Geodesic
A~nonlinear method for solving the problems of radiation transfer in medium
Matematičeskoe modelirovanie, Tome 8 (1996) no. 12, pp. 3-28.

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A nonlinear method is described for solving the time-dependent multigroup radiative transfer equation coupled with the energy balance equation. The method is based on the Quasi-Diffusion approach. The idea of this approach is to reduce problem dimension by averaging the equations over angular and energy variables. The functionals weakly depending on the solution of problem are introduced to close equivalently the resulting system of equations. The temperature is determined by solving the linearized energy balance and the efficient grey quasi-diffusion equations. The Frechet derivative of an averaged absorption cross-section with respect to temperature is used to improve the solution of the linearized equations. The one-dimensional geometries are considered. The numerical results are presented to show the efficiency of the proposed method. 
@article{MM_1996_8_12_a0,
     author = {D. Yu. Anistratov and E. N. Aristova and V. Ya. Gol'din},
     title = {A~nonlinear method for solving the problems of radiation transfer in medium},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--28},
     publisher = {mathdoc},
     volume = {8},
     number = {12},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1996_8_12_a0/}
}
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D. Yu. Anistratov; E. N. Aristova; V. Ya. Gol'din. A~nonlinear method for solving the problems of radiation transfer in medium. Matematičeskoe modelirovanie, Tome 8 (1996) no. 12, pp. 3-28. http://geodesic.mathdoc.fr/item/MM_1996_8_12_a0/