Neural network approach in modelling vibrational kinetics of carbon dioxide
DOI:
https://doi.org/10.21638/spbu01.2022.409Abstract
The study is devoted to modeling nonequilibrium vibrational kinetics of carbon dioxide taking into account complex mechanisms of relaxation and intermode energy exchanges. The possibilities of using machine learning methods to improve the performance of numerical simulation of non-equilibrium carbon dioxide flows are studied. Various strategies for increasing the efficiency of the hybrid four-temperature model of CO2 kinetics are considered. The neural network approach proposed by the authors to calculate the rate of vibrational relaxation in each mode turned out to be the most promising. For the problem of spatially homogeneous relaxation, estimates of the error and computational costs of the developed algorithm are carried out, and its high accuracy and efficiency are demonstrated. For the first time, the carbon dioxide flow behind a plane shock wave was simulated in a full state-to-state approximation. A comparison with the results obtained in the framework of the hybrid four-temperature approach is carried out, and the equivalence of the approaches is shown. This makes it possible to recommend developed multitemperature approxima tions as the main tool for solving problems of nonequilibrium kinetics and gas dynamics. The hybrid four-temperature approach using the neural network method for calculating relaxation terms showed the acceleration of numerical simulation in time by more than an order of magnitude, while maintaining accuracy. This technique can be recommended for solving complex multidimensional problems of nonequilibrium gas dynamics, including state-to-state chemical reactions.Keywords:
vibrational relaxation rate, state-to-state and multi-temperature kinetics, artificial neural network, carbon dioxide, machine learning
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References
Литература
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References
1. Kustova E.V., Mekhonoshina M.A. Multi-temperature vibrational energy relaxation rates in CO2. Physics of Fluids 32, 096101 (2020). https://doi.org/10.1063/5.0021654
2. Kosareva A.A., Kunova O.V., Kustova E.V., Nagnibeda E.A. Four-temperature kinetic model for CO2 vibrational relaxation. Physics of Fluids 33 (1), 016103 (2021). https://doi.org/10.1063/5.0035171
3. Regazzoni F., Dede’ L., Quarteroni A. Machine learning for fast and reliable solution of time-dependent differential equations. J. Comput. Phys. 397, 108852 (2019). https://doi.org/10.1016/j.jcp.2019.07.050
4. Gorikhovskii V.I., Evdokimova T.O., Poletanskii V.A. Neural networks in solving differential equations. Journal of Physics: Conference Series 2308 (1), 012008 (2022). https://doi.org/10.1088/1742-6596/2308/1/012008
5. Stokes P.W., Cocks D.G., Brunger M.J., White R.D. Determining cross sections from transport coefficients using deep neural networks. Plasma Sources Science Technology 29 (5), 055009 (2020). http://dx.doi.org/10.1088/1361-6595/ab85b6
6. Istomin V.A., Kustova E.V. PAINeT: Implementation of neural networks for transport coefficients calculation. Journal of Physics: Conference Series 1959 (1), 012024 (2021). https://doi.org10.1088/1742-6596/1959/1/012024
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8. Campoli L., Kustova E., Maltseva P. Assessment of machine learning methods for state-to-state approaches. Mathematics, 10 (6), 928 (2022). https://doi.org/10.3390/math10060928
9. Sahai A., Lopez B.E., Johnston C.O., Panesi M. Adaptive coarse graining method for energy transfer and dissociation kinetics of polyatomic species. J. Chem. Phys., 147, 054107, 2017. https://doi.org/10.1063/1.4996654
10. Gorikhovskii V.E., Nagnibeda Е.А. Optimization of CO2 vibrational kinetics modeling in the full state-to-state approach. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 7 (65), iss. 3, 527-538 (2020). https://doi.org/10.21638/spbu01.2020.315 (In Russian) [Eng. transl.: Vestnik St Petersburg University. Mathematics 53, iss. 3, 358-365 (2020). https://doi.org/10.1134/S1063454120030085].
11. Kunova O.V., Kosareva A.A., Kustova E.V., Nagnibeda E.A. Vibrational relaxation of carbon dioxide in various approaches. Physical Review Fluids 5, 123401 (2020). https://doi.org/10.1103/PhysRevFluids.5.123401
12. Park C. Nonequilibrium Hypersonic Aerothermodynamics. New York; Chichester; Brisbane; Toronto; Singapore, J. Wiley and Sons (1990).
13. Schwartz R.N., Slawsky Z.I., Herzfeld K.F. Calculation of vibrational relaxation times in gases. J. Chem. Phys., 20, 1591-1599 (1952).
14. Gorikhovsky V.I., Nagnibeda E.A. Energy exchange rate coefficients in modeling carbon dioxide kinetics: Calculation optimization. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 6 (64), iss. 1, 659-671 (2019). https://doi.org/10.21638/11701/spbu01.2019.402 (In Russian) [Eng. transl.: Vestnik St Petersburg University, Mathematics 52, iss. 4, 428-435 (2019). https://doi.org/10.1134/S1063454119040046].
15. Adamovich I.V., Macheret S.O., Rich J.W., Treanor C.E. Vibrational energy transfer rates using a forced harmonic oscillator model. J. Thermophys. Heat Transf. 12 (1), 57-65 (1998).
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Published
2022-12-26
How to Cite
Gorikhovskii, V. I., & Kustova, E. V. (2022). Neural network approach in modelling vibrational kinetics of carbon dioxide. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(4), 665–678. https://doi.org/10.21638/spbu01.2022.409
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
