Second-order Rosenbrock method applied to photochemical dispersion problems

SIAM Journal of Scientific Computing

Volumn 20, Issue 4, 1999, Pages 1456-1480

  Verwer, J G ^a   Spee, E J ^a   Blom, J G ^a   Hundsdorfer, W ^a  

^a CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

AIR POLLUTION; APPROXIMATION THEORY; ATMOSPHERIC CHEMISTRY; DIFFUSION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PHOTOCHEMICAL REACTIONS; REACTION KINETICS;

APPROXIMATE FACTORIZATION; ATMOSPHERIC CHEMICAL KINETICS; ATMOSPHERIC DISPERSION; JACOBIAN MATRIX; LONG RANGE TRANSPORT AIR POLLUTION MODEL; ROSENBROCK METHOD; STIFF ORDINARY DIFFERENTIAL EQUATION; STRANG-TYPE OPERATOR SPLITTING; TIME DEPENDENT ADVECTION DIFFUSION REACTION;

PROBLEM SOLVING;

EID: 0033279637     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827597326651     Document Type: Article

References (32)

1. I. AHMAD AND M. BERZINS, An algorithm for ODEs from atmospheric dispersion problems, Appl. Numer. Math., 25 (1997), pp. 137-150.
2. R. M. BEAM AND R. F. WARMING, An implicit finite-difference algorithm for hyperbolic systems in conservation-law form, J. Comput. Phys. 22 (1976), pp. 87-110.
3. R. F. WARMING AND R. M. BEAM, An extension of A-stability to alternating direction methods, BIT 19 (1979), pp. 395-417.
4. V. DAMIAN-IORDACHE AND A. SANDU, KPP-A Symbolic Preprocessor for Chemistry Kinetics-User's Guide, Department of Mathematics, University of Iowa, Iowa City, IA, 1995.
5. K. DEKKER AND J. G. VERWER, Stability of Runge Kutta Methods for Stiff Nonlinear Differential Equations, Elsevier-North Holland, Amsterdam, 1984.
6. H. ELBERN, Parallelization and load balancing of a comprehensive atmospheric chemistry transport model, Atmos. Environ., 31 (1997), pp. 3561-3574.
7. E. HAIRER AND G. WANNER, Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, 2nd ed., Springer-Verlag, Berlin, 1996.
8. O. HERTEL, R. BERKOWICZ, J. CHRISTENSEN, AND Ø. HOV, Test of two numerical schemes for use in atmospheric transport-chemistry models, Atmos. Environ., 27 (1993), pp. 2591-2611.
9. W. HUNDSDORFER, B. KOREN, M. VAN LOON, AND J. G. VERWER, A positive finite-difference advection scheme, J. Comput. Phys., 117 (1995), pp. 35-46.
10. M. Z. JACOBSON AND R. P. TURCO, SMVGEAR: A sparse-matrix, vectorized gear code for atmospheric models, Atmos. Environ., 28 (1994), pp. 273-284.
11. L. O. JAY, A. SANDU, F. A. POTRA, AND G. R. CARMICHAEL, Improved quasi-steady-state-approximation methods for atmospheric chemistry integration, SIAM J. Sci. Comput., 18 (1997), pp. 182-202.
12. CHR. KESSLER, Entwicklung eines Effizienten Lösungsverfahrens zur Modellmäßigen Beschreibung der Ausbreitung und Chemischen Umwandlung Reaktiver Luftschadstoffe, Ph.D. thesis, Fakultät für Maschinenbau der Universität Karlsruhe, Verlag Shaker, Aachen, 1995.
13. O. KNOTH AND R. WOLKE, A comparison of fast chemical kinetic solvers in a simple vertical diffusion model, in Proceedings 20th International Meeting on Air Pollution Modelling and its Applications, Valencia, Spain, 1993.
