Numerical analysis of the second-order characteristic FEM for nonlinear aerosol dynamic equations

Aerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. In this paper we consider the nonlinear aerosol dynamic equations on time and particle size, which involve the advection-condensation process and the nonlinear coagulation process. For solving accurately the multiple sharp log-normal aerosol distributions, we study and analyze the second order characteristic finite element method for the aerosol dynamic equations. We strictly prove that the developed method has second-order accuracy in time. The scheme improves the first-order accuracy in time comparing to the classical characteristic method. Numerical experiments for the multiple log-normal aerosol distributions are further given to confirm the theoretical results.

[1]  M. Memmesheimer,et al.  Modal aerosol dynamics model for Europe: development and first applications , 1998 .

[2]  J. R. Brock,et al.  Moment simulation of aerosol evaporation , 1987 .

[3]  Peter H. McMurry,et al.  Modal Aerosol Dynamics Modeling , 1997 .

[4]  J. Seinfeld,et al.  Sectional representations for simulating aerosol dynamics , 1980 .

[5]  S. Pratsinis.  Simultaneous nucleation, condensation, and coagulation in aerosol reactors , 1988 .

[6]  Numerical simulation of the general dynamic equation (GDE) for aerosols with two collocation methods , 2007 .

[7]  J. Seinfeld,et al.  Atmospheric Chemistry and Physics: From Air Pollution to Climate Change , 1997 .

[8]  Anthony S. Wexler,et al.  Numerical schemes to model condensation and evaporation of aerosols , 1996 .

[9]  Panagiotis D. Christofides,et al.  Nonlinear control of spatially inhomogenous aerosol processes , 1999 .

[10]  C. Housiadasa,et al.  Eulerian modelling of lung deposition with sectional representation of aerosol dynamics , 2004 .

[11]  Adrian Sandu,et al.  A framework for the numerical treatment of aerosol dynamics , 2003 .

[12]  J. Seinfeld,et al.  Numerical solution of the dynamic equation for particulate systems , 1978 .

[13]  J. Brock,et al.  Distributions for moment simulation of aerosol evaporation , 1990 .

[14]  K. Lehtinen,et al.  MECCO: A method to estimate concentrations of condensing organics—Description and evaluation of a Markov chain Monte Carlo application , 2010 .

[15]  Dong Liang,et al.  An efficient second‐order characteristic finite element method for non‐linear aerosol dynamic equations , 2009, International Journal for Numerical Methods in Engineering.

[16]  J. Seinfeld,et al.  Simulation of Aerosol Dynamics: A Comparative Review of Algorithms Used in Air Quality Models , 1999 .

[17]  T. F. Russell,et al.  NUMERICAL METHODS FOR CONVECTION-DOMINATED DIFFUSION PROBLEMS BASED ON COMBINING THE METHOD OF CHARACTERISTICS WITH FINITE ELEMENT OR FINITE DIFFERENCE PROCEDURES* , 1982 .

[18]  Benjamin Jourdain,et al.  A stochastic approach for the numerical simulation of the general dynamics equation for aerosols , 2003 .

[19]  Dong Liang,et al.  A new splitting wavelet method for solving the general aerosol dynamics equation , 2008 .

[20]  Adrian Sandu,et al.  Piecewise Polynomial Solutions of Aerosol Dynamic Equation , 2006 .

[21]  Bruno Sportisse,et al.  A review of current issues in air pollution modeling and simulation , 2007 .

[22]  S. H. Park,et al.  Size distribution of polydispersed aerosols during condensation in the continuum regime: Analytic approach using the lognormal moment method , 2006 .

[23]  K. T. Whitby.  THE PHYSICAL CHARACTERISTICS OF SULFUR AEROSOLS , 1978 .

[24]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.