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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。
Based on the analysis and research of DSMC method simulation criterion based on stochastic statistical simulation of particle transport, the noise, relative statistical fluctuation and confidence of the statistics in this method are defined. By introducing the Chebyshev inequality in probability theory and using the statistic theory of normal distribution equilibrium flow, the statistical noise theoretical formula for simulating the macro-velocity and temperature in the flow field is deduced by the DSMC method. The plane Couette shear flow and the shock structure Internal flow is an example for numerical simulation verification and theoretical analysis. The results show that under the certain confidence level, the appropriate statistical reference value is selected, the noise of DSMC statistic is inversely proportional to the square root of sample size (number of simulated molecules and number of statistical sampling) The field Mach number is inversely proportional to, and the relative statistical temperature fluctuation has nothing to do with the macroscopic parameter of the flow field. This provides theoretical guidance and calculation basis for controlling the relative statistical fluctuation of DSMC simulation results.