Tensor transformation technique for the transport equation

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A step-wise tensor transformation technique is presented for the transformation of the single energy group transport equation to an arbitrary spatial coordinate system. Both gradient and divergence forms of the equation are given and the same method is applied to the derivation of the diffusion approximation. It is demonstrated that using an orthogonal representation of the propagation vector will simplify the divergence form of the equation. The application of this technique is in the representation of the transport equation in coordinate systems other than the usual rectangular, cylindrical and spherical ones. Its use is demonstrated by transforming the transport equation ... continued below

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Pages: 33

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Gralnick, S.L. October 1, 1975.

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Description

A step-wise tensor transformation technique is presented for the transformation of the single energy group transport equation to an arbitrary spatial coordinate system. Both gradient and divergence forms of the equation are given and the same method is applied to the derivation of the diffusion approximation. It is demonstrated that using an orthogonal representation of the propagation vector will simplify the divergence form of the equation. The application of this technique is in the representation of the transport equation in coordinate systems other than the usual rectangular, cylindrical and spherical ones. Its use is demonstrated by transforming the transport equation to a toroidal coordinate system consisting of nested circular toroids. (auth)

Physical Description

Pages: 33

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Dep. NTIS

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  • Other Information: Orig. Receipt Date: 30-JUN-76

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  • Report No.: MATT--1154
  • Grant Number: E(11-1)-3073
  • DOI: 10.2172/4176176 | External Link
  • Office of Scientific & Technical Information Report Number: 4176176
  • Archival Resource Key: ark:/67531/metadc870532

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Office of Scientific & Technical Information Technical Reports

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Creation Date

  • October 1, 1975

Added to The UNT Digital Library

  • Sept. 16, 2016, 12:32 a.m.

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  • Oct. 27, 2016, 7:40 p.m.

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Gralnick, S.L. Tensor transformation technique for the transport equation, report, October 1, 1975; New Jersey. (digital.library.unt.edu/ark:/67531/metadc870532/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.