Geodesic
Comparison of hybrid DDAD/ST and DDAD-TVDR schemes for solving 2D radiative heat transfer
Matematičeskoe modelirovanie, Tome 33 (2021) no. 8, pp. 114-126.

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The development of monotone second-order difference schemes for solving radiative heat transfer is a topic of many papers. Hybrid schemes comprise one of their classes. They exploit monotone first-order schemes where solutions are not monotone, and higher order schemes where they are smooth. Their construction in 1D does not cause severe difficulties, but in case of more than one dimension these schemes may bring s nonmonotonic behavior in time and non-converging iterations because of changing from one scheme to another. That is why the development of monotonic second-order schemes for radiative heat transfer is still a question of the hour. The paper discusses a standard hybrid scheme for solving 2D radiative heat transfer. The scheme changes from secondorder to first-order approximation when the non-monotonic behavior occurs. The scheme is show to be monotonic in space, but produce non-monotonic time dependences in some cases. We show how to avoid such dependencies by constructing the scheme in another way.
Keywords: hybrid difference scheme, radiative heat transfer. 
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A. A. Shestakov. Comparison of hybrid DDAD/ST and DDAD-TVDR schemes for solving 2D radiative heat transfer. Matematičeskoe modelirovanie, Tome 33 (2021) no. 8, pp. 114-126. http://geodesic.mathdoc.fr/item/MM_2021_33_8_a6/

[1] L. P. Bass, A. M. Woloshchenko, T. A. Germogenova, Metody diskretnykh ordinat, IPM im. M.V. Keldysha AN SSSR, M., 1986

[2] IU. I. Shokin, Metod differenzialnogo priblizheniia, Nauka, Novosibirsk, 1974

[3] R. P. Fedorenko, “The application of difference schemes of high accuracy to the numerical solution of hyperbolic equations”, Comp. Math. Math. Phys., 2:6 (1963), 1355–1365 | DOI | MR | Zbl

[4] W. A. Rhoades, W. W. Engle, “A new weighted-difference formulation for discrete ordinates calculations”, Trans. Am. Nucl. Soc., 27 (1977), 776–777

[5] A. A. Shestakov, “Chislennye effekty pri modelirovanii perenosa teplovogo izlucheniia”, VANT, seriia «Matematicheskoe modelirovanie fizicheskikh protsessov», 2019, no. 1, 44–56 | Zbl

[6] B. Karlson, “Chislennoe reshenie zadachi kineticheskoi teorii neitronov”, Teoriya yadernykh reaktorov, Atomizdat, M., 1963, 243–258

[7] A. Harten, “High Resolution Schemes for Hyperbolic Conservation Laws”, J. Comput. Phys., 49 (1983), 357–393 | DOI | MR | Zbl

[8] A. D. Gadzhiev, I. A. Kondakov, V. N. Pisarev, O. I. Starodumov, A. A. Shestakov, “Metod diskretnich ordinat s iskustvennoi dissipaziei (DDAD-skhema) dlia chislennogo resheniia uravneniia perenosa neitronov”, VANT, seriia «Matematicheskoe modelirovanie fizicheskikh protsessov», 2003, no. 4, 13–24

[9] B. V. Rogov, V. N. Mikhailovskaya, “Monotone High-Accuracy Compact Running Scheme for Quasi-LinearHyperbolic Equations”, Math. Models Comp. Simul., 4 (2012), 375–384 | DOI | MR | Zbl

[10] A. I. Bochkov, V. A. Shumilin, “Schema tipa DSn-metoda resheniia dvumernogo uravneniia perenosa na chetyrekhugolnich prostranstvennich setkach”, VANT, seriia «Matematicheskoe modelirovanie fizicheskikh protsessov», 2008, no. 4, 13–18

[11] A. D. Gadzhiev, V. V. Zaviyalov, A. A. Shestakov, “Primenenie TVD podkhoda k DSn metodu resheniia uravneniia perenosa teplovogo izlucheniia v osesimmetrichnoi RZ geometrii”, VANT, seriia «Matematicheskoe modelirovanie fizicheskikh protsessov», 2010, no. 2, 30–39

[12] A. A. Shestakov, “TVDR skhemi dlia resheniia sistemi uravnenii perenosa teplovogo izlucheniia”, VANT, seriia «Matemat. modelirovanie fizich. protsessov», 2019, no. 2, 17–36