Piecewise Polynomial Solutions of Aerosol Dynamic Equation

REFERENCES

• Atkinson , K. E. 1988 . An Introduction to Numerical Analysis , New York : John Wiley and Sons .
   Google Scholar
• Atkinson , K. E. 1997 . The Numerical Solution of Integral Equations of the Second Kind. , Cambridge : Cambridge University Press .
   Google Scholar
• Binkowski , F. S. and Shankar , U. 1995 . The Regional Particulate Matter Model: 1: Model Description and Preliminary Results . J. Geophys. Res. , 100 ( 26 ) : 191 – 26, 209 . [CSA]
   Google Scholar
• Bott , A. 1989 . A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of the Advection Fluxes . Monthly Weather Rev. , 117 : 1006 – 1115 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Carmichael , G. R. , Daescu , D. , Sandu , A. and Chai , T. 2003 . Computational Aspects of Chemical Data Assimilation into Atmospheric Models. ICC SO3, Melbourne, Australia, June 2003 . Springer Lecture Notes in Computer Science , vol. 2660 : pp. 269 – 278 . [CSA]
   Google Scholar
• Cockburn , B. 2003 . An Introduction to the Discontinuous Galerkin Method for Convection-Dominated Problems Lecture Notes, University of Minnesotta . [CSA]
   Google Scholar
• Cockburn , B. , Lin , S. Y. and Shu , C. W. 1989 . TVB Runge Kutta Local Projection Discontinuous Galerkin Finite Element Method for Scalar Conservation Laws. II-General Framework . Math. Comput. , 52 : 411 – 435 . [CSA]
   Web of Science ®Google Scholar
• de Boor , C. 1978 . A Practical Guide to Splines , New York : Springer-Verlag .
   Google Scholar
• Delves , L. M. and Mohamed , J. L. 1985 . Computational Methods for Integral Equations , Cambridge : Cambridge University Press .
   Google Scholar
• Dhaniyala , S. and Wexler , A. S. 1996 . Numerical Schemes to Model Condensation and Evaporation of Aerosols . Atmos. Environ. , 30 : 919 – 928 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Duran , D. R. 1998 . Numerical Methods for Wave Equations in Geophysical Fluid Dynamics , Berlin, Heidelberg : Springer Verlag New-York .
   Google Scholar
• Fuchs , N. A. and Sutugin , A. G. 1971 . “ High Dispersed Aerosols ” . In Topics in Current Aerosol Research Edited by: Hidy , G. M. and Brock , J. R. pp. 160
   Google Scholar
• Gelbard , F. M. and Seinfeld , J. H. 1978a . Coagulation and Growth of a Multicomponent Aerosol . J. Coll. Interface Sci. , 63 ( 3 ) : 472 – 479 . [CSA]
   Google Scholar
• Gelbard , F. M. and Seinfeld , J. H. 1978b . Numerical Solution of the Dynamic Equation for Particulate Systems . J. Computat. Phys. , 28 : 357 – 375 . [CROSSREF] [CSA]
   Google Scholar
• Gelbard , F. M. and Seinfeld , J. H. 1980 . Simulation of Multicomponent Aerosol Dynamics . J. Coll. Interface Sci. , 78 ( 2 ) : 485 – 501 . [CSA]
   Web of Science ®Google Scholar
• Jacobson , M. Z. 1997aa . Development and Application of a New Air Pollution Modeling System—II. Aerosol Module Structure and Design . Atmos. Environ. , 31 ( 2 ) : 131 – 144 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Jacobson , M. Z. 1997b . Numerical Techniques to Solve Condensational and Dissolutional Growth Equations When Growth is Coupled to Reversible Reactions . Aerosol Sci. Technol. , 27 : 491 – 498 . [CSA]
   Web of Science ®Google Scholar
• Jacobson , M. Z. 1999 . Fundamentals of Atmospheric Modeling , Cambridge : Cambridge University Press .
   Google Scholar
• Jacobson , M. Z. 2002 . Analysis of Aerosol Interactions with Numerical Techniques for Solving Coagulation, Nucleation, Condensation, Dissolution, and Reversible Chemistry among Multiple Size Distributions . J. Geophys. Res. , 107 ( D19 ) : 4366 doi:10.029/2001JD002044[CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Jacobson , M. Z. and Turco , R. P. 1995 . Simulating Condensational Growth, Evaporation, and Coagulation of Aerosols Using a Combined Moving and Stationary Grid Size . Aerosol Sci. Technol. , 22 : 73 – 92 . [CSA]
   Web of Science ®Google Scholar
• Johnson , C. 1987 . Numerical Solution of Partial Differential Equations by the Finite Element Method , Cambridge : Cambridge University Press .
