Simulation of radiative heat transfer in supersonic plasma flows taking into account the doppler shift of lines
Matematičeskoe modelirovanie, Tome 33 (2021) no. 4, pp. 95-115.

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A version of the Lebesgue averaging method of the radiative transfer equation over the photon energy is presented, taking into account the directional Doppler shift of the lines. The method is designed to simulate heat transfer by radiation in supersonic plasma flows with extremely high velocity and temperature gradients. In order to assess the influence of the Doppler effect on heat transfer, calculations of model test problems were carried out.
Keywords: collisional-radiative plasmas, Doppler shift of lines, radiative heat transfer, Lebesgue averaging method.
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A. V. Shilkov; N. A. Sivakov. Simulation of radiative heat transfer in supersonic plasma flows taking into account the doppler shift of lines. Matematičeskoe modelirovanie, Tome 33 (2021) no. 4, pp. 95-115. http://geodesic.mathdoc.fr/item/MM_2021_33_4_a5/

[1] W. H. McCrea, K. K. Mitra, “Schuster's problem for a moving atmosphere”, Zeitschrift für Astrophysik, 11 (1936), 359–378 (Mit 5 Abbildungen) | Zbl

[2] D. Mihalas, Stellar Atmospheres, 2-nd ed., W.H. Freeman, San Francisco, 1978

[3] A. Peraiah, An Introduction to Radiative Transfer, Cambridge Univ. Press, 2001 | MR

[4] I. L. Tsvetkova, A. V. Shilkov, “Osrednenie uravneniia perenosa v rezonansno pogloshchaiushchei srede”, Matem. modelirovanie, 1:1 (1989), 91–100 | MR | Zbl

[5] A. V. Shilkov, “Metody osredneniia sechenii i energeticheskogo spektra v zadachakh perenosa neitronov”, Matem. modelirovanie, 3:2 (1991), 63–81 | MR

[6] A. V. Shilkov, “Generalized multigroup approximation and Lebesgue averaging method in particle transport problems”, Transp. Theory and Stat. Phys., 23:6 (1994), 781–814 | DOI | MR | Zbl

[7] A. V. Shilkov, M. N. Gertsev, “Verification of the Lebesgue averaging method”, Math. Models and Comp. Simulations, 8:2 (2016), 93–107 | DOI | MR | MR | Zbl

[8] V. Ambartzumian, “The effect of the absorption lines on the radiative equilibrium of the outer layers of the stars”, Uch. zapiski Leningr. univ. Seriya Mat. nauk (Astronomiya), 6:1 (1936), 7–18 | MR

[9] K. Ia. Kondratev, Perenos dlinnovolnovogo izlucheniia v atmosfere, Gostekhizdat, M., 1950

[10] J. C. Stewart, “Non-grey radiative transfer”, Quant. Spectr. and Rad. Transfer, 4 (1964), 723–729 | DOI

[11] M. N. Nikolaev, A. A. Ignatov, N. V. Isaev, V. F. Kokhlov, “The method of subgroups for considering the resonance structure of the cross sections in neutron calculations. Part 1”, Soviet Atomic Energy, 29:1 (1970), 689–695 | DOI

[12] V. Ya. Gol'din, B. N. Chetverushkin, “Methods of solving one-dimentional problems of radiation gas dynamics”, USSR Comp. Math. and Math. Physics, 12:4 (1972), 177–189 | DOI | MR

[13] A. A. Arking, K. Grossman, “The Influence of line shape and band structure on temperatures in planetary atmospheres”, J. Atmosph. Sci., 29 (1972), 937–949 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[14] D. E. Cullen, “Application of the probability table method to multigroup calculations of neutron transport”, Nuclear Sci. Eng., 55 (1974), 387–400 | DOI

[15] V. M. Krivtsov, “Ob odnom podkhode k raschetu selektivnogo izlucheniia”, Zh. vych. mat. i mat. fiziki, 14:6 (1974), 1595–1599

[16] M. F. Modest, “The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer”, ASME J. Heat Transfer, 113:3 (1991), 650–656 | DOI

[17] M. F. Modest, H. Zhang, “The full-spectrum correlated-k distribution for thermal radiation from molecular gas-particulate mixtures”, ASME J. Heat Transfer, 124:1 (2002), 30–38 | DOI

[18] A. A. Lacis, V. Oinas, “A description of the correlated k-distribution method for modeling nongray gaseous absorption. Thermal emission and multiple scattering in vertically inhomogeneous atmospheres”, J. Geoph. Research, 96:D5 (1991), 9027–9063 | DOI

[19] M. K. Denison, B. W. Webb, “The spectral-line-based weighted-sum-of-gray-gases model in nonisothermal nonhomogeneous media”, ASME J. of Heat Transfer, 117:2 (1995), 359–365 | DOI

[20] S. D. Tvorogov, “Primenenie riadov eksponent dlia integrirovaniia uravneniia perenosa po chastote”, Optika atm. i okeana, 12:9 (1999), 763–766

[21] W. M. Elsasser, “Mean absorption and equivalent absorption coefficient of a band spectrum”, Phys. Rev., 54 (1938), 126–129 | DOI

[22] B. M. Smirnov, G. V. Shlyapnikov, “Infrared radiation transfer in molecular gases”, Soviet Physics Uspekhi, 23:3 (1980), 179 | DOI | DOI

[23] Y. B. Raizer Y. P. Zel'dovich, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, v. 1, Academic Press, New York, 1966; v. 2, 1967

[24] I. I. Sobelman, L. A. Vainshtein, E. A. Yukov, Excitation of Atoms and Broadening of Spectral Lines, Springer, Heidelberg, 1981

[25] A. F. Nikiforov, V. G. Novikov, V. B. Uvarov, Quantum-Statistical Models of Hot Dense Matter. Methods for Computation Opacity and Equation of State, Birkhauser-Verlag, 2005 | MR | Zbl

[26] S. T. Surzhikov, Opticheskie svoistva gazov i plazmy, Izd-vo MGTU im. N.E. Baumana, M., 2004

[27] A. V. Shilkov, “The moment method of Lebesgue aggregation and spectrum recovery in particle transport problems”, Math. Models and Comp. Simulations, 9:3 (2017), 263–280 | DOI | MR | Zbl

[28] A. V. Shilkov, “Metod lebegovykh momentov dlia resheniia uravneniia perenosa neitronov”, Matem. modelirovanie, 32:5 (2020), 59–94 | MR | Zbl

[29] A. V. Shilkov, S. V. Shilkova, “Sistema ATRAD dlia raschetov atmosfernoi radiatsii: raschety perenosa teplovogo izlucheniia dlia bezoblachnoi letnei atmosfery srednikh shirot”, Matem. modelirovanie, 11:1 (1999), 18–24

[30] E. N. Aristova, V. Ia. Goldin, A. V. Shilkov, S. V. Shilkova, “Sistema ATRAD dlia raschetov atmosfernoi radiatsii: raschety perenosa solnechnogo izlucheniia dlia letnei atmosfery srednikh shirot”, Matem. modelirovanie, 11:5 (1999), 117–125