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Diffusion form of the transport equation and the method of kinetic diffusion (application to one-dimensional planar geometry)

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Abstract

A form of the transport equation with the same structure as the elementary diffusion equation is proposed. It is distinguished by the fact that the diffusion coefficient depends not only on the properties of the medium but also on certain angular moments of the differential flux. The existence of a reciprocal relation between the angular moments and the spatial distribution of the scalar flux makes it possible to obtain an exact numerical solution of the transport equation, expressed in diffusion form, by means of a simple iteration pocedure (the method of kinetic diffusion). The relation between the transport equation in the diffusion form and the elementary theory of diffusion is examined, the results of calculations of certain variants of the the Milne problem are presented, and the inherent properties of the method, which make it effective in many practical applications, are noted. 3 Tables, 5 references.

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References

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Authors
  1. V. V. Seliverstov
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Additional information

Federal Science Center of the Russian Federation—Institute of Theoretical and Experimental Physics. Translated from Atomnaya Energiya, Vol. 86, No. 1, pp. 16–27, January, 1999.

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Seliverstov, V.V. Diffusion form of the transport equation and the method of kinetic diffusion (application to one-dimensional planar geometry). At Energy 86, 13–25 (1999). https://doi.org/10.1007/BF02672929

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  • DOI: https://doi.org/10.1007/BF02672929

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