Purpose

The purpose of this study is to investigate the aerosol dynamics of the particle coagulation process using a newly developed weighted fraction Monte Carlo (WFMC) method.

Design/methodology/approach

The weighted numerical particles are adopted in a similar manner to the multi-Monte Carlo (MMC) method, with the addition of a new fraction function (α). Probabilistic removal is also introduced to maintain a constant number scheme.

Findings

Three typical cases with constant kernel, free-molecular coagulation kernel and different initial distributions for particle coagulation are simulated and validated. The results show an excellent agreement between the Monte Carlo (MC) method and the corresponding analytical solutions or sectional method results. Further numerical results show that the critical stochastic error in the newly proposed WFMC method is significantly reduced when compared with the traditional MMC method for higher-order moments with only a slight increase in computational cost. The particle size distribution is also found to extend for the larger size regime with the WFMC method, which is traditionally insufficient in the classical direct simulation MC and MMC methods. The effects of different fraction functions on the weight function are also investigated.

Originality Value

Stochastic error is inevitable in MC simulations of aerosol dynamics. To minimize this critical stochastic error, many algorithms, such as MMC method, have been proposed. However, the weight of the numerical particles is not adjustable. This newly developed algorithm with an adjustable weight of the numerical particles can provide improved stochastic error reduction.

中文翻译：

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一种新的粒子凝聚加权分数蒙特卡罗方法

目的

本研究的目的是使用新开发的加权分数蒙特卡罗 (WFMC) 方法研究粒子凝结过程的气溶胶动力学。

设计/方法/方法

加权数值粒子以类似于多蒙特卡罗 (MMC) 方法的方式采用，并添加了新的分数函数 (α)。还引入了概率去除以保持常数方案。

发现

模拟和验证了具有恒定内核、自由分子凝聚内核和不同粒子凝聚初始分布的三个典型案例。结果表明蒙特卡罗 (MC) 方法与相应的解析解或分段方法结果之间具有极好的一致性。进一步的数值结果表明，与传统的高阶矩 MMC 方法相比，新提出的 WFMC 方法中的临界随机误差显着降低，而计算成本仅略有增加。还发现使用 WFMC 方法可以扩展更大的粒度范围，这在传统的直接模拟 MC 和 MMC 方法中是不够的。还研究了不同分数函数对权函数的影响。

原创价值

在气溶胶动力学的 MC 模拟中，随机误差是不可避免的。为了最小化这种关键的随机误差，已经提出了许多算法，例如 MMC 方法。然而，数值粒子的权重是不可调整的。这种新开发的算法具有可调整的数值粒子权重，可以提供改进的随机误差减少。