Key Laboratory of Ministry of Education for Coastal Disaster and Protection, Hohai University, Nanjing 210098, China; College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China; Engineering Research Center of Ministry of Education for Dredging Technology, Hohai University, Nanjing 210098, China.
College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China.
Water Res. 2021 Apr 15;194:116953. doi: 10.1016/j.watres.2021.116953. Epub 2021 Feb 22.
The quasi-Monte Carlo (QMC) method was enhanced to solve the population balance model (PBM) including aggregation and fragmentation processes for simulating the temporal evolutions of characteristic sizes and floc size distributions (FSDs) of cohesive sediments. Ideal cases with analytical solutions were firstly adopted to validate this QMC model to illustrate selected pure aggregation, pure fragmentation, and combined aggregation and fragmentation systems. Two available laboratory data sets, one with suspended kaolinite and the other with a mixture of kaolinite and montmorillonite, were further used to monitor the FSDs of cohesive sediments in controlled shear conditions. The model results show reasonable agreements with both analytical solutions and laboratory experiments. Moreover, different QMC schemes were tested and compared with the standard Monte Carlo scheme and a Latin Hypercube Sampling scheme to optimize the model performance. It shows that all QMC schemes perform better in both accuracy and time consumption than standard Monte Carlo scheme. In particular, compared with other schemes, the QMC scheme using Halton sequence requires the least particle numbers in the simulated system to reach reasonable accuracy. In the sensitivity tests, we also show that the fractal dimension and the fragmentation distribution function have large impacts on the predicted FSDs. This study indicates a great advance in employing QMC schemes to solve PBM for simulating the flocculation of cohesive sediments.
拟蒙特卡罗（QMC）方法得到了增强，以解决包括聚集和破碎过程的颗粒平衡模型（PBM），用于模拟粘性泥沙特征粒径和絮体粒径分布（FSD）的时间演化。首先采用具有解析解的理想情况来验证这个 QMC 模型，以说明选择的纯聚集、纯破碎和聚集与破碎相结合的系统。进一步利用两个现有的实验室数据集，一个是悬浮高岭石，另一个是高岭石和蒙脱石的混合物，监测粘性泥沙在受控剪切条件下的 FSD。模型结果与解析解和实验室实验都有很好的一致性。此外，测试了不同的 QMC 方案，并与标准蒙特卡罗方案和拉丁超立方抽样方案进行了比较，以优化模型性能。结果表明，所有 QMC 方案在准确性和时间消耗方面都比标准蒙特卡罗方案表现更好。特别是，与其他方案相比，使用哈顿序列的 QMC 方案在模拟系统中需要最少的粒子数就能达到合理的精度。在敏感性测试中，我们还表明分形维数和破碎分布函数对预测的 FSD 有很大影响。这项研究表明，采用 QMC 方案来解决 PBM 以模拟粘性泥沙的絮凝是一个很大的进展。
