Flux limiting nature`s own way -- A new method for numerical solution of the transport equation

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The transport equation may be solved by expanding it in spherical harmonics, Y{sub lm}, and truncating the resultant infinite set of equations at some finite order L. This procedure leaves the (L + 1)th order moments which appear in the Lth order equation undetermined, and the standard procedure for obtaining a closed set of equations has been to set all the (L + 1)th order moments to zero. It has been shown here that this procedure actually violates the apriori knowledge that one is solving for the moments of a probability measure on the unit sphere. Using the theory of ... continued below

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25 p.

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Kershaw, D.S. July 29, 1976.

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Description

The transport equation may be solved by expanding it in spherical harmonics, Y{sub lm}, and truncating the resultant infinite set of equations at some finite order L. This procedure leaves the (L + 1)th order moments which appear in the Lth order equation undetermined, and the standard procedure for obtaining a closed set of equations has been to set all the (L + 1)th order moments to zero. It has been shown here that this procedure actually violates the apriori knowledge that one is solving for the moments of a probability measure on the unit sphere. Using the theory of moments of a probability measure on the unit sphere. Using the theory of moments as discussed above, the (L + 1)th order moments can be chosen in accordance with apriori knowledge. The resultant truncated set of equations has properties much truer to the original transport equation than the usual set obtained by setting the (L + 1)th order moments to zero. In particular the truncated set of equations gets the solution of the transport equation exactly right in both the diffusion limit and the free streaming limit. Furthermore, this has been achieved by merely truncating the set of equations properly and not by any ad hoc changes in the basic equations as is the case in the approaches that use flux limiters.

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25 p.

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OSTI as DE95017708

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  • Other Information: PBD: 29 Jul 1976

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  • Other: DE95017708
  • Report No.: UCRL--78378
  • Grant Number: W-7405-ENG-48
  • DOI: 10.2172/104974 | External Link
  • Office of Scientific & Technical Information Report Number: 104974
  • Archival Resource Key: ark:/67531/metadc628247

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  • July 29, 1976

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • Feb. 16, 2016, 7:15 p.m.

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Kershaw, D.S. Flux limiting nature`s own way -- A new method for numerical solution of the transport equation, report, July 29, 1976; California. (digital.library.unt.edu/ark:/67531/metadc628247/: accessed June 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.