On solving systems of chemical kinetics equations by explicit methods
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 74-86.

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We present some versions of the methods for solving systems of differential equations of chemical kinetics that base on approximations of a quasisteady state and a partial equilibrium. These methods are explicit and guarantee the positivity and boundedness of solutions for each time step. In contrast to the existing methods, the methods we propose ensure mass conservation and the fulfillment of the stoichiometric relations, which makes it possible to significantly increase the time meshsize while preserving accuracy.
Keywords: chemical kinetics, ordinary differential equation, explicit method, quasisteady state
Mots-clés : partial equlibrium.
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A. M. Lipanov; A. A. Bolkisev. On solving systems of chemical kinetics equations by explicit methods. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 74-86. http://geodesic.mathdoc.fr/item/SJIM_2014_17_2_a7/

[1] Westbrook C. K. et al., The Role of Comprehensive Detailed Chemical Kinetic Reaction Mechanisms in Combustion Research, Tech. Rep. LLNL-BOOK-405431, Lawrence Livermore National Laboratory, 2008

[2] Tropin A. V., Spivak S. I., “Priblizhennoe analiticheskoe integrirovanie pryamoi kineticheskoi zadachi”, Sib. zhurn. industr. matematiki, 10:4(32) (2007), 135–148 | MR | Zbl

[3] Korepanov M. A., “Matematicheskoe modelirovanie khimicheski reagiruyuschikh techenii”, Khim. fizika i mezoskopiya, 10:3 (2008), 268–279

[4] 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. Chemistry, 81:25 (1977), 2424–2427 | DOI

[5] Verwer J. G., “Gauss-Seidel iteration for stiff odes from chemical kinetics”, SIAM J. Sci. Comput., 15:5 (1994), 1243–1250 | DOI | MR | Zbl

[6] Verwer J. G., Simpson D., “Explicit methods for Stiff ODEs from atmospheric chemistry”, Appl. Numer. Math., 18 (1994), 413–430 | DOI

[7] Jay L. O. et al., “Improved quasi-steady-state-approximation methods for atmospheric chemistry integration”, SIAM J. Sci. Comput., 18:1 (1997), 182–202 | DOI | MR | Zbl

[8] Mott D. R., New Quasi-Steady State and Partial-EquilibriumMethods for Integrating Chemically Reacting Systems, Diss. Doct. Phylosophy, Univ. Michigan, 1999 | Zbl

[9] Qureshi S. R., Prosser R., “Implementation of alpha-QSS stiff integration methods for solving the detailed combustion chemistry”, Proc. World Congress on Engineering, v. 2, 2007 URL: http://www.iaeng.org/publication/WCE2007/WCE2007_pp1352-1357.pdf

[10] Guidry M., “Algebraic stabilization of explicit numerical integration for extremely stiff reaction networks”, J. Comput. Physics, 231:16 (2012), 5266–5288 | DOI | MR | Zbl

[11] Yanenko N. N., Metod drobnykh shagov resheniya mnogomernykh zadach matematicheskoi fiziki, Nauka, Novosibirsk, 1967 | Zbl

[12] Damian V. et al., “The kinetic preprocessor KPP – a software environment for solving chemical kinetics”, Computers and Chemical Engineering, 26:11 (2002), 1567–1579 | DOI

[13] Eggels R., Modelling of combustion processes and NO formation with reduced reaction mechanisms, Diss. Doct. Phylosophy, Eindhoven Univ. of Technology, 1995

[14] Mott D. R., Oran E., van Leer B., “Identifying and Imposing Partial Equilibriumin Chemically Reacting Systems”, 41St AIAA Aerospace Sciences Meeting (Reno, NV AIAA), American Institute of Aeronautics and Astronautics, 2003