考虑时间相关性的DSMC方法统计误差分析（英文）

发布时间：2018-03-03 03:30

本文选题：DSMC方法　切入点：统计误差　出处：《应用数学和力学》2016年12期 　论文类型：期刊论文

【摘要】：过去的半个世纪,DSMC方法已经成为求解稀薄气体流动最有力的数值工具.它的精度问题得到了许多研究者的关注.DSMC方法的误差可以分为两类,一类是统计误差,另一类是数值误差.在DSMC方法中,宏观流动性质是通过对微观分布信息的抽样平均而得到的,因此模拟结果本质上是符合概率统计的,需要对由于有限的抽样步数而导致的统计误差进行仔细地量化考察.统计误差在DSMC方法中占有重要的地位,但是直到今天仍没有被完全研究清楚.尽管前人做了一些研究,但是通常都假设抽样结果是相互独立的,对于获得精确结果所需的最小抽样步数,还没有清晰统一的认识.时间相关性会增加统计误差理论分析的难度,因此在已有的工作中很少被考虑到.使用统计学中的自相关函数以及修正的中心极限定理,可以量化抽样结果中的时间相关性.在考虑抽样结果时间相关性的基础上,研究了DSMC方法中的统计误差,考核算例为一维的Couette流动问题.量化的结果显示,时间相关性对统计误差的影响很大.时间相关性可增大随机变量抽样序列的方差.
[Abstract]:The past half century, DSMC has become the most powerful numerical tool for the rarefied gas flow. It obtained the error precision of.DSMC method on many researchers can be divided into two categories, one is the statistical error, the other is the numerical error. In the DSMC method, which is the macroscopic flow properties by sampling on the micro average distribution information, so the simulation result is consistent with the nature of probability statistics, careful quantitative study need statistical error caused due to the limited number of sampling step. The statistical error plays an important role in the DSMC method, but until today is still not fully understood. Although previous do some research, but usually assume that the sampling results are independent of each other, the minimum sampling step to obtain accurate results required number, no clear and unified understanding. The time correlation will increase The difficulty with statistical analysis of error theory, so the existing work is rarely taken into account. The use of statistics in the autocorrelation function and the correction of the central limit theorem can be quantified in time correlation sampling results. Considering the time dependence on the sampling results, the statistical error in the DSMC method, examples for the problem of one-dimensional Couette flow. Quantitative results show that the influence of time correlation of statistical error. The variance time correlation can increase the sampling sequence of random variables.

【作者单位】：中国空气动力研究与发展中心计算空气动力研究所;
【分类号】：O35

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