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Analysis of the Quasi-Transfer Approximation in Problems with Analytical Solution

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Abstract

The quasi-transfer approximation reduces the numerical solution of the kinetic equation to solving the diffusion equation through introducing correction factors. The transition to the diffusion equation simplifies the numerical solution of the kinetic equation and makes it possible to use monotonic schemes of the second order of accuracy in solving problems of radiative heat transfer. In this case, it is very important to know the behavior of the correction coefficients, because, for the correctness of the diffusion equation, it is necessary that the diffusion coefficient be positive. This can be verified most easily in problems having analytical solutions. The aim of this work is to study the quasi-transfer approximation in problems with an analytical solution and the behavior of correction coefficients in optically dense and transparent media.

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REFERENCES

  1. V. Ya. Gol’din, “A quasi-diffusion method of solving the kinetic equation,” USSR Comput. Math. Math. Phys. 4 (6), 136–149 (1964).

    Article  MathSciNet  Google Scholar 

  2. N. G. Karlykhanov and M. Yu. Kozmanov, “Account for kinetic effects in the diffusion approximation for computing radiation transfer,” VANT, Ser. Mat. Model. Fiz. Protsessov, No. 4, 3–9 (2010).

    Google Scholar 

  3. E. N. Aristova, V. Ya. Gol’din, and A. V. Kolpakov, “Radiation transfer through an annular slot in a body of revolution,” Mat. Model. 9 (4), 1–10 (1997).

    MATH  Google Scholar 

  4. A. D. Gadzhiev, V. V. Zav’yalov, S. A. Grabovenskaya, and A. A. Shestakov, “Application of the TVD approach to quasi-diffusion solution of the thermal radiation transfer equation,” VANT, Ser. Mat. Model. Fiz. Protsessov, No. 3, 3–14 (2010).

    Google Scholar 

  5. J. A. Fleck and J. D. Cummings, “An implicit Monte Carlo scheme for calculating time and frequency dependent nonlinear radiation transport,” J. Comput. Phys. 8 (3), 313–342 (1971).

    Article  MathSciNet  Google Scholar 

  6. V. V. Zav’yalov and A. A. Shestakov, “Simplified solutions of the Fleck problems,” VANT, Ser. Mat. Model. Fiz. Protsessov, No. 1, 45–52 (2013).

    Google Scholar 

  7. E. W. Larsen, G. Thommes, A. Klar, M. Sead, and T. Gotz, “Simplified PN approximations to the equations of radiative heat transfer and applications,” J. Comput. Phys. 183, 652–675 (2002).

    Article  MathSciNet  Google Scholar 

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  1. Russian Federal Nuclear Center—All-Russian Research Institute of Technical Physics, 456770, Snezhinsk, Chelyabinsk oblast, Russia

    A. A. Shestakov

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  1. A. A. Shestakov
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Correspondence to A. A. Shestakov.

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Translated by E. Chernokozhin

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Shestakov, A.A. Analysis of the Quasi-Transfer Approximation in Problems with Analytical Solution. Comput. Math. and Math. Phys. 60, 833–843 (2020). https://doi.org/10.1134/S0965542520050152

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  • DOI: https://doi.org/10.1134/S0965542520050152

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