聚合物流体数值模拟的多层蒙特卡罗方法  

Multilevel Monte Carlo method for numerical simulation of polymer fluid

作　　者：后翠红 苏进[1] HOU Cuihong;SU Jin(School of Science,Xi’an Polytechnic University,Xi’an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2020年第2期85-92,共8页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11601411)。

摘　　要：探讨聚合物流体分子模型的应力计算问题,给出了基于Euler格式随机Brown轨道的多层蒙特卡罗(multilevel Monte Carlo,MLMC)方法。该方法利用多尺度时间步长思想优化尺度样本数,提高计算效率。Hooke和FENE模型的数值结果表明:在低Wi(Weissenberg)数情况下,MLMC方法比标准蒙特卡罗(StdMC)方法的计算成本更低,随机误差更小;而且目标精度越高,MLMC方法的计算效率提升越明显。进一步研究发现,由于在W i数较小时随机系统的Brown力比弹性力占优,应力的样本方差对MLMC层数的变化较敏感。因此,MLMC方法可以有效的降低随机误差。For the molecular model of polymer fluids,a multilevel Monte Carlo(MLMC)method based on the random Brown orbit of the Euler scheme is presented to calculate polymer stress.This method mainly optimizes the number of scale samples through the idea of multi-scale time step to improve the calculation efficiency.Through the numerical simulation of Hooke and FENE models,it is found that the MLMC method has lower calculation cost and less random error than the standard Monte Carlo(StdMC)method under low Wi(Weissenberg)numbers.Moreover,the higher the accuracy of the target grows,the more greatly the calculation efficiency of MLMC method is improved.Further research shows that the Brownian force of the stochastic system is superior to the elastic force when the Wi number is small,so the variance of polymer stress is more sensitive to the change in levels of MLMC method,and increasing the number of levels can reduce the random error effectively.

关 键 词：聚合物流体 Brown构型场方法 数值模拟 多层蒙特卡罗方法 

分 类 号：O368[理学—流体力学]