A quasi-Monte Carlo based flocculation model for fine-grained cohesive sediments in aquatic environments

Shen, Xiaoteng; Lin, Mingze; Zhu, Yanan; Ha, Ho Kyung; Fettweis, M.; Hou, Tianfeng; Toorman, Erik; Maa, Jerome P.‐Y.; Zhang, Jinfeng

doi:10.1016/j.watres.2021.116953

Cited by 13 publications

(15 citation statements)

References 100 publications

(152 reference statements)

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“…In addition, the proposed bi‐QMC model shows the potential to more accurately predict the settling velocity in the future because it is capable of providing more information about the floc system. The information (e.g., volume fraction, see Figure 10d) of the organic part can be easily tracked by the model, which is seldom implemented in models (e.g., Shen et al., 2021; Verney et al., 2011) at present. By incorporating biological processes, the model could be more generally applicable for capturing the seasonal variations in floc properties observed in marine and coastal zones.…”

Section: Discussionmentioning

confidence: 99%

“…The aggregation kernels A ij = α i , j · β i , j ( i ≠ j ≤ N ) of all possible pairs of particles are calculated and the breakage probability function P frag (Equation ) is used to determine whether the next event is aggregation or fragmentation, as suggested by Khelifa and Hill (2006) and Shen et al. (2021) based on the number of overlarge particles, which need to be eliminated if their sizes are unrealistic. The probability function is calculated as follows:

{P}_{\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{g}}=\left\{\begin{array}{c}0,\quad {n}_{b}=0\\ 0.5,\quad {\,n}_{b}=1\\ 1,\quad {\quad n}_{b} > 1\end{array}\right.

where n b is the number of overlarge flocs that are larger than the maximum flocs with size D max .…”

Section: Methodsmentioning

confidence: 99%

“…In Shen et al. (2021), the quasi‐Monte Carlo (QMC) method was applied to consider physical processes such as aggregation and fragmentation as discrete events by using probabilistic tools, showing that the discretization nature of this stochastic method makes it possible to address multivariate biomineral flocculation problems.…”

Section: Introductionmentioning

confidence: 99%

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Biomineral Flocculation of Kaolinite and Microalgae: Laboratory Experiments and Stochastic Modeling

et al. 2022

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The transportation of cohesive sediments has attracted great attention for decades due to the significant influences of sediments on various coastal and offshore engineering (e.g., siltation, dredging, seawall foundation treatment, and riverbed morphology) and environmental (e.g., pollutant transport, phytoplankton photosynthesis, and coastal wetland sustainability) issues (Coats et al., 1989;Edmonds & Slingerland, 2010;Sun et al., 2021;Teisson, 1991). It is a challenge to precisely predict the dynamic processes of cohesive sediments because they exist in the form of flocs (clusters) rather than single particles, which further controls the size and the settling velocity (

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Section: Discussionmentioning

confidence: 99%

{P}_{\mathrm{f}\mathrm{r}\mathrm{a}\mathrm{g}}=\left\{\begin{array}{c}0,\quad {n}_{b}=0\\ 0.5,\quad {\,n}_{b}=1\\ 1,\quad {\quad n}_{b} > 1\end{array}\right.

where n b is the number of overlarge flocs that are larger than the maximum flocs with size D max .…”

Section: Methodsmentioning

confidence: 99%

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Biomineral Flocculation of Kaolinite and Microalgae: Laboratory Experiments and Stochastic Modeling

et al. 2022

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“…In contrast to the above deterministic models, there has also been a kind of flocculation model in a stochastic form based on some probability knowledge [46][47][48]. By considering a sequence of stochastic aggregation and breakup events among particles, Maggi (2008) formulated a stochastic Lagrangian model to describe the flocculation of suspended cohesive sediment flocs in water [46].…”

Section: Introductionmentioning

confidence: 99%

“…Zhu (2018) derived a simple and explicit expression for floc size variation in a fixed flow shear environment based on the entropy concept. Recently, Shen et al (2021) developed a quasi-Monte Carlo model to predict the temporal evolution of floc size distribution of cohesive sediment in aquatic environments, and its validity has been tested by comparing with known simple analytical solutions and two series of laboratory experimental data [48].…”

Section: Introductionmentioning

confidence: 99%

An Extended Entropic Model for Cohesive Sediment Flocculation in a Piecewise Varied Shear Environment

Zhu

Dou

2021

Entropy

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In this study, an extended model for describing the temporal evolution of a characteristic floc size of cohesive sediment particles when the flocculation system is subject to a piecewise varied turbulent shear rate was derived by the probability methods based on the Shannon entropy theory following Zhu (2018). This model only contained three important parameters: initial and steady-state values of floc size, and a parameter characterizing the maximum capacity for floc size increase (or decay), and it can be adopted to capture well a monotonic pattern in which floc size increases (or decays) with flocculation time. Comparison with 13 literature experimental data sets regarding floc size variation to a varied shear rate showed the validity of the entropic model with a high correlation coefficient and few errors. Furthermore, for the case of tapered shear flocculation, it was found that there was a power decay of the capacity parameter with the shear rate, which is similar to the dependence of the steady-state floc size on the shear rate. The entropic model was further parameterized by introducing these two empirical relations into it, and the finally obtained model was found to be more sensitive to two empirical coefficients that have been incorporated into the capacity parameter than those in the steady-state floc size. The proposed entropic model could have the potential, as an addition to existing flocculation models, to be coupled into present mature hydrodynamic models to model the cohesive sediment transport in estuarine and coastal regions.

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Improved accuracy and convergence of homotopy‐based solutions for aggregation–fragmentation models

Kushwah

Saha

2022

Math Methods in App Sciences

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We discuss the formulation of a numerical scheme based on the homotopy method to solve different aggregation–fragmentation models including the simultaneous event. Several test cases are considered and analyzed qualitatively and quantitatively to ascertain the improved accuracy and efficiency of the proposed model over the existing semi‐analytical models. The generalized solution of the truncated problem is obtained for some test cases, which in the limiting sense tends to the exact solution. A detailed convergence analysis of the scheme is also studied.

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A quasi-Monte Carlo based flocculation model for fine-grained cohesive sediments in aquatic environments

Cited by 13 publications

References 100 publications

Biomineral Flocculation of Kaolinite and Microalgae: Laboratory Experiments and Stochastic Modeling

Biomineral Flocculation of Kaolinite and Microalgae: Laboratory Experiments and Stochastic Modeling

An Extended Entropic Model for Cohesive Sediment Flocculation in a Piecewise Varied Shear Environment

Improved accuracy and convergence of homotopy‐based solutions for aggregation–fragmentation models

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