Error Analysis of Variations on Larsen's Benchmark Problem

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Error norms for three variants of Larsen's benchmark problem are evaluated using three numerical methods for solving the discrete ordinates approximation of the neutron transport equation in multidimensional Cartesian geometry. The three variants of Larsen's test problem are concerned with the incoming flux boundary conditions: unit incoming flux on the left and bottom edges (Larsen's configuration); unit, incoming flux only on the left edge; unit incoming flux only on the bottom edge. The three methods considered are the Diamond Difference (DD) method, and the constant-approximation versions of the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of ... continued below

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18 pages

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Azmy, YY June 27, 2001.

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Error norms for three variants of Larsen's benchmark problem are evaluated using three numerical methods for solving the discrete ordinates approximation of the neutron transport equation in multidimensional Cartesian geometry. The three variants of Larsen's test problem are concerned with the incoming flux boundary conditions: unit incoming flux on the left and bottom edges (Larsen's configuration); unit, incoming flux only on the left edge; unit incoming flux only on the bottom edge. The three methods considered are the Diamond Difference (DD) method, and the constant-approximation versions of the Arbitrarily High Order Transport method of the Nodal type (AHOT-N), and of the Characteristic (AHOT-C) type. The cell-wise error is computed as the difference between the cell-averaged flux computed by each method and the exact value, then the L{sub 1}, L{sub 2}, and L{sub {infinity}} error norms are calculated. The results of this study demonstrate that while integral error norms, i.e. L{sub 1}, L{sub 2}, converge to zero with mesh refinement, the pointwise L{sub {infinity}} norm does not due to solution discontinuity across the singular characteristic. Little difference is observed between the error norm behavior of the three methods considered in spite of the fact that AHOT-C is locally exact, suggesting that numerical diffusion across the singular characteristic as the major source of error on the global scale. However, AHOT-C possesses a given accuracy in a larger fraction of computational cells than DD.

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18 pages

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  • International Meeting on Mathematical Methods for Nuclear Applications, Salt Lake City, UT (US), 09/09/2001--09/13/2001

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  • Report No.: P01-110943
  • Grant Number: AC05-00OR22725
  • Office of Scientific & Technical Information Report Number: 786337
  • Archival Resource Key: ark:/67531/metadc722538

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Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • June 27, 2001

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  • Sept. 29, 2015, 5:31 a.m.

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  • March 30, 2016, 12:36 p.m.

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Azmy, YY. Error Analysis of Variations on Larsen's Benchmark Problem, article, June 27, 2001; United States. (digital.library.unt.edu/ark:/67531/metadc722538/: accessed November 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.