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An efficient second‐order characteristic finite element method for non‐linear aerosol dynamic equations
Author(s) -
Liang Dong,
Wang Wenqia,
Cheng Yu
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2639
Subject(s) - extrapolation , finite element method , logarithm , aerosol , mathematics , advection , mathematical analysis , physics , meteorology , thermodynamics
In the paper we consider the non‐linear aerosol dynamic equation on time and particle size, which contains the advection process of condensation growth and the process of non‐linear coagulation. We develop an efficient second‐order characteristic finite element method for solving the problem. A high accurate characteristic method is proposed to treat the condensation advection while a second‐order extrapolation along the characteristics is proposed to approximate the non‐linear coagulation. The method has second‐order accuracy in time and the optimal‐order accuracy of finite element spaces in particle size, which improves the first‐order accuracy in time of the classical characteristic method. Numerical experiments show the efficient performance of our method for problems of log‐normal distribution aerosols in both the Euler coordinates and the logarithmic coordinates. Copyright © 2009 John Wiley & Sons, Ltd.