Benchmarking stiff ode solvers for atmospheric chemistry problems--I. Implicit vs explicit

Atmospheric Environment

Volumn 31, Issue 19, 1997, Pages 3151-3166

  Sandu, A ^a   Verwer, J G ^b   Van Loon, M ^b   Carmichael, G R ^c   Potra, F A ^a   Dabdub, D ^d   Seinfeld, J H ^e  

^a UNIVERSITY OF IOWA   (United States)

^b CWI   (Netherlands)

^c UNIVERSITY OF IOWA   (United States)

^d University of California at Irvine   (United States)

^e California Institute of Technology   (United States)

Author keywords

Air pollution modeling; Atmospheric chemistry; Benchmarking; Dedicated explicit solvers; Numerical stiff ODEs; Sparse implicit solvers

Indexed keywords

AIR POLLUTION; DIFFERENTIAL EQUATIONS; LINEAR ALGEBRA; MATHEMATICAL MODELS; TROPOSPHERE;

AIR POLLUTION MODELING; ORDINARY DIFFERENTIAL EQUATIONS;

ATMOSPHERIC CHEMISTRY;

ALGORITHM; ATMOSPHERIC CHEMISTRY; ATMOSPHERIC TRANSPORT; BENCHMARK; NUMERICAL METHOD;

ACCURACY; AIR POLLUTION; ALGORITHM; CONFERENCE PAPER; ERROR; PHOTOCHEMISTRY; POLLUTION TRANSPORT; PRIORITY JOURNAL; TROPOSPHERE;

EID: 0031259690     PISSN: 13522310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1352-2310(97)00059-9     Document Type: Conference Paper

References (30)

1. Atkinson, R. D., Baulch, D. L., Cox, R. A., Hampson, R. F. JR., Kerr, J. A. and Troe, J. (1989) Evaluated kinetic and photochemical data for atmospheric chemistry. J. Chem. Kinet. 21, 115-190.
2. Brown, P. N., Byrne, G. D. and Hindmarsh, A. C. (1989) VODE: A variable coefficient ODE Solver. SIAM J. Sci. Stat. Comput. 10, 1038-1051.
3. Carmichael, G. R., Peters, L. K. and Kitada, T. (1986) A second generation model for regional-scale transport/ chemistry/deposition. Atmospheric Environment 20, 173-188.
4. Dabdub, D. and Seinfeld, J. H. (1995) Extrapolation techniques used in the solution of stiff ODEs associated with chemical kinetics of air quality models. Atmospheric Environment 29, 403-410.
5. Damian-Iordache, V. and Sandu, A. (1995) KPP - A symbolic preprocessor for chemistry kinetics - User's guide. Technical Report, Department of Mathematics, University of Iowa.
6. Eisenstat, S. C., Gursky, M. C., Schultz, M. H. and Sherman, A. H. (1977) Yale Sparse Matrix Package.ii. The nonsymmetric codes. Research Report 114, Department of Computer Science, Yale University.
7. Eisenstat, S. C., Gursky, M. C., Schultz, M. H. and Sherman, A. H. (1982) Yale Sparse Matrix Package.i. The symmetric codes. Int. J. Num. Meth. Eng. 18, 1145-1151.
8. Prather et. al., M. (1995) Intercomparison of tropospheric chemistry/transport models. In Scientific Assesment of Ozone Depletion, World meteorological organization.
9. ftp.cgrer.uiowa.edu. (1996) Ftp. site at the Center for Global and Regional Environmental Research, University of Iowa (cd pub/Ode_benchmark, mget *).
10. 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. J. geophy. Res. 94, 12925-12956.
11. Hairer, E. and Wanner, G. (1991) Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Springer, Berlin.
12. Hov, Ø., Isaksen, I. and Hesstvedt, E. (1978) A numerical method to predict secondary air pollutants with an application on oxidant generation in an urban atmosphere. WMO publication 510, 219-226.
13. Hesstvedt, E., Hov, Ø. and Isaksen, I. (1978) Quasi-steady-state-approximation in air pollution modelling: comparison of two numerical schemes for oxidant prediction. Int. J. chem. Kinet. 10, 971-994.
14. Hindmarsh, A. C. (1983) ODEPACK: A systematized collection of ODE solvers. In R. S. Stepleman (ed.), IMACS Trans. on Scientific Computation, Vol. 1, Scientific Computing, ed. R. S. Stepleman, North Holland, Amsterdam.
15. Jacobson, M. Z. and Turco, R. P. (1994) SMVGEAR: a sparse-matrix, vectorized Gear code for atmospheric models. Atmospheric Environment 17, 273-284.
16. Jay, L. O., Sandu, A., Potra, F. A. and Carmichael, G. R. (1995) Improved QSSA methods for atmospheric chemistry integration. Technical report 67, Department of Mathematics, University of Iowa.
17. Lurmann, F. W., Loyd, A. C. and Atkinson, R. (1986) A chemical mechanism for use in long-range transport/acid deposition computer modeling. J. geophys. Res. 91, 10,905-10,936.
18. McRae, G. J., Goodin, W. R. and Seinfeld, J. H. (1982) Numerical solution of the atmospheric diffusion equation for chemically reacting flows. J. comput. Phys. 45, 1-42.
19. Matthijssen, J. (1995) Private communication, Laboratoire d'Aerologie OMP, Toulouse, France.
20. Sandu, A., Potra, F. A., Damian, V. and Carmichael, G. R. (1996) Efficient implementation of fully implicit methods for atmospheric chemistry. J. Comp. Phys. 129, 101-110.
21. 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.
22. Simpson, D., Andersson-Sköld, Y. and Jenkin, M. E. (1993) Updating the chemical scheme for the EMEP MSC-W oxidant model: current status. Technical Report 2/93, EMEP MSC-W, The Norwegian Meteorological Institute, Oslo.
23. van Loon, M. (1995a) Numerical smog prediction I: The physical and chemical model. CWI Report NM-R9411, Center for Mathematics and Computer Science, Amsterdam.
24. van Loon, M. (1995b) Numerical smog prediction II: Grid refinement and its application to the Dutch smog prediction model. CWI Report NM-R9523, Center for Mathematics and Computer Science, Amsterdam.
25. Verwer, J. G. (1994) Gauss-Seidel iterations for stiff ODEs from chemical kinetics. SIAM J. Sci. Comput. 15, 1243-1250.
26. Verwer, J. G., Blom, 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.
27. Verwer, J. G. and Simpson, D. (1995) Explicit Methods for stiff ODEs from atmospheric chemistry. Appl. Numer. Math. 18, 413-430.
28. Verwer, J. G., Blom, J. G. and Hundsdorfer, W. H. (1996) An implicit-explicit approach for atmospheric transport-chemistry problems. Appl. Numer. Math. 20, 191-209.
29. Yamartino, R., Scire, J., Carmichael, G. R. and Chang, Y. S. (1992) The CALGRID mesoscale photochemical grid model. Atmospheric Environment 26A, 1493-1512.
30. Young, T. R. and Boris, J. P. (1977) A numerical technique for solving stiff ODEs associated with the chemical kinetics of reactive flow problems. J. phys. Chem. 81, 2424-2427.