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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 512, Pages 89–95
DOI: https://doi.org/10.31857/S2686954323600295 (Mi danma405) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Three-layer scheme for solving the radiation diffusion equation

B. N. Chetverushkin, O. G. Olkhovskaya, V. A. Gasilov

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russian Federation
Citations (1)
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DOI: https://doi.org/10.31857/S2686954323600295
Abstract: A method has been developed for the numerical solution of a nonlinear equation describing the diffusion transfer of radiation energy. The method is based on the introduction of the second time derivative with a small parameter into the parabolic equation and an explicit difference scheme. Explicit approximation of the initial equation makes it possible to implement on its basis an algorithm that is effectively adapted to the architecture of high-performance computing systems. The new scheme provides, in comparison with the original scheme, a larger time integration step and a sufficiently high resolution quality of the solution structure, providing the second order of accuracy. A heuristic algorithm for choosing the parameters of a three-layer difference scheme is proposed. A promising field of application of the method can be problems of plasma physics and astrophysics.
Keywords: radiative transfer of energy, radiation diffusion model, nonlinear parabolic equation, explicit difference scheme, high-performance computing.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics 075-15-2022-283
This work was supported by the Moscow Center for Fundamental and Applied Mathematics, agreement no. 075-15-2022-283 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 11.05.2023
Revised: 11.07.2023
Accepted: 13.07.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 1, Pages 320–325
DOI: https://doi.org/10.1134/S1064562423700837
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: B. N. Chetverushkin, O. G. Olkhovskaya, V. A. Gasilov, “Three-layer scheme for solving the radiation diffusion equation”, Dokl. RAN. Math. Inf. Proc. Upr., 512 (2023), 89–95; Dokl. Math., 108:1 (2023), 320–325
Citation in format AMSBIB
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\by B.~N.~Chetverushkin, O.~G.~Olkhovskaya, V.~A.~Gasilov
\paper Three-layer scheme for solving the radiation diffusion equation
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 512
\pages 89--95
\mathnet{http://mi.mathnet.ru/danma405}
\crossref{https://doi.org/10.31857/S2686954323600295}
\elib{https://elibrary.ru/item.asp?id=54538935}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 1
\pages 320--325
\crossref{https://doi.org/10.1134/S1064562423700837}
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