Abstract
Large ozone concentrations have harmful effects on forests and crops when these exceed some critical levels. It is believed that the damages in USA due to high ozone concentrations exceed several billions dollars. Therefore it is worthwhile to investigate different actions that could be applied in the attempts to reduce the harmful effects. One needs reliable mathematical models in such studies. Reliable models are normally very big and it is difficult to treat them numerically, because they lead, after some kind of discretization and after the implementation of some appropriate splitting procedure, to several very huge systems of ordinary differential equations (up to order of 106). Moreover, these systems have to be treated numerically during many time-steps (typically several thousand time-steps per run are necessary). The use of modern parallel and/or vector machines is an important condition in the efforts to handle successfully big air pollution models. If the numerical algorithms are both sufficiently fast and sufficiently accurate, then different simulations can be carried out.
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References
Bott, A., ”A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes”, Mon. Weather Rev., 117(1989), 1006–1015.
Brandt, J., Wasniewski, J. and Zlatev, Z., ”Handling the chemical part in large air pollution models”, Appl. Math. and Comp. Sci., 6 (1996), 101–121.
Chock, D. P., Winkler, S. L. and Sun, P., ”Comparison of stiff chemistry solvers for air quality models”, Environ. Sci. Technol., 28 (1994), 1882–1892.
Crowley, W. P., ”Numerical advection experiments”, Mon. Weath. Rev., 96 (1968), 1–11.
Deuflhard, P., Nowak, U. and Wulkow, M., ”Recent development in chemical computing”, Computers Chem. Engng., 14 (1990), 1249–1258.
Forester, C. K., ”Higher order monotonic convective difference schemes”, J. Comput. Phys., 23(1977), 1–22.
Fornberg, B., ”A practical guide to pseidospectral methods”. Cambridge University Press, Cambridge, 1996.
Hertel, O., Berkowicz, R., Christensen, J. and Hov, Ø., ”Test of two numerical schemes for use in atmospheric transport-chemistry models”, Atmos. Environ., 27A (1993), 2591–2611.
Hesstvedt, E., Hov, Ø. and Isaksen, I. A., ”Quasi-steady-state approximations in air pollution modelling: comparison of two numerical schemes for oxidant prediction”, Internat. J. Chem. Kinetics, 10 (1978), 971–994.
Holm, E. V., ”High-order numerical methods for advection in atmospheric models”, PhD Thesis, Department of Meteorology, Stockholm University, 1994.
Hov, Ø., Zlatev, Z., Berkowicz, R., Eliassen, A. and Prahm, L. P., ”Comparison of numerical techniques for use in air pollution models with non-linear chemical reactions”, Atmos. Environ., 23 (1988), 967–983.
Lambert, J. D., ”Numerical methods for ordinary differential equations”, Wiley, Chichester-New York-Brisbane-Toronto-Singapore, 1991.
Marchuk, G. I., ”Mathematical modeling for the problem of the environment”, Studies in Mathematics and Applications, No. 16, North-Holland, Amsterdam, 1985.
McRae G. J., Goodin, W. R. and Seinfeld, J. H., ”Numerical solution of the atmospheric diffusion equations for chemically reacting flows”, J. Comp. Phys., 45 (1984), 1–42.
Molenkampf, C. R., ”Accuracy of finite-difference methods applied to the advection equation”, J. Appl. Meteor., 7 (1968), 160–167.
Odman, M. T., Kumar, N. and Russell, A. G., ”A comparison of fast chemical kinetic solvers for air quality modeling”, Atmos. Environ., 26A (1992), 1783–1789.
Peters, L. K., Berkowitz, C. M., Carmichael, G. R., Easter, R. C., Fairweather, G., Ghan, S. J., Hales, J. M., Leung, L. R., Pennell, W. R., Potra, F. A., Saylor, R. D. and Tsang, T. T., ”The current state and future direction of Eulerian models in simulating the tropospherical chemistry and transport of trace species: A review”, Atmos. Environ., 29 (1995), 189–221
Petzold, L. R., ”Order results for implicit Runge-Kutta methods applied to differential-algebraic systems”, SIAM J. Numer. Anal., 23 (1986), 837–852.
Shieh, D. S., Chang, Y. and Carmichael, G. R., ”The evaluation of numerical techniques for solution of stiff ordinary differential equations arising from chemical kinetic problems”, Environ. Software, 3 (1988), 28–38.
Skelboe, S. and Zlatev, Z., ”Exploiting the natural partitioning in the numerical solution of ODE systems arising in atmospheric chemistry”, Springer, Berlin, to appear.
Verwer, J. G. and Simpson, D., ”Explicit methods for stiff ODE's from atmospheric chemistry”, Appl. Numer. Math., to appear.
Zlatev, Z., ”Application of predictor-corrector schemes with several correctors in solving air pollution problems”, BIT, 24 (1984), 700–715.
Zlatev, Z., ”Computer treatment of large air pollution models”, Kluwer Academic Publishers, Dordrecht-Boston-London, 1995.
Zlatev, Z., Fenger, J. and Mortensen, L., ”Relationships between emission sources and excess ozone concentrations”, Comput. Math. Applics., to appear.
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© 1997 Springer-Verlag Berlin Heidelberg
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Brandt, J., Christensen, J., Dimov, I., Georgiev, K., Uria, I., Zlatev, Z. (1997). Treatment of large air pollution models. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_80
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DOI: https://doi.org/10.1007/3-540-62598-4_80
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