Abstract: Sparse-Lagrangian simulation based on Multiple Mapping Conditioning (MMC) can dramatically decrease the computational costs for Probability Density Function (PDF) methods. In the present research，a series of round jets is simulated to investigate an improved MMC model and analyze the stochastic noise in RMS statistical results of Sparse-Lagrangian simulation. Based on the analysis of the effects of particles number on the performance of characteristic value in the reference space，and the effect of MMC model is more significant in the shear layer where the scalar gradient is large，a generalized model of sparse-Lagrangian MMC is developed to model the small-scale mixing process. Large eddy simulations of several round jet cases are performed by the improved model. The predicted results by the improved model have the same accuracy as previous study using the specific constant characteristic value in the reference space. The production and variation of stochastic noise of RMS statistics are also investigated in the sparse particle field. The results indicate that the stochastic noise depends on the access method from the scalar value of particles to the corresponding LES grid，and the more particles are selected the smaller noise is produced.

Key words: Mapping closure；Probability density function(PDF)；Small scale mixing model；Sparse-Lagrangian simulations；Large eddy simulation；Turbulent combustion

摘要： 发展基于MMC(多维条件映射模型)的稀疏拉格朗日模拟，可大幅降低PDF方法的计算量。通过计算一系列简单的圆管射流算例来验证改进的MMC模型的适用性，并分析稀疏拉格朗日模拟RMS统计结果中的随机噪音误差。由于MMC模型对标量梯度较大的剪切层作用较为明显，同时考虑粒子数变化对参考空间特征值的影响，提出一个稀疏拉格朗日MMC的普适模型，对MMC模型中的小尺度混合过程的模化进行改进。采用改进的模型对圆管射流问题进行模拟，计算结果表明，提出的模型具有通用性，与文献报道中的给定相空间特征值的方法模拟结果基本一致；同时，开展了稀疏粒子场统计均方根中噪声的产生及变化规律的研究，计算结果表明稀疏的拉格朗日模拟中出现的随机噪音干扰大小取决于LES网格从粒子场取值的方式，选取的粒子越多则噪音越小。

关键词: 条件映射；概率密度函数；小尺度混合模型；稀疏拉格朗日模拟；大涡模拟；紊流燃烧