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High-Order Finite Volume Methods for Aerosol Dynamic Equations

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Partial differential equations, boundary value problems

Published online by Cambridge University Press:  27 January 2016

Ming Cui ,
Yanxin Su  and
Dong Liang
Ming Cui*
Affiliation:
College of Applied Sciences, Beijing University of Technology, Beijing 100124, China School of Mathematics, Shandong University, Jinan 250100, China
Yanxin Su
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, China
Dong Liang
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, China Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada
*
*Corresponding author. Email:[email protected] (M. Cui), [email protected] (Y. X. Su), [email protected] (D. Liang)
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Abstract

Aerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. In this paper we consider numerical methods for the nonlinear aerosol dynamic equations on time and particle size. The finite volume element methods based on the linear interpolation and Hermite interpolation are provided to approximate the aerosol dynamic equation where the condensation and removal processes are considered. Numerical examples are provided to show the efficiency of these numerical methods.

Keywords

Aerosol dynamic equationfinite volume methodcondensationremoval

MSC classification

Secondary: 65M15: Error bounds 65N15: Error bounds
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 213 - 235
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Ackermann, I. J., Hass, H., Memmesheimer, M., Ebel, A., Binkowski, F. S. and Shankar, F., Modal aerosol dynamics model for Europe: development and first applications, Atmos. Environ., 32 (1998), pp. 2981–2999.CrossRefGoogle Scholar
[2]Brock, J. R., Oates, J., and Seinfeld, J. H., Moment simulation of aerosol evaporation, J. Aerosol Sci., 18 (1987), pp. 59–64.Google Scholar
[3]Cai, Z., Mandel, J. and McCormick, S., The finite volume element method for diffusion equations on general triangulations, SIAM J. Numer. Anal., 28 (1991), pp. 392–403.Google Scholar
[4]Chou, S. H. and Li, Q., Error estimates in L2, H1 and L1 in covolume methods for elliptic and parabolic problems, a unified approach, Math. Comput., 69 (2000), pp. 103–120.CrossRefGoogle Scholar
[5]Elagarayhi, A., Solution of the dynamic equation of aerosols by means of maximum entropy technique, J. Quant. Spectrosc. Ra., 75 (2002), pp. 1–11.Google Scholar
[6]Gerbard, F., Tambour, Y. and Seinfeld, J. H., Sectional representation for simulating aerosol dynamics, J. Colloid Inter. Sci., 76 (1980), pp. 541–556.Google Scholar
[7]Jung, C. H., Kim, Y. P., Lee, K. W. and Seinfeld, J. H., Simulation of the influence of coarse mode particles on the properties of fine mode particles, J. Aerosol Sci., 33 (2002), pp. 1201–1216.CrossRefGoogle Scholar
[8]Jung, C. H., Kim, Y. P. and Lee, K. W., Analytic solution for polydispersed aerosol dynamics by a wet removal process, J. Aerosol Sci., 33 (2002), pp. 753–767.CrossRefGoogle Scholar
[9]Jung, C. H., Kim, Y. P. and Lee, K. W., A moment model for simulating raindrop scavenging of aerosols, J. Aerosol Sci., 34 (2003), pp. 1217–1233.Google Scholar
[10]Kim, J., Jung, C. H., Choi, B. C., Oh, S. N., Brechtel, F. J., Yoon, S. C., Kim, S. W., Number size distribution of atmospheric aerosols during ACE-Asia dust and precipitation events, Atmos. Environ., 41 (2007), pp. 4841–4855.Google Scholar
[11]Lee, K. W., Chen, H., and Gieseke, J. A., Log-normally preserving size distribution for Brownian coagulation in the free-molecule regime, Aerosol Sci. Tech., 3 (1984), pp. 53–62.Google Scholar
[12]Lee, K. W., Curtis, L. A. and Chen, H., An analytic solution to free molecule aerosol coagulation, Aerosol Sci. Tech., 12 (1990), pp. 457–462.Google Scholar
[13]Li, R., Chen, Z. and Wu, W., Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods, Marcel Dekker, 2000.Google Scholar
[14]Liang, D., Wang, W. and Cheng, Y., An efficient second-order characteristic finite element method for non-linear aerosol dynamic equations, Int. J. Numer. Meth. Eng., 80 (2009), pp. 338–354.Google Scholar
[15]Liang, D., Guo, Q. and Gong, S., A new splitting wavelet method for solving the general aerosol dynamics equations, J. Aerosol Sci., 39 (2008), pp. 467–487.Google Scholar
[16]Liang, D., Guo, Q. and Gong, S., Wavelet Galerkin methods for aerosol dynamic equations in atmosheric environment, Commun. Comput. Phys., 6 (2009), pp. 109–130.Google Scholar
[17]Sandu, A. and Borden, C., A framework for the numerical treatment of aerosol dynamics, Appl. Numer. Math., 45 (2003), pp. 475–497.Google Scholar
[18]Seinfeld, J. H. and Pandis, S. N., Atmospheric Chemistry and Physics, New York, USA, Wiley, 1998.Google Scholar
[19]Seo, Y. and Brock, J. R., Distribution for moment simulation of aerosol evaporation, J. Aerosol Sci., 4 (1990), pp. 511–514.Google Scholar
[20]Whitby, K. T., The physical characteristics of sulfur aerosols, Atmos. Environ., 12 (1978), pp. 135–159.Google Scholar
[21]Ye, X., On the relationship between finite volume and finite element methods applied to the Stokes equations, Numer. Method PDE, 17 (2001), pp. 440–453.Google Scholar
[22]Zhao, H. and Zheng, C., Monte Carlo sulution of wet removal of aerosols by precipitation, Atmos. Environ., 40 (2006), pp. 1510–1525.Google Scholar