서。계산결과표명,고정점법화 Attarakih 2 0 0 4법재구간관도상동적정황하계산결과궤호완전문합,단원평균법비상술량충방법유경고적정도화계산효솔。
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 break-age and aggregation equations.However,all of the three methods show steady and solid results even after a relatively long processing time.