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A nonnegativity preserved efficient chemical solver applied to the air pollution forecast. (English) Zbl 1426.80016
Summary: Air pollution forecast is becoming more and more important nowadays. The numerically sticky chemical ordinary differential equations (ODEs) is a critical component of air pollution models. Various solvers have been designed for the chemical ODEs in the past. However, they are either slow or imprecise. In our previous work, we have designed a nonnegativity preserved efficient chemical solver MBE, which is an acronym for Modified-Backward-Euler. In this paper, we review MBE method and prove its convergence and stability mathematically, which guarantee that MBE results converge to the exact solutions as the step-size becomes smaller and MBE results with relatively small step-size can be used as the standard. Then we apply MBE to the Nested Air Quality Prediction Modeling System (NAQPMS). Comparison between MBE and the most popular solver LSODE is also made. Considering the speed and precision, MBE is a better choice for the air pollution forecast.

80M25 Other numerical methods (thermodynamics) (MSC2010)
80A32 Chemically reacting flows
65L05 Numerical methods for initial value problems
76V05 Reaction effects in flows
92E20 Classical flows, reactions, etc. in chemistry
Full Text: DOI
[1] Aro, C. J., CHEMSODE: a stiff ODE solver for the equations of chemical kinetics, Comput. Phys. Commun., 97, 304-314, (1996) · Zbl 0926.65072
[2] Chen, H. S.; Wang, Z. F.; Wu, Q. Z.; Wu, J. B.; Yan, P. Z.; Tang, X.; Wang, Z., Application of air quality multi-model forecast system in Guangzhou: model description and evaluation of PM10 forecast performance, Chin. J. Clim. Envi. Res., 18, 427-435, (2013)
[3] Feng, F.; Wang, Z. F.; Li, J.; Carmichael, G. R., A nonnegativity preserved efficient algorithm for atmospheric chemical kinetic equations, Appl. Math. Comput., 271, 519-531, (2015) · Zbl 1410.80013
[4] Gong, W. M.; Cho, H. R., A numerical scheme for the integration of the gas-phase chemical rate equations in three-dimensional atmospheric models, Atmos. Environ., 27, 2147-2160, (1993)
[5] Hindmarsh, A. C., LSODE and LSODI, two new initial value ordinary differential equation solvers, ACM-SIGNUM Newslett, 15, 10-11, (1980)
[6] Horowitz, L. W.; Walters, S.; Mauzerall, D. L.; Emmons, L. K.; Rasch, P. J.; Granier, C.; Tie, X.; Lamarque, J. F.; Schultz, M. G.; Tyndall, G. S.; Orlando, J. J.; Brasseur, G. P., A global simulation of tropospheric ozone and related tracers: description and evaluation of MOZART, version 2, J. Geophys. Res., 108, 4784, (2003)
[7] Houyoux, M. R.; Vukovich, J. M., Updates to the sparse matrix operator kernel emissions (SMOKE) modeling system and integration with models-3, Proceedings of the Emission Inventory: Regional Strategies for the Future, 1461, (1999), Air Waste Management Association Raleigh, NC
[8] Jacobson, M. Z.; Turco, R. P., SMVGEAR: a sparse-matrix, vectorized gear code for atmospheric models, Atmos. Environ., 28, 273-284, (1994)
[9] Jay, L. O.; Sandu, A.; Potra, F. A.; Carmichael, G. R., Improved quasi-steady-state-approximation methods for atmospheric chemistry integration, SIAM J. Sci. Comput., 18, 182-202, (1997) · Zbl 0869.65045
[10] Mathura, R.; Younga, J. O.; Schere, K. L.; Gipson, G. L., A comparison of numerical techniques for solution of atmospheric kinetic equations, Atmos. Environ., 32, 1535-1553, (1998)
[11] Mott, D. R.; Oran, E. S.; Leer, B. V., A quasi-steady-state solver for the stiff ordinary differential equations of reaction kinetics, J. Comput. Phys., 164, 407-428, (2000) · Zbl 0967.65083
[12] Sandu, A.; Verwer, J. G.; Loon, M. V.; Carmichael, G. R.; Potra, F. A.; Dabdub, D.; Seinfeld, J. H., Benchmarking stiff ODE solvers for atmospheric chemistry problems-i. implicit vs explicit, Atmos. Environ., 31, 3151-3166, (1997)
[13] Sandu, A.; Verwer, J. G.; Blom, J. G.; Spee, E. J.; Carmichael, G. R.; Potra, F. A., Benchmarking stiff ODE solvers for atmospheric chemistry problems II: rosenbrock solvers, Atmos. Environ., 31, 3459-3472, (1997)
[14] Seinfeld, J. H.; Pandis, S. N., Atmospheric chemistry and physics: from air pollution to climate change, (2006), John Wiley and Sons, Inc.
[15] Sun, P.; Chock, D. P.; Winkler, S. L., An implicit-explicit hybrid solver for a system of stiff kinetic equations, J. Comput. Phys., 115, 515-523, (1994) · Zbl 0812.65061
[16] Tang, X.; Zhu, J.; Wang, Z. F.; Wang, M.; Gbaguidi, A.; Li, J.; Shao, M.; Tang, G. Q.; Ji, D. S., Inversion of CO emissions over Beijing and its surrounding areas with ensemble Kalman filter, J. Atmos. Environ., 81, 676-686, (2013)
[17] Verwer, J. G.; Blom, J. G.; Loon, M. V.; Spee, E. J., A comparison of stiff ODE solvers for atmospheric chemistry problems, Atmos. Environ., 30, 49-58, (1996)
[18] Wang, Z. F.; Xie, F. Y.; Wang, X. Q.; An, J. L.; Zhu, J., Development and application of nested air quality prediction modeling system, Chin. J. Atmos. Sci., 30, 778-790, (2006)
[19] Wu, Q. Z.; Wang, Z. F.; Gbaguidi, A.; Gao, C.; Li, L. N.; Wang, W., A numerical study of contributions to air pollution in Beijing during carebeijing-2006, Atmos. Chem. Phys, 11, 5997-6011, (2011)
[20] Young, T. R.; Boris, J. P., A numerical technique for solving stiff ordinary differential equations associated with the chemical kinetics of reactive-flow problems, J. Phys. Chem., 81, 2424-2427, (1977)
[21] Zaveri, R. A.; Peters, L. K., A new lumped structure photochemical mechanism for large-scale applications, J. Geophys. Res., 104, 30387-30415, (1999)
[22] Zhang, Q.; Streets, D. G.; Carmichael, G. R.; He, K. B.; Huo, H.; Kannari, A.; Klimont, Z.; Park, I. S.; Reddy, S.; Fu, J. S.; Chen, D.; Duan, L.; Lei, Y.; Wang, L. T.; Yao, Z. L., Asian emissions in 2006 for the NASA INTEX-B mission, Atmos. Chem. Phys., 9, 5131-5153, (2009)
[23] Zhang, X.; Wang, T. J.; Shen, F. H.; Zhao, Y. Z., The comparison of numerical schemes for nonlinear atmospheric chemical kinetic equations, Sci. Meteorol. Sin., 30, 427-437, (2010)
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