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

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 numeric...

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Published in:	Aerosol science and engineering Vol. 1; no. 3; pp. 119 - 137
Main Authors:	Yu, Mingzhou, Liu, Yueyan, Koivisto, Antti J.
Format:	Journal Article
Language:	English
Published:	Singapore Springer Singapore 01.10.2017
Subjects:	Atmospheric Protection/Air Quality Control/Air Pollution Atmospheric Sciences Earth and Environmental Science Earth Sciences Environmental Science and Engineering Monitoring/Environmental Analysis Nanochemistry Nanotechnology and Microengineering Research Article Taylor-series expansion method of moments Population balance equation Algorithm scheme
ISSN:	2510-375X, 2510-3768
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Abstract	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 ϕ , 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 non-quadrature-based methods of moments.
AbstractList	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 ϕ , 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 non-quadrature-based methods of moments.
Author	Koivisto, Antti J. Yu, Mingzhou Liu, Yueyan
Author_xml	– sequence: 1 givenname: Mingzhou orcidid: 0000-0002-4681-9287 surname: Yu fullname: Yu, Mingzhou email: yumingzhou1738@yahoo.com organization: China Jiliang University, Key Laboratory of Aerosol Chemistry and Physics, Chinese Academy of Science – sequence: 2 givenname: Yueyan surname: Liu fullname: Liu, Yueyan organization: China Jiliang University – sequence: 3 givenname: Antti J. surname: Koivisto fullname: Koivisto, Antti J. organization: National Research Centre for the Working Environment
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Snippet	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...
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SubjectTerms	Atmospheric Protection/Air Quality Control/Air Pollution Atmospheric Sciences Earth and Environmental Science Earth Sciences Environmental Science and Engineering Monitoring/Environmental Analysis Nanochemistry Nanotechnology and Microengineering Research Article
Title	An Efficient Algorithm Scheme for Implementing the TEMOM for Resolving Aerosol Dynamics
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