A. J. Krukovskiy, M. E. Ladonkina, Yu. A. Poveshchenko, I. V. Popov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (Moscow, Russian Federation)

Abstract. This paper presents a method for calculating the radiative energy transfer in the back and forth approximation for the case of cylindrically symmetric currents. The key element of the method is the scheme for calculating radiative heat transfer in a medium with opacity that strongly varies in space and time. The paper discusses the possibility of improving accuracy of solving a difference equations’ system by making the approximation of absorption coefficients more accurate. The numerical technique proposed for multi-parameter computing experiments makes it possible to obtain the radiation energy density as a quadrature of plasma opacity and emissivity. In two-temperature model of gas dynamics and magnetohydrodynamics, this determines the contribution of radiative heat transfer into the energy balance of the plasma electronic component. Numerical comparison of the proposed method with some diffusion methods was implemented via test examples simulating spatial inhomogeneity of the radiation field. It is shown that the calculations performed according to the methodology considered in this paper, give a qualitatively correct match with the analytical solution of the problem, in contrast to calculations performed by the method of diffuse approximation. The obvious advantage of the back and forth approximation is that integrality is inherent in its structure.

Key Words: radiative heat transfer, radiation gas dynamics, magnetohydrodynamics, “back and forth” approximation, finite-difference scheme

For citation: A. J. Krukovskiy, M. E. Ladonkina, Yu. A. Poveshchenko, I. V. Popov. Method for calculating radiative energy transfer in the “back and forth” approximation. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 24:4(2022), 436–451. DOI: https://doi.org/10.15507/2079-6900.24.202204.436-451

Information about the authors:

Alexander Ju. Krukovskiy, Senior Researcher, M.V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (4 Miusskaya Sq., Moscow 125047, Russia), D. Sci. (Physics and Mathematics), alexander-krukovskiy@yandex.ru

Marina E. Ladonkina, Senior Researcher, M.V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (4 Miusskaya Sq., Moscow 125047, Russia), Ph. D. (Physics andMathematics), ORCID: https://orcid.org/0000-0001-7596-1672, ladonkina@imamod.ru

Yuri A. Poveshchenko, Leading Researcher, M.V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (4 Miusskaya Sq., Moscow 125047, Russia), Dr. Sci. (Physics and Mathematics), ORCID: https://orcid.org/0000-0001-9211-9057, hecon@mail.ru

Igor V. Popov, Senior Researcher, M.V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (4 Miusskaya sq., Moscow, 125047), Ph. D. (Physics and Mathematics), ORCID: https://orcid.org/0000-0002-7347-8174, e-mail: piv2964@mail.ru