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首页> 外文期刊>Nuclear science and engineering >Error Comparison of Diamond Difference, Nodal, and Characteristic Methods for Solving Multidimensional Transport Problems with the Discrete Ordinates Approximation
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Error Comparison of Diamond Difference, Nodal, and Characteristic Methods for Solving Multidimensional Transport Problems with the Discrete Ordinates Approximation

机译：离散差近似下解决多维输运问题的菱形差，节点和特征方法的误差比较

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摘要

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, the arbitrarily high order transport (AHOT) method of the nodal type (AHOT-N), and of the characteristic type (AHOT-C). The last two methods are employed in constant, linear, and quadratic orders of spatial approximation. 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_1, L_2, and L_∞ error norms are calculated. The new result of this study is that while integral error norms, i.e., L_1 and L_2, converge to zero with mesh refinement, the cellwise L_∞ norm does not. Via numerical experiments we relate this behavior to solution discontinuity across the singular characteristic. Little difference is observed between the error norm behavior of the methods in spite of the fact that AHOT-C is locally exact, suggesting that numerical diffusion across the singular characteristic is the major source of error on the global scale. Nevertheless, increasing the order of spatial approximation in AHOT methods yields higher accuracy in the integral error norms sense. In general, the characteristic methods possess a given accuracy in a larger fraction of the number of computational cells compared to nodal methods or DD.
机译：使用三种数值方法来评估Larsen基准问题的三个变体的误差范数，以解决多维笛卡尔几何中的中子输运方程的离散坐标近似。 Larsen检验问题的三个变体与入射通量边界条件有关：左侧和底部边缘的单位入射通量（Larsen的配置）；仅在左边缘输入单位通量；单位输入通量仅在底部边缘。所考虑的三种方法是菱形差（DD）方法，节点类型（AHOT-N）和特征类型（AHOT-C）的任意高阶传输（AHOT）方法。后两种方法用于空间近似的恒定，线性和二次阶。逐单元误差计算为每种方法计算的单元平均通量与精确值之间的差，然后计算L_1，L_2和L_∞误差范数。这项研究的新结果是，虽然积分误差范数L_1和L_2通过网格细化收敛到零，但按单元格的L_∞范数却没有。通过数值实验，我们将此行为与整个奇异特征的解不连续性联系起来。尽管AHOT-C是局部精确的，但在方法的错误规范行为之间几乎没有观察到差异，这表明跨单一特征的数值扩散是全局范围内错误的主要来源。但是，在AHOT方法中增加空间逼近的阶数会在积分误差范数意义上产生更高的精度。通常，与节点方法或DD相比，特征方法在较大数量的计算像元中具有给定的精度。

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  • 来源
    《Nuclear science and engineering》 |2007年第2期|p.139-153|共15页
  • 作者

    J. I. Duo; Y. Y. Azmy;

  • 作者单位

    The Pennsylvania State University, 138 Reber Building University Park, Pennsylvania 16802;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 原子能技术;
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