Error estimation of TEMOM for Brownian coagulation

Xie, Minge

doi:10.1080/02786826.2016.1207058

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…In addition, the derivation of the TEMOM is completely based on a mathematical method, and no artificial assumption is introduced. The estimated truncation error of TEMOM model for Brownian coagulation has been examined [26], and the particle dimensionless moments corresponding to the deviation of PSD tends to a constant at long time [27], which is consistent with the self-preserving hypothesis. This method provides a new way for analyzing the coagulation problem theoretically.…”

Section: Introductionmentioning

confidence: 65%

Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium

Xie¹

2021

Preprint

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The information entropy for Smoluchowski coagulation equation is proposed based on statistical mechanics. And the normalized particle size distribution is a lognormal function at equilibrium from the principle of maximum entropy and moment constraint. The geometric mean volume and standard deviation in the distribution function are determined as simple constant. The results reveal that the assumption that algebraic mean volume be unit in self-preserving hypothesis is reasonable in some sense. Based on the present definition of information entropy, the Cercignani’s conjecture holds naturally for Smoluchowski coagulation equation. Together with the proof that the conjecture is also true for Boltzmann equation, Cercignani’s conjecture will holds for any two-body collision systems, which will benefit the understanding of Brownian motion and molecule kinematic theory, such as the stability of the dissipative system, and the mathematical theory of convergence to thermodynamic equilibrium.

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Section: Introductionmentioning

confidence: 65%

Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium

Xie¹

2021

Preprint

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“…Xie (2016) verified the TEMOM with H = 2 and / = 1 as a highly reliable closure scheme for solving the PBE. With an increase in / in the present study, the reliability of the algorithm scheme is high.…”

Section: Breakagementioning

confidence: 83%

An Efficient Algorithm Scheme for Implementing the TEMOM for Resolving Aerosol Dynamics

Liu

Koivisto

2017

Aerosol Sci Eng

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This paper presents a new algorithm scheme for implementing the Taylor-series expansion method of moments (TEMOM), which is a general method for solving the population balance equation. Instead of deriving moment ordinary differential equations (ODEs) for particular aerosol dynamics, the new numerical algorithm develops a subroutine that corresponds to types of kernels of aerosol dynamics rather than a particular kernel. Consequently, the TEMOM can be conveniently applied to types of dynamics rather than a particular dynamics, and the derivation from the PBE to moment ODEs is avoided. A key aspect to the new algorithm scheme is that the particle kernels are written in a general form, allowing for a universal expression of aerosol dynamics. The closure of ODEs for moments was accomplished by implementing a new Taylor-series expansion closure function with two varying parameters H and /, which enables the TEMOM applicable to any type of moment sequence. The feasibility of the new algorithm scheme was verified by comparing it with other recognized methods for six classic aerosol dynamics. The new algorithm scheme makes the TEMOM much easier to be used for users as compared to its original version (Aerosol Sci Tech 49(2015):1021-1036). The idea of the algorithm scheme can be applied to other nonquadrature-based methods of moments.

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“…Using the three order Taylor-series expansion approximation, the k th fractional order moment can be approximated as [20,25]:…”

Section: Mathematical Modelmentioning

confidence: 99%

Steady-state solutions for particles undergoing Brownian coagulation and breakage by the TEMOM model

Lin

2018

THERM SCI

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Error estimation of TEMOM for Brownian coagulation

Cited by 13 publications

References 14 publications

Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium

Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium

An Efficient Algorithm Scheme for Implementing the TEMOM for Resolving Aerosol Dynamics

Steady-state solutions for particles undergoing Brownian coagulation and breakage by the TEMOM model

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