14. J. MATTHIJSEN, private communication, Laboratoire d'Aerologie OMP, Toulouse, France, 1995.
15. G. J. MCRAE, W. R. GOODIN, AND J. H. SEINFELD, Numerical solution of the atmospheric diffusion equation for chemically reacting flows, J. Comput. Phys., 45 (1982), pp. 1-42.
16. A. SANDU, F. A. POTRA, G. R. CARMICHAEL, AND V. DAMIAN, Efficient implementation of fully implicit methods for atmospheric chemical kinetics, J. Comput. Phys., 129 (1996), pp. 101-110.
17. A. SANDU, J. G. VERWER, J. G. BLOM, E. J. SPEE, AND G. R. CARMICHAEL, Benchmarking stiff ODE solvers for atmospheric chemistry problems II: Rosenbrock solvers, Atmos. Environ., 31 (1997), pp. 3459-3472.
18. A. SANDU, J. G. VERWER, M. VAN LOON, G. R. CARMICHAEL, F. A. POTRA, D. DABDUB, AND J. H. SEINFELD, Benchmarking stiff ODE solvers for atmospheric chemistry problems I: Implicit versus explicit, Atmos. Environ., 31 (1997), pp. 3151-3166.
19. A. SANDU, Numerical Aspects of Air Quality Modeling, Ph.D. thesis, University of Iowa, Iowa City, IA, 1997.
20. P. K. SMOLARKIEWICZ AND P. J. RASCH, Monotone advection on the sphere: An Eulerian versus semi-Lagrangian approach, J. Atmos. Sci., 48 (1991), pp. 793-810.
21. E. J. SPEE, P. M. DE ZEEUW, J. G. VERWER, J. G. BLOM, AND W. HUNDSDORFER, A Numerical Study for Global Atmospheric Transport-Chemistry Problems, Revision of CWI Report MAS-R9702, CWI, Amsterdam, 1997.
22. B. SPORTISSE, A. JAUBERTIE, AND P. PLION, Reducing mechanism in chemical kinetics for the simulation of reactive transport: An application to air pollution modeling, in Proceedings Saint-Venant Symposium, INRIA, Paris, 1997.
23. G. STRANG, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506-517.
24. P. SUN, A pseudo-non-time-splitting method in air quality modeling, J. Comput. Phys., 127 (1996), pp. 152-157.
25. P. J. VAN DER HOUWEN, B. P. SOMMEIJER, AND J. KOK, The iterative solution of fully implicit discretizations of three-dimensional transport models, Appl. Numer. Math., 25 (1997), pp. 243-256.
26. J. G. VERWER, S-stability properties for generalized Runge-Kutta methods. Numer. Math., 27 (1977), pp. 359-370.
27. J. G. VERWER, Gauss-Seidel iteration for stiff ODEs from chemical kinetics, SIAM J. Sci. Comput., 15 (1994), pp. 1243-1250.
28. J. G. VERWER AND J. G. BLOM, On the coupled solution of diffusion and chemistry in air pollution models, in Proceedings of the Third International Congress on Industrial and Applied Mathematics (ICIAM/GAMM 95), ZAMM, Issue 4: Applied Sciences, Especially Mechanics, E. Kreuzer and O. Mahrenholtz, eds., Akademie Verlag, Berlin, 1996, pp. 454-457.
29. J. G. VERWER, J. G. BLOM, M. VAN LOON, AND E. J. SPEE, A comparison of stiff ODE solvers for atmospheric chemistry problems, Atmos. Environ., 30 (1995), pp. 49-58.
30. J. G. VERWER AND D. SIMPSON, Explicit methods for stiff ODEs from atmospheric chemistry, Appl. Numer. Math, 18 (1995), pp. 413-430.
31. P. WARNECK, Chemistry of the Natural Atmosphere, Academic Press, San Diego, CA, 1988.
32. Z. ZLATEV, Computer Treatment of Large Air Pollution Models, Kluwer Academic Publishers, Norwell, MA, 1995.