A new iterative scheme for solving the discrete Smoluchowski equation

Smith, A. J.; Wells, Clive G.; Kraft, Markus

doi:10.1016/j.jcp.2017.09.045

Cited by 5 publications

(3 citation statements)

References 55 publications

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“…Further issues include numerical diffusion when modelling growth, stiffness due to timescale discrepancies and instability introduced by matrix inversions. Stadnichuk et al (2015) and Smith et al (2018) describe iterative schemes for efficient steady state solutions.…”

Section: Numerical Methods For Homogeneous Systemsmentioning

confidence: 99%

Stochastic population balance methods for detailed modelling of flame-made aerosol particles

Boje

Kraft

2022

Journal of Aerosol Science

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Section: Numerical Methods For Homogeneous Systemsmentioning

confidence: 99%

Stochastic population balance methods for detailed modelling of flame-made aerosol particles

Boje

Kraft

2022

Journal of Aerosol Science

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“…In this section, first different mathematical approaches to solving the general dynamics equation are illustrated. This is followed by the description of different Geng, Park, and Sajo 2013;Harrington and Kreidenweis 1998;Kommu, Khomami, and Biswas 2004;Pirjola et al 1999;Seigneur et al 1986;Talukdar and Swihart 2004;Tsantilis, Kammler, and Pratsinis 2002;Zhang et al 1999) Discrete model PSD is divided into discrete sizes and the increment volume of the two neighboring discrete sizes is the volume of the monomer Most accurate; Computationally expensive (Frenklach and Harris 1987;Friedlander 2000;Gelbard and Seinfeld 1979;Landgrebe and Pratsinis 1989;Lehtinen and Kulmala 2003;Smith, Wells, and (Frenklach and Harris 1987;Harrington and Kreidenweis 1998;Lin, Sethi, and Biswas 1992;McGraw 1997;Pirjola et al 1999;Pratsinis 1988;Seigneur et al 1986;Suh, Zachariah, and Girshick 2001;Talukdar and Swihart 2004;Williams 1986;Yamamoto 2014;Zhang et al 1999Zhang et al , 2018 (Biswas et al 1997;Chadha et al 2017;Gao et al 2017;Kommu et al 2004;Landgrebe and Pratsinis 1990;Moniruzzaman and Park 2006;Wu and Biswas 1998;Wu and Flagan 1988) Modal model Assume monodisperse for each mode; 2n...…”

Section: Model Developmentmentioning

confidence: 99%

Comparison of discrete, discrete-sectional, modal and moment models for aerosol dynamics simulations

Zhang

Sharma

Dhawan

et al. 2020

Aerosol Science and Technology

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An open source software (Aerosol and Air Quality Research Lab-Aerosol Dynamics Model, AAQRL-ADM) used for aerosol dynamics simulations is developed by including four models: discrete, discrete-sectional, method of moments, and modal. First, the mathematical description of these models as well as the effects of aerosol dynamics available in the software are reviewed, and a modal model is developed to use multiple modes to represent particle size spectrum. Second, the design of a working principle and user graphical interface (GUI) of AAQRL-ADM is described. Third, the models in AAQRL-ADM are validated by investigating the evolution of particle size distribution (PSD) in considering the effects of coagulation, condensation, and nucleation. Next, the trade-off between simulation accuracy and numerical efficiency is discussed for all of the four models, and a guide to choosing the appropriate aerosol dynamic model in practical simulation is presented. Finally, discrete-sectional, moment, and modal models are used to investigate the particle size distribution in a furnace aerosol reactor along a streamline, coupled with the velocity and temperature profiles. AAQRL-ADM is provided free of charge for the use of public researchers.

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“…Low dimensional type spaces allow direct integration of the ordinary differential equations (ODE) through transport of the moments of the particle size distribution (PSD) or discretization. Stadnichuk et al [21] and Smith et al [22] describe iterative schemes for efficient steady state solutions and H-matrices are used as low rank, separable approximations to the coagulation and fragmentation kernels in Koch et al [23] to reduce computational cost and memory requirements.…”

Section: Introductionmentioning

confidence: 99%

A hybrid particle-number and particle model for efficient solution of population balance equations

Boje

Akroyd

Kraft

2019

Journal of Computational Physics

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This work presents a hybrid particle-number and particle model to improve efficiency in solving population balance equations for type spaces spanning spherical and aggregate particles. The particle-number model tracks simpler, spherical particles cheaply by storing only the number of particles with a given one-dimensional internal coordinate, while the particle model allows resolution of the detailed aggregate structure that occurs due to collision and coagulation between particles by storing distinct computational entries for each particle. This approach is exact if primary particles are defined by their monomer count and the particle-number model increments in single monomers. A stochastic method is used to solve the population balance equations for the combined type space. The hybrid method works well for large ensembles (> 2 12 particles) with a detailed particle model, where per

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A new iterative scheme for solving the discrete Smoluchowski equation

Cited by 5 publications

References 55 publications

Stochastic population balance methods for detailed modelling of flame-made aerosol particles

Stochastic population balance methods for detailed modelling of flame-made aerosol particles

Comparison of discrete, discrete-sectional, modal and moment models for aerosol dynamics simulations

A hybrid particle-number and particle model for efficient solution of population balance equations

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