摘要
通过对基于颗粒输运随机统计模拟的DSMC方法模拟准则的分析研究,定义了该方法中统计量的噪声、相对统计涨落及置信度。引入概率论中的切比雪夫不等式,利用正态分布平衡流统计理论,推导出DSMC方法模拟流场宏观速度和温度的统计噪声理论公式,并以过渡流区平面Couette剪切流和激波结构内流动为算例进行数值模拟验证与理论分析。结果表明,在一定的置信度下,选择适当的模拟参考值,DSMC统计量的噪声除与样本容量(模拟分子数及统计抽样次数)的平方根成反比例外,速度的相对统计涨落还与流场马赫数成反比,而温度的相对统计涨落与流场宏观参数无关。这为控制DSMC模拟结果的相对统计涨落提供了理论指导和计算依据。
On the basis of analysis of the simulation principles for the DSMC method based on particle transportation stochastic simulations, the statistical noise, relative statistical fluctuations and their confi- dences are defined. According to the Chebysheve inequality in probability theory, the theoretical formulas on statistical fluctuations of flow velocity and temperature in the flow field are deduced and presented by using equilibrium statistical theory of normal distribution. Then, their correctness and adaptability are numerically validated and theoretically analyzed by examples of the planar Couette shear flow in the transition flow re- gime and the normal shock wave flow. It is shown that, under certain confidences and the proper choice of simulating parameters, the statistical noise from the DSMC simulation is inversely proportional to the square root of the sample size （number of simulated molecules and statistical sampling times）, and the relative sta- tistical fluctuation of the flow velocity is inversely proportional to local Mach number of the flow field, but the relative statistical fluctuation of the temperature is independent of macroscopic flow parameters besides. The studies provide theoretical guidelines and computational criteria for controlling the relative statistical fluctuations from the DSMC simulation.
出处
《空气动力学学报》
CSCD
北大核心
2013年第1期1-8,共8页
Acta Aerodynamica Sinica
基金
国家自然科学基金(91016027)
国防基础科研基金(51313030104)
