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首页> 外文学位 >Nonlinear finite element and characteristic-based transport methods in the thick diffusion limit in Cartesian coordinates.
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Nonlinear finite element and characteristic-based transport methods in the thick diffusion limit in Cartesian coordinates.

机译：笛卡尔坐标系中厚扩散极限中的非线性有限元和基于特征的传输方法。

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摘要

We analyze the multi-dimensional, solution-dependent family of discontinuous finite element and characteristic methods in the thick, diffusive limit in Cartesian geometry on an arbitrary grid of polygons or polyhedra. We develop various conditions that must be satisfied by the weight and basis functions in order for an individual spatial discretization to have any chance of succeeding in this limit. In addition, we emphasize the various deviations required by this analysis from the solution-independent families.; We provide several specific one and two-dimensional spatial discretizations within this family and analyze them in this limit to validate the results of the general analysis. We stress properties of each method's weight and/or basis functions that result in the method's success or failure in this limit. We further provide several relevant numerical examples for each of the individual methods considered to emphasize the utility and predictive capability of the general analysis.; We describe in great detail how the algebraically nonlinear spatial discretization equations are solved. We present a modified Newton-Raphson iterative scheme used to eliminate the basis function coefficients in favor of known quantities. Furthermore, we propose an extension to the transport synthetic acceleration (TSA) algorithm for accelerating source iteration as applied to the class of solution-dependent spatial discretizations. We then test this acceleration scheme on a simple family of problems with variable scattering ratios. Finally, we select two different solution-dependent spatial discretizations contained in these families and analyze them in other limits of interest.
机译：我们在多边形或多面体的任意网格上，在笛卡尔几何的厚扩散极限中分析了多维，不依赖解的有限元族和特征方法。我们开发了权重和基函数必须满足的各种条件，以使单个空间离散化有机会成功达到此限制。此外，我们强调了此分析与不依赖解的族的各种偏差。我们在该族内提供了几个特定的​​一维和二维空间离散化，并在此范围内对其进行了分析，以验证一般分析的结果。我们强调每种方法的权重和/或基函数的属性，这些属性会导致该方法在此限制范围内成功或失败。我们进一步为考虑用来强调一般分析的效用和预测能力的每种方法提供几个相关的数值示例。我们将详细描述代数非线性空间离散方程的求解方法。我们提出了一种改进的Newton-Raphson迭代方案，该方案用于消除基函数系数，而采用已知量。此外，我们提出了一种扩展的传输合成加速（TSA）算法，用于加速源迭代，该算法适用于与解决方案相关的空间离散化。然后，我们在具有可变散射比的简单问题系列上测试此加速方案。最后，我们选择这些族中包含的两个不同的依赖解决方案的空间离散化，并在其他关注范围内对其进行分析。

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  • 作者

    Castrianni, Christopher Lee.;

  • 作者单位

    Texas A&M University.;

  • 授予单位 Texas A&M University.;
  • 学科 Engineering Nuclear.
  • 学位 Ph.D.
  • 年度 1997
  • 页码 185 p.
  • 总页数 185
  • 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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