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. 
@article{MM_2021_33_8_a6,
     author = {A. A. Shestakov},
     title = {Comparison of hybrid {DDAD/ST} and {DDAD-TVDR} schemes for solving {2D} radiative heat transfer},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {114--126},
     publisher = {mathdoc},
     volume = {33},
     number = {8},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_8_a6/}
}
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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/