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EXACT SOLUTIONS TO THE STATIONARY SYSTEM OF RADIATION AND ENERGY TRANSPORT EQUATIONS IN MULTIDIMENSIONAL CASE

A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc 2023. Вып.3. С. 3-16.

For code testing purposes, it is desirable to select model problems having exact solutions. In spite of the advances achieved in constructing analytical solutions to the radiation transport equation these solutions are not always sufficient for different classes of the transport problems. In a stationary case, one can find the analytical solution to the radiation transport problem by expanding in von Neumann series the transport operator resolvent. The expansion in von Neumann series allows obtaining the spectral-angular characteristics of the radiation field using the known temperature profiles. The paper presents the developed analytical formulas for finding the thermal radiation parameters in a multidimensional geometry. These formulas allow explicitly finding the analytical expressions for the main spectral quantities, such as intensity, density and radiation flux, using the known equilibrium intensity determined by the temperature distribution only and the given absorption and dispersion factors. The grey and spectral approximation solutions for 1D, 2D, and 3D geometries are presented.

Keywords: exact solutions, system of thermal radiation transport equations.








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