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首页> 外文期刊>Annals of nuclear energy >A One-D Simplified Discrete-Ordinates Method with No Spatial Truncation Error
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A One-D Simplified Discrete-Ordinates Method with No Spatial Truncation Error

机译：无空间截断误差的一维简化离散-正交方法

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摘要

A simplified Discrete-Ordinates (S_N) method completely free from all spatial truncation errors is proposed for the solution of one-group and isotropic source plane-geometry transport problems with an arbitrary anisotropic scattering of order L (≤ N - 1). The method is based on the expansion of the angular flux in spherical harmonic (P_(N-1)) solutions. The analytic expression for the angular flux for each discrete-ordinates direction depends on the exponential functions, arbitrary constants and interior source. Two iterative methods are described to obtain the solution of heterogeneous S_N problems. In the first method, the arbitrary constants as well as the outgoing angular fluxes in each spatial cell are iteratively computed by using the external boundary or cell-interface conditions. The solution of the S_N equations for homogeneous problems is obtained without any iteration. In the second method, the outgoing angular fluxes in each spatial cell for each discrete-ordinates direction are defined in terms of a Green's function, the incoming angular fluxes from all directions and the interior source. In this case, the cell-interface fluxes are iteratively calculated. Both methods result in nonstandard spatially discretized S_N equations for the outgoing angular fluxes where the scattering source does not appear. Numerical results with various quadrature sets such as the Gauss-Legendre, Double Gauss-Legendre and Level Symmetric quadrature sets are given to demonstrate the accuracy of the method and compared with the previous studies.
机译：提出了一种完全不具有所有空间截断误差的简化离散-正交（S_N）方法，用于求解具有L阶（≤N-1）的任意各向异性散射的单组和各向同性源平面几何传输问题。该方法基于球谐（P_（N-1））解中角通量的扩展。每个离散坐标方向的角通量的解析表达式取决于指数函数，任意常数和内部源。描述了两种迭代方法来获得异构S_N问题的解决方案。在第一种方法中，通过使用外部边界或单元界面条件来迭代计算每个空间单元中的任意常数以及输出角通量。无需任何迭代即可获得S_N方程用于齐次问题的解。在第二种方法中，根据格林函数，来自所有方向的入射角通量和内部源来定义每个离散坐标方向上每个空间像元中的输出角通量。在这种情况下，迭代计算单元界面通量。两种方法都导致不出现散射源的传出角通量的非标准空间离散S_N方程。给出了各种正交集（例如高斯勒格德勒，双高斯勒格德勒和水平对称正交集）的数值结果，以证明该方法的准确性，并与以前的研究进行了比较。

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  • 来源
    《Annals of nuclear energy》 |1995年第4期|p.203-214|共12页
  • 作者

    Musa Yavuz;

  • 作者单位

    Turkish Atomic Energy Authority, Nuclear Computing & Design Group Fen Fakueltesi Arkasi, Besevler, Ankara 06100 Turkey;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 原子能技术;
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