   Google Scholar
• Kim , Y. P. and Seinfeld , J. H. 1990 . Simulation of Multicomponent Aerosol Condensation by the Moving Sectional Method . J. Coll. Interface Sci. , 135 ( 1 ) : 185 – 199 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Lurmann , F. W. , Wexler , A. S. , Pandis , S. N. , Musara , S. , Kumar , N. and Seinfeld , J. H. 1997 . Modeling Urban and Regional Aerosols—ii. Application to California's South Coast Air Basin . Atmos. Environ. , 31 : 2695 – 2715 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Lushnikov , A. A. 1976 . Evolution of Coagulating Systems iii. Coagulating Mixtures . J. Coll. Interface Sci. , 54 ( 1 ) : 94 – 101 . [CROSSREF] [CSA]
   Google Scholar
• Meng , Z. , Dabdub , D. and Seinfeld , J. H. 1998 . Size-Resolved and Chemically Resolved Model of Atmospheric Aerosol Dynamics . J. Geophys. Res. , 103 ( D3 ) : 3419 – 3435 . [CROSSREF] [CSA]
   Google Scholar
• Nguyen , K. and Dabdub , D. 2001 . Two-Level Time-Marching Scheme Using Splines for Solving the Advection Equation . Atmos. Environ. , 35 : 1627 – 1637 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Nguyen , K. and Dabdub , D. 2002 . Semi-Lagrangian Flux Scheme for the Solution of the Aerosol Condensation/Evaporation Equation . Aerosol Sci. Technol. , 36 : 407 – 418 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Pandis , S. N. , Wexler , A. S. and Seinfeld , J. H. 1993 . Secondary Organic Aerosol Formation and Transport: II. Predicting the Ambient Secondary Organic Aerosol Size Distribution . Atmos. Environ , 27 : 2403 – 2416 . [CSA]
   Web of Science ®Google Scholar
• Phadnis , M. J. and Carmichael , G. R. 2000 . Transport and Distribution of Primary and Secondary Nonmethane Volatile Organic Compounds in East Asia Under Continental-Outflow Conditions . J. Geophys. Res. , 105 ( D17 ) : 22311 – 22336 . [CROSSREF] [CSA]
   Google Scholar
• Pilinis , C. 1990 . Derivation and Numerical Solution of the Species Mass Distribution Equation for Multicomponent Particulate Systems . Atmos. Environ. , 24A ( 7 ) : 1923 – 1928 . [CSA]
   Web of Science ®Google Scholar
• Ramanathan , V. , Crutzen , P. J. , Andreae , M. O. , Coakley , J. , Dickerson , R. , Heintzenberg , J. , Heymsfield , A. , Kiehl , J. T. , Kley , D. , Krishnamurti , T. N. , Kuettner , J. , Lelieveld , J. , Liu , S. C. , Mitra , A. P. , Prospero , J. , Sadourny , R. , Tuck , A. F. and Valero , F. P. J. 1998 . Indoex White Paper . Indian Ocean Experiment, http://www-indoex.ucsd.edu/publications/white_paper [CSA]
   Google Scholar
• Sandu , A. 2001 . “ A Spectral Method for Solving Aerosol Dynamics Technical Report CSTR-01-04 ” . Houghton, MI : Department of Computer Science, Michigan Technological University . 1400 Townsend Drive, 49931
   Google Scholar
• Sandu , A. 2002 . A Newton-Cotes Quadrature Approach for Solving the Aerosol Coagulation Equation . Atmos. Environ. , 36 : 583 – 589 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Sandu , A. 2003 . “ AeroSolve: A Solver Package for Aerosol Dynamic Equation ” . Computer Science Department, Virginia Polytechnic Institute and State University . http://people.cs.vt.edu/simasandu/Software/AeroSolve
   Google Scholar
• Sandu , A. and Borden , C. T. 2003 . A Framework for the Numerical Treatment of Aerosol Dynamics . Appl. Numer. Math. , 45 : 475 – 497 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Song , C. H. and Carmichael , G. R. 1999 . Partitioning of HNO3 Modulated by Alkaline Aerosol Particles . J. Geophys. Res. , [CSA]
   Google Scholar
• Song , C. H. and Carmichael , G. R. 2001 . A Three-Dimensional Modeling Investigation of the Evolution Processes of Dust and Sea-Salt Particles in East Asia . J. Geophys. Res. , 106 ( D16 ) : 18131 – 18154 . [CROSSREF] [CSA]
   Google Scholar
• Trefethen , L. N. 2000 . “ Spectral Methods in Matlab ” . Philadelphia : SIAM Software, Environments, Tools Series .
   Google Scholar
• Tsang , H. and Hippe , J. M. 1988 . Asymptotic Behavior of Aerosol Growth in the Free Molecule Regime . Aerosol Sci. Technol. , 8 : 265 – 278 . [CSA]
   Web of Science ®Google Scholar
• Underwood , G. M. , Song , C. H. , Phadnis , M. , Carmichael , G. R. and Grassian , V. H. 2001 . Heterogeneous Reactions of NO_2 and HNO_3 on Oxides and Mineral Dust: A Combined Laboratory and Modeling Study . J. Geophys. Res. , 106 ( D16 ) : 18055 – 18066 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Wexler , A. S. , Lurmann , F. W. and Seinfeld , J. H. 1994 . Modeling Urban and Regional Aerosols: I. Model Development . Atmos. Environ. , 28 : 531 – 546 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Zhang , K. M. and Wexler , A. S. 2002 . Modeling the Number Distributions of Urban and Regional Aerosols . Atmos. Environ. , 36 : 1863 – 1874 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Zhang , Y. , Seinfeld , J. H. , Jacobson , M. Z. and Binkowski , F. S. 1999 . Simulation of Aerosol Dynamics: A Comparative Review of Algorithms Used in Air Quality Models . Aerosol Sci. Technol. , 31 : 487 – 514 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar