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\begin{document}

\title{Efficient method of moments for simulating atmospheric aerosol growth:
model description, verification and application}



\author[1,2]{M. Yu}%
\author[3,3]{J. Shen}%
\author[3,3]{Y. Liu}%
\author[4,4]{T.L. Chan}%
\author[3,3]{C. Tu}%
\affil[1]{Zhejiang University}%
\affil[2]{China Jiliang University; Zhejiang University}%
\affil[3]{China Jiliang University}%
\affil[4]{The Hong Kong Polytechnic University}%


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  \date{May 19, 2024}


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\begin{abstract}
The atmospheric aerosol dynamics model (AADM) has been widely used in
both comprehensive air quality model systems and chemical transport
modeling from road to global scales. The AADM consists of the
Smoluchowski coagulation equation (SCE) which describes the atmospheric
aerosol size growth due to coagulation. The numerical solution to the
SCE undergoing Brownian coagulation in the free molecular regime is a
direct challenge because of a stumbling block for the kernel to be
expressed by an equivalent linear expression and a predefined lognormal
size distribution, which is inconsistent with aerosols having bimodal or
multimodal size distribution. Thus, a new mathematical method for
solving the SCE without the strong assumption of log-normal size
distribution is proposed and developed. This method is verified with a
referenced sectional method (SM) with excellent agreement. The accuracy
of the method approaches closely to the TEMOM, but overcomes the
limitation of the classical log MOM. The computational time of this
scheme is largely reduced when comparing to the SM. The new method is
successfully implemented to reveal the formation and growth of secondary
particles emitted from the vehicle exhaust tailpipe. It is surprisingly
found that the formation of new particles only appears in the interface
region of the turbulent exhaust jet which is very close to the tailpipe
exit, while there is no new particle formation in the strong mixture
along the downstream. The new method is finally verified to be an
efficient and reliable numerical scheme for studying atmospheric aerosol
dynamics.%
\end{abstract}%



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