On the degraded effectiveness of diffusion synthetic acceleration for multidimensional sn calculations in the presence of material discontinuities

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We investigate the degradation in performance of diffusion synthetic acceleration (DSA) methods in problems with discontinuities in material properties. A loss in the effectiveness of DSA schemes has been Observed before with other discretizations in two dimensions under certain conditions. We present more evidence in support of the conjecture that DSA effectiveness can degrade in multidimensional problems with discontinuities in total cross section, regardless of the particular physical configuration or spatial discretization. Through Fourier analysis and numerical experiments, we identify a set of representative problems for which established DSA schemes are ineffective, focusing on highly diffusive problems for which DSA ... continued below

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17 p.

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Warsa, J. S. (James S.); Wareing, T. A. (Todd A.) & Morel, J. E. January 1, 2002.

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Description

We investigate the degradation in performance of diffusion synthetic acceleration (DSA) methods in problems with discontinuities in material properties. A loss in the effectiveness of DSA schemes has been Observed before with other discretizations in two dimensions under certain conditions. We present more evidence in support of the conjecture that DSA effectiveness can degrade in multidimensional problems with discontinuities in total cross section, regardless of the particular physical configuration or spatial discretization. Through Fourier analysis and numerical experiments, we identify a set of representative problems for which established DSA schemes are ineffective, focusing on highly diffusive problems for which DSA is most needed. We consider a lumped, linear discontinuous spatial discretization of the S N transport equation on three-dimensional, unstructured tetrahedral meshes and look ata fully consistent and a 'partially consistent' DSA method for this discretization. We find that the effectiveness of both methods can be significantly degraded in the presence of material discontinuities. A Fourier analysis in the limit of decreasing cell optical thickness is shown that supports the view that the degraded effectiveness of a fully consistent DSA scheme simply reflects the failure of the spatially continuous DSA method in problems where material discontinuities are present. Key Words: diffusion synthetic acceleration, discrete ordinates, deterministic transport methods, unstructured meshes

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17 p.

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  • Submitted to: Proceedings of the 2003 Nuclear Mathematical and Computational Sciences Conference, Gatlinburg, TN, 6-11 April 2002

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  • Report No.: LA-UR-02-6667
  • Grant Number: none
  • Office of Scientific & Technical Information Report Number: 976407
  • Archival Resource Key: ark:/67531/metadc929994

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  • January 1, 2002

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 12:36 p.m.

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Warsa, J. S. (James S.); Wareing, T. A. (Todd A.) & Morel, J. E. On the degraded effectiveness of diffusion synthetic acceleration for multidimensional sn calculations in the presence of material discontinuities, article, January 1, 2002; United States. (digital.library.unt.edu/ark:/67531/metadc929994/: accessed September 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.