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RUSSIAN FEDERAL NUCLEAR CENTER 
ALLRUSSIAN RESEARCH INSTITUTE OF EXPERIMENTAL PHYSICS 

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ACCOUNT FOR KINETIC EFFECTS IN APPROXIMATION OF RADIATING HEAT TRANSFER TO COMPUTE RADIATION TRANSFER PROBLEMS
D. A. Koshutin, A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc 2024. Вып.1. С. 3741.
One of the most difficult problems of radiation gas dynamics is solution of a multidimensional equation of radiative heat transfer, the difficulty of which mostly comes from the largedimensional character of the phase space. Because of this, they implement different approximations that simplify the radiation transfer problem. These approximations comprise, for example, approximation of radiative heat transfer. Here, complex enough problems of selecting an effective iteration method and construction of a monotonous scheme of upgraded accuracy for the kinetic equation are eliminated. When we implement approximation of radiative heat transfer, different correction factors are used. The need in accurate correction factors in approximation of the radiative heat transfer stimulated development of new mathematical models. In 2016, M. Yu. Kozmanov, D. A. Koshutin and A. A. Shestakov suggested replacing a system of 2D transfer equations with the equations of quasithermal conductivity, where the solutions are obtained by parabolic equations. This is a generalization of the quasitransfer method offered by M. Yu. Kozmanov and N. G. Karlykhanov. To solve a 2D system of parabolic equations of quasiheat transfer, they used the method splitting by directions and the difference scheme of the second order of approximation. In the approximation of quasiheat transfer, a parabolic system is solved, for which you can construct a monotonous difference scheme of the second order of approximation. The paper describes algorithms proposed in 2016, but not previously published. The ideas of quasithermal conductivity were further developed in the works by N. G. Karlykhanov, where averaging of multigroup equation of transfer by the spectrum of photons was additionally applied. Keywords: radiative heat transfer, account for kinetic effects.
 50 YEARS OF FLECK PROBLEMS
A. A. Shestakov VANT. Ser.: Mat. Mod. Fiz. Proc 2024. Вып.1. С. 4856.
In 1971, specialists on radiation transfer from Livermore National Lab (LLNA) of the USA suggested problems that with time became classical tests for radiation transfer. In all problems, a flat layer is heated with the radiation flux that corresponds to the temperature of 1 keV. The basic advantages of these problems are: – the simplicity of the setup of the boundary and initial conditions that allows computing these problems in different approximations; – simple analytical formulas for spectral runs; – a wide range of implementation of spectral coefficient of absorption; – simulation of disruptors of the spectral coefficient разрывов of absorption in space and energy spectrum; – the simplest equation of state of the material. The paper is devoted to the fiftyyear anniversary of Fleck tests in the method of numerical solution of heat radiation transfer. The paper provides the setups and numerical computations of two modifications of these problems. Keywords: heat radiation transfer, Fleck problems.

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