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The moments method for multi‐modal multi‐component aerosols as applied to the coagulation‐type equation
Author(s) -
Koziol A. S.,
Leighton H. G.
Publication year - 2007
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.51
Subject(s) - aerosol , laguerre polynomials , mathematics , ordinary differential equation , gaussian , mathematical analysis , distribution (mathematics) , modal , coagulation , differential equation , physics , meteorology , chemistry , quantum mechanics , polymer chemistry , psychology , psychiatry
The idea of self‐preserving functions as solutions to a coagulation‐type equation for aerosol is investigated. The aerosol spectrum is assumed to be well represented by a finite but not limited sum of self‐preserving functions (modes). An original set of aerosol dynamics equations for an unlimited number of modes is formulated for self‐preserving functions in the form of the log‐normal distribution, gamma distribution and Laguerre expansion. Additional equations governing the composition of the aerosol are derived. The system of the obtained ordinary integro–differential equations is solved using the Runge–Kutta method with Gaussian quadratures to estimate integrals. The solutions are then successfully tested against direct high resolution numerical solutions of the coagulation‐type equation. Some physical examples illustrating the use of the developed numerical method are also presented. Copyright © 2007 Royal Meteorological Society