A hybrid sectional moment projection method for discrete population balance dynamics involving inception, growth, coagulation and fragmentation

Wu, Shaohua; Yang, Shiliang; Tay, Kun Lin; Yang, Wenming

doi:10.1016/j.ces.2021.117333

Cited by 6 publications

(3 citation statements)

References 63 publications

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“…The onset of high-speed computing has facilitate many researchers to work on the solutions of different types of PBEs as they bear significant responsibilities in different manufacturing units as well as in CFD-simulations. [17][18][19][20][21][22][23] However, the complicated nature of the PBE models has rendered the search for exact solutions within a few number of simple kernels. [24][25][26] Therefore, numerical methods are required to solve the PBEs.…”

Section: Literature Review and Motivationmentioning

confidence: 99%

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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Section: Literature Review and Motivationmentioning

confidence: 99%

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

Kushwah

Saha

2022

Math Methods in App Sciences

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“…To solve the PBE, there are different solution approaches in literature, such as lattice Boltzmann method [7] , [8] , sectional method [9] , [10] and homotopy method [10] , [11] . A critical review that provides a comprehensive analysis of the state of the art in numerical approaches with emphasis in algorithmic details and their applications for solving PBEs can be found in Singh et al [12] .…”

Section: Introductionmentioning

confidence: 99%

Further developments of the extended quadrature method of moments to solve population balance equations

Turan¹,

Dutta²

2023

Heliyon

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“…These existing analytical solutions are of great significance and can be used as a useful benchmark for validating different numerical methods. Different numerical approaches aiming at different problems of aerosol dynamics are developed to approximate the solution of the GDE for an aerosol system of interest, such as the sectional method (SM) (Gelbard et al , 1980; Prakash et al , 2003; Zhang et al , 2020; Wu et al , 2022), method of moments (MOMs) (Frenklach and Harris, 1987; McGraw, 1997; Yu et al , 2008; Yu and Chan, 2015; Chan et al , 2018; Li et al , 2019; Liu et al , 2019c; Shen et al , 2020; Yang et al , 2020; Jiang et al , 2021; Shen et al , 2022) and Monte Carlo (MC) method (Gillespie, 1975; Garcia et al , 1987; Liffman, 1992; Smith and Matsoukas, 1998; Kruis et al , 2000; Lin et al , 2002; Zhao et al , 2009; Xu et al , 2014; Kotalczyk and Kruis, 2017; Liu and Chan, 2017; Liu and Chan, 2018a, 2018b; Liu et al , 2019a, 2019b; Liu and Chan, 2020; Liu et al , 2021; Jiang and Chan, 2021; Liu et al , 2022). As the discrete nature of the MC method perfectly matches the stochastic properties of particle motion, it can be used to closely simulate the behaviour of particles.…”

Section: Introductionmentioning

confidence: 99%

A new sorting algorithm-based merging weighted fraction Monte Carlo method for solving the population balance equation for particle coagulation dynamics

Wang

Chan

2022

HFF

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Purpose The purpose of this study is to present a newly proposed and developed sorting algorithm-based merging weighted fraction Monte Carlo (SAMWFMC) method for solving the population balance equation for the weighted fraction coagulation process in aerosol dynamics with high computational accuracy and efficiency. Design/methodology/approach In the new SAMWFMC method, the jump Markov process is constructed as the weighted fraction Monte Carlo (WFMC) method (Jiang and Chan, 2021) with a fraction function. Both adjustable and constant fraction functions are used to validate the computational accuracy and efficiency. A new merging scheme is also proposed to ensure a constant-number and constant-volume scheme. Findings The new SAMWFMC method is fully validated by comparing with existing analytical solutions for six benchmark test cases. The numerical results obtained from the SAMWFMC method with both adjustable and constant fraction functions show excellent agreement with the analytical solutions and low stochastic errors. Compared with the WFMC method (Jiang and Chan, 2021), the SAMWFMC method can significantly reduce the stochastic error in the total particle number concentration without increasing the stochastic errors in high-order moments of the particle size distribution at only slightly higher computational cost. Originality/value The WFMC method (Jiang and Chan, 2021) has a stringent restriction on the fraction functions, making few fraction functions applicable to the WFMC method except for several specifically selected adjustable fraction functions, while the stochastic error in the total particle number concentration is considerably large. The newly developed SAMWFMC method shows significant improvement and advantage in dealing with weighted fraction coagulation process in aerosol dynamics and provides an excellent potential to deal with various fraction functions with higher computational accuracy and efficiency.

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A hybrid sectional moment projection method for discrete population balance dynamics involving inception, growth, coagulation and fragmentation

Cited by 6 publications

References 63 publications

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

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

Further developments of the extended quadrature method of moments to solve population balance equations

A new sorting algorithm-based merging weighted fraction Monte Carlo method for solving the population balance equation for particle coagulation dynamics

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