Efficient Method of Moments for Simulating Atmospheric Aerosol Growth: Model Description, Verification, and Application

Abstract

The atmospheric aerosol dynamics model (AADM) has been widely used in both comprehensive air quality model systems and chemical transport modeling globally. The AADM consists of Smoluchowski's coagulation equation (SCE), whose solution undergoing Brownian coagulation in the free molecular regime is a challenge because it is inconsistent with aerosols whose size distribution cannot exactly follow the lognormal size distribution. Thus, a new method for solving the SCE without assuming lognormal size distribution is proposed and developed. The underlying principle of this method is that the hybridization of the well‐established method of moments with the assumed lognormal size distribution (log MOM) and Taylor‐series expansion method of moments (TEMOM) is implemented. This method shows excellent agreement with the sectional method (SM) which is used as reference. The accuracy of these two specific models closely approaches that of the TEMOM, but overcomes the limitation of the classical log MOM. The computational time of this scheme is considerably lower than that of the SM. The new method was successfully implemented to reveal the formation and growth of secondary particles emitted from a vehicle exhaust tailpipe. It was found that the formation of new particles only occurs in the interface region of the turbulent exhaust jet (which is very close to the tailpipe exit), whereas no new particles are formed in the mixture of the exhaust jet plume and the surrounding cold air downstream. The new method is verified as an efficient and reliable numerical scheme for studying atmospheric aerosol dynamics.

Realization of Self-Preserving Size Distribution Theory for the Evolution of Tropospheric Atmospheric Aerosols Through an Inverse Gaussian Distribution

“…In this paper, the SM is also used as a reference to validate the method proposed in this study. To ensure high numerical accuracy of this SM method, the section number is 800 and the section spacing factor is 1.045 (Shen et al 2020a).…”

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

“…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.…”