Discrete ordinates transport methods for problems with highly forward-peaked scattering

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The author examines the solutions of the discrete ordinates (S{sub N}) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S{sub N} equations. This analysis shows that in this asymptotic limit the S{sub N} solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and ... continued below

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162 p.

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Pautz, S.D. April 1, 1998.

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Description

The author examines the solutions of the discrete ordinates (S{sub N}) method for problems with highly forward-peaked scattering kernels. He derives conditions necessary to obtain reasonable solutions in a certain forward-peaked limit, the Fokker-Planck (FP) limit. He also analyzes the acceleration of the iterative solution of such problems and offer improvements to it. He extends the analytic Fokker-Planck limit analysis to the S{sub N} equations. This analysis shows that in this asymptotic limit the S{sub N} solution satisfies a pseudospectral discretization of the FP equation, provided that the scattering term is handled in a certain way (which he describes) and that the analytic transport solution satisfies an analytic FP equation. Similar analyses of various spatially discretized S{sub N} equations reveal that they too produce solutions that satisfy discrete FP equations, given the same provisions. Numerical results agree with these theoretical predictions. He defines a multidimensional angular multigrid (ANMG) method to accelerate the iterative solution of highly forward-peaked problems. The analyses show that a straightforward application of this scheme is subject to high-frequency instabilities. However, by applying a diffusive filter to the ANMG corrections he is able to stabilize this method. Fourier analyses of model problems show that the resulting method is effective at accelerating the convergence rate when the scattering is forward-peaked. The numerical results demonstrate that these analyses are good predictors of the actual performance of the ANMG method.

Physical Description

162 p.

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INIS; OSTI as DE98006034

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  • Other Information: DN: Thesis submitted to Texas A and M Univ., Dept. of Nuclear Engineering, College Station, TX (US); TH: Thesis (Ph.D.)

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  • Other: DE98006034
  • Report No.: LA--13444-T
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/663189 | External Link
  • Office of Scientific & Technical Information Report Number: 663189
  • Archival Resource Key: ark:/67531/metadc709472

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  • April 1, 1998

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

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  • March 1, 2016, 3:56 p.m.

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Pautz, S.D. Discrete ordinates transport methods for problems with highly forward-peaked scattering, report, April 1, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc709472/: accessed July 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.