A comparison of numerical techniques for solution of atmospheric kinetic equations

Atmospheric Environment

Volumn 32, Issue 9, 1998, Pages 1535-1553

  Mathur, Rohit ^a   Young, Jeffrey O ^b   Schere, Kenneth L ^b   Gipson, Gerald L ^c  

^a MCNC   (United States)

^b NOAA EARTH SYSTEM RESEARCH LABORATORY   (United States)

^c U S ENVIRONMENTAL PROTECTION AGENCY   (United States)

Author keywords

Air quality modeling; Atmospheric chemistry; Numerical integration; Photochemical mechanism; Stiff ODEs

Indexed keywords

AIR QUALITY; ATMOSPHERIC CHEMISTRY; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; INTEGRATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PHOTOCHEMICAL REACTIONS; REACTION KINETICS;

ATMOSPHERIC KINETIC EQUATIONS;

AIR POLLUTION;

ACCURACY; AIR MONITORING; AIR POLLUTION; AIR QUALITY; ARTICLE; CALCULATION; CHEMICAL INTERACTION; PRIORITY JOURNAL; TROPOSPHERE;

EID: 0032076506     PISSN: 13522310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1352-2310(97)00381-6     Document Type: Article

References (28)

1. Carmichael, G. R., Peters, L. K. and Saylor, R. D. (1991) The STEM-II regional-scale acid deposition and photochemical oxidant model. I. An overview of model developments and applications. Atmospheric Environment 25A, 2077-2090.
2. Chang, J. S., Brost, R. A., Isaksen, I. S. A., Madronich, S., Middleton, P., Stockwell, W. R. and Walcek, C. J. (1987) A three-dimensional acid deposition model: physical concepts and formulation. Journal of Geophysical Resarch 92, 14,681-14,700.
3. Chock, D. P., Winkler, S. L. and Sun, P. (1994) Comparison of stiff chemistry solvers for air quality modeling. Environmental Science and Technology 28, 1882-1892.
4. Curtiss, C. F. and Hirschfelder, J. O. (1952) Integration of stiff equations. Proceedings of the National Academy of Science, U.S.A. 38, 235-243.
5. Dabdub, D. and Seinfeld, J. H. (1995) Extrapolation techniques used in the solution of stiff ODE's associated with chemical kinetics of air quality models. Atmospheric Environment 29, 403-410.
6. Dennis, R. L., Byun, D. W., Novak, J. H., Galluppi, K. J., Coats, C. J. and Vouk, M. A. (1996) The next generation of integrated air quality modeling: EPA's models-3. Atmospheric Environment 30, 1925-1938.
7. Gear, C. W. (1971) Numerical Initial Value problems in Ordinary Differential Equations. Pretince-Hall, Englewood Cliffs, New Jersy.
8. Gery, M. W., Whitten, G. Z., Killus, J. P and Dodge, M. C. (1989) A photochemical kinetics mechanism for urban and regional scale computer modeling. Journal of Geophysical Research 94, 12,925-12,956.
9. Gong, W. and Cho, H.-R. (1993) A numerical scheme for the integration of the gas-phase chemical rate equations in three-dimensional atmospheric models. Atmospheric Environment 27A, 2147-2160.
10. Hertel, O., Berkowicz, R., Christensen, J. and Hov, Ø. (1993) Test of two numerical schemes for use in atmospheric transport-chemistry models. Atmospheric Environment 27A, 2591-2611.
11. Hesstvedt, E., Hov, Ø. and Isaksen, I. S. A. (1978) Quasi-steady-state approximations in air pollution modeling: Comparison of two numerical schemes for oxidant prediction. International Journal of Chemical Kinetics 10, 971-994.
12. Hindmarsh, A. C. (1983) ODEPACK: a systemized collection of ODE solvers. In Scientific Computing, eds R. S. Stepleman et al., pp. 55-64. North-Holland,Amsterdam.
13. Jacobson, M. Z. and Turco, R. P. (1994) SMVGEAR: a sparse-matrix, vectorized Gear code for atmospheric models. Atmospheric Environment 28A, 273-284.
14. Lamb, R. G. (1983) A regional scale (1000 km) model of photochemical air pollution: Part 1, theoretical formulation. EPA/600/3-83/035, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina.
15. McRae, G. J., Goodin, W. R. and Seinfeld, J. H. (1982) Numerical solution of atmospheric diffusion equation for chemically reactive flows. Journal of Computational Physics 45, 1-42.
16. Odman, M. T., Kumar, N. and Russell, A. G. (1992) A comparison of fast chemical solvers for air quality modeling. Atmospheric Environment 26A, 1783-1789.
17. Sandu, A., Verwer, J. G., van Loon, M., Carmichael, G. R., Potra, F. A., Dabdub, D. and Seinfeld, J. H. (1997) Benchmarking stiff ODE solvers for atmospheric chemistry problems I: implicit versus explicit. Atmospheric Environment 31, 3151-3166.
18. Saylor, R. D. and Ford, G. D. (1995) On the comparison of numerical methods for the integration of kinetic equations in atmospheric chemistry and transport models. Atmospheric Environment 29, 2585-2593.
19. Seinfeld, J. H., Lapidus, L. and Hwang, M. (1970) Review of numerical integration techniques for stiff ordinary differential equations. Industrial and Engineering Chemistry Fundamentals 9, 266-275.
20. Sillman, S. (1991) A numerical solution of equations of tropospheric chemistry based on analysis of sources and sinks of odd hydrogen. Journal of Geophysical Research 96, 20,735-20,744.
21. Stockwell, W. R. (1986) A homogeneous gas phase mechanism for use in a regional acid deposition model. Atmospheric Environment 20, 1615-1632.
22. Stockwell, W. R., Middleton, P. and Chang, J. S. (1990) The second generation regional acid deposition model chemical mechanism for regional air quality modeling. Journal of Geophysical Research 95, 16,343-16,367.
23. Sun, P., Chock, D. P. and Winkler, S. L. (1994) An implicit-explicit hybrid solver for a system of stiff kinetic equations. Journal of Computational Physics 115, 515.
24. Verwer, J. G., Bloom, J. G., Van Loon, M. and Spee, E. J. (1996) A comparison of stiff ODE solvers for atmospheric chemistry problems. Atmospheric Environment 30, 49-58.
25. Winkler, S. L. and Chock, D. P. (1996) Air quality predictions of the urban airshed model containing improved advection and chemistry algorithms. Environmental Science and Technology 30, 1163-1175.
26. Yamartino, R. J., Scire, J. S., Carmichael, G. R. and Chang, Y. S. (1992) The CALGRID mesoscale photochemical grid model I. Model formulation. Atmospheric Environment 26A, 1493-1512.
27. Young, J. O., Sills, E. and Jorge, D. A. (1993) Optimization of the regional oxidant model for the CRAY Y-MP. EPA/600/R-94/065, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina.
28. Young, T. R. and Boris, J. P. (1977) A numerical technique for solving stiff ordinary differential equations associated with the chemical kinetics of reactive flow problems. Journal of Physical Chemistry 81, 2424-2427.