"Completion of Multiple Reciprocity Boundary Element Method for Liquid Criticality System Having Irregular Geometry"

研究的目的是最终完成基于多重互易边界元方法(MRBEM)的临界安全分析系统的开发。系统的主要部分是求解三维两群中子扩散方程，以分析后处理厂液态核材料系统的核临界性。在这种分析中，人们经常会遇到不规则几何的问题，例如地震引起的液面倾斜或晃动。MRBEM非常适合于分析这种不规则的几何形状，因为该方法只需要离散化曲面而不需要离散化体积。不需要将区域细分为网格点或有限元，因为关键特征值本身也只使用边界积分来计算。此外，在项目的第一年就引入了“前处理器”，以高效地生成边界元数据，扩大了复杂几何分析的灵活性。MRBEM现在已被重新定义为在强中子吸收器域中分析修正的Helmholtz通量模式，以及普通Helmholtz通量模式。在公式中起重要作用的数学量是两群中子扩散方程的零阶和高阶矩阵型基本解。试验计算证明了本文所提公式的有效性和应用于多域临界系统分析的有效性。上述研究成果已在BEM21(1999)和BEM22(2000)国际边界元研究会议上发表。此外，对实际晃动实验的分析结果表明，当盘饼形状的液体发生晃动运动时，反应性增加。作为该项目的产物，整个计算机系统得到了高度的优化和完善，成为进行广泛危害性分析的强大工具。

The aim of the research is to finalize the development of the criticality safety analyzing system based on the multiple reciprocity boundary element method (MRBEM). The main part of the system solves the three-dimensional, two-group neutron diffusion equation in order to analyze the nuclear criticality of liquid nuclear material systems in a reprocessing plant. In such analyses one often meets problems of irregular geometry, e.g., a listing or sloshing of liquid surface arising from an earthquake. The MRBEM is well suited for the analysis of such an irregular geometry since the method requires the discretization of the surface only rather than of the volume. Subdivision of a domain into mesh points or finite elements is not required since the critical eigenvalue itself is also calculated using only boundary integrals. In addition to this, the "preprocessor", which was introduced in the first year of the project to make boundary element data efficiently, has expanded the flexibility of analysis of complicated geometry. The MRBEM has been now reformulated to analyze the modified Helmholtz flux mode in a strong neutron absorber domain, as well as the ordinary Helmholtz one. Mathematical quantities that play an important role in the formulations are the zero-order and the higher order matrix-type fundamental solutions for the two-group neutron diffusion equation. Test calculations demonstrate the validity of the present reformulation and the usefulness when applied to the analysis of multi-domain criticality system The above research results were reported at the international conferences of boundary element research : BEM21 (1999) and BEM22 (2000). Further, results of analyses for actual sloshing experiments indicate the fact that the reactivity increases when a pan-cake shaped liquid suffers sloshing motion. As the product of the project, the whole computer system has been highly optimized and completed as a powerful tool for wide criticality analyses.(<300 words)