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A characteristic-based multiple balance approach for solving the S(N) equations of arbitrary polygonal meshes.

机译：基于特征的多重平衡方法，用于求解任意多边形网格的S（N）方程。

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摘要

We introduce a new approach for solving the neutral particle transport problem on arbitrary two-dimensional meshes in a multigroup discrete ordinates (S{dollar}rmsb{lcub}n{rcub}{dollar}) context. Our approach includes spatial discretization of regions with uniform material properties and solution of the transport problem with prescribed conditions. The spatial discretization involves approximating a general surface as an arbitrary polygon, rotating to a coordinate system aligned with the direction of particle travel, and decomposing the polygonal cell into subregions called slices. This simple and intuitively appealing geometry decomposition follows from a characteristic-based view of the transport problem. Most balance-based characteristic methods use this decomposition implicitly: we include it explicitly and exploit its properties. Our mathematical approach to the transport problem is a multiple balance approach, using exact spatial moments balance equations on whole cells and slices, together with approximate auxiliary equations on slices to close the system. Therefore, we call our approach the slice balance approach and describe it as a characteristic-based multiple balance approach. In our view, the most salient result of this research is that our slice balance approach is very general and facilitates extension of planar geometry S{dollar}rmsb{lcub}n{rcub}{dollar} spatial differencing schemes to arbitrarily complex polygonal meshes.; We derive a general-order characteristic family of slice balance schemes, along with specific step- and linear-characteristic schemes. We also derive a simple "diamond-difference-like" scheme to demonstrate the flexibility of the slice balance approach. The step characteristic scheme is implemented in the standard computational module of the CENTAUR-123 computer code package. The other schemes are implemented in new proof-of-principle computational modules. Our current implementations are limited to isotropic scattering and vacuum boundary conditions, but extensions to general scattering and boundary conditions are straightforward. Numerical results are compared against analytical solutions and against industry-accepted S{dollar}rmsb{lcub}n{rcub}{dollar} computer codes for a range of problems. These results demonstrate the ability of the slice balance approach to closely approximate complicated geometric configurations. Properties of the numerical solutions depend on the differencing scheme used within the slice balance framework and are analogous to properties observed in traditional methods based on the same differencing.
机译：我们引入了一种新的方法来解决多组离散坐标（S {dollar} rmsb {lcub} n {rcub} {dollar}）上下文中任意二维网格上的中性粒子传输问题。我们的方法包括对具有均匀材料特性的区域进行空间离散化，并在规定条件下解决运输问题。空间离散化涉及将一般曲面近似为任意多边形，旋转到与粒子传播方向对齐的坐标系，并将多边形像元分解为称为切片的子区域。这种简单直观的几何分解是基于运输问题的基于特征的观点。大多数基于余额的特征方法都隐式使用此分解：我们显式包括它并利用其属性。我们针对运输问题的数学方法是多重平衡方法，在整个像元和切片上使用精确的空间矩平衡方程，并在切片上使用近似辅助方程来关闭系统。因此，我们称此方法为切片平衡法，并将其描述为基于特征的多重平衡法。我们认为，这项研究的最显着结果是我们的切片平衡方法非常通用，有助于将平面几何空间微分方案扩展到任意复杂的多边形网格。 ;我们推导了切片平衡方案的一般顺序特征族，以及特定的阶跃和线性特征方案。我们还派生了一个简单的“类似于钻石的差异”方案，以展示切片平衡方法的灵活性。步进特性方案在CENTAUR-123计算机代码包的标准计算模块中实现。其他方案在新的原理证明计算模块中实现。我们当前的实现方式仅限于各向同性散射和真空边界条件，但是扩展到常规散射和边界条件很简单。将数值结果与分析解决方案以及行业认可的S {dollar} rmsb {lcub} n {rcub} {dollar}计算机代码进行比较，以解决一系列问题。这些结果证明了切片平衡方法能够近似近似复杂的几何构造的能力。数值解的性质取决于切片平衡框架中使用的差异方案，并且类似于基于相同差异的传统方法中观察到的性质。

著录项

  • 作者

    Grove, Robert Ernest.;

  • 作者单位

    University of Michigan.;

  • 授予单位 University of Michigan.;
  • 学科 Engineering Nuclear.
  • 学位 Ph.D.
  • 年度 1996
  • 页码 138 p.
  • 总页数 138
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 原子能技术;
  • 关键词

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