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首页> 外文会议>International conference on the physics of reactors;PHYSOR 2010 >A COMPARISON BETWEEN NODAL EXPANSION METHOD AND NODAL GREEN'S FUNCTION METHOD
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A COMPARISON BETWEEN NODAL EXPANSION METHOD AND NODAL GREEN'S FUNCTION METHOD

机译：节点扩展法与节点格林函数法的比较

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This paper presents a unified formulation of the Nodal Expansion Method (NEM) and Nodal Green's Function Method (NGFM) in Cartesian geometry although there is a significant difference between them. Both methods employ the same inner iterative scheme namely Row-Column iteration strategy to solve the interface current equation. It's generally believed that the NEM is somewhat faster than the NGFM. However, calculations of IAEA3D benchmark problem carried out by newly implemented NGFM and NEM show that not only the accuracy but also the performance of the NGFM are better than that of the NEM in Cartesian geometry.Both the NGFM and NEM are extended to solve neutron diffusion equation in cylindrical geometry. Since the traditional transverse integration fails to produce a 1-D transverse integrated equation in θ-direction, a simple approach is introduced to obtain this equation in θ-direction. The 1-D transverse integrated equations in r-direction are solved by the NEM using the special polynomials and by the NGFM using Green's function based on modified Bessel function respectively. The same iterative scheme employed for Cartesian geometry can be readily applied to the cylindrical geometry case. The Cylindrical Nodal Expansion Method (CNEM) and the Cylindrical Nodal Green's Function Method (CNGFM) codes are developed and applied to Dodd's r-z benchmark problem. The results show that both the CNEM and CNGFM are capable of very high performance and accuracy in cylindrical geometry. Meanwhile this paper demonstrates that nodal methods have prominent advantages over traditional finite difference method in both Cartesian geometry and cylindrical geometry.
机译：本文介绍了笛卡尔几何中的节点扩展方法（NEM）和节点格林函数方法（NGFM）的统一表述，尽管它们之间存在显着差异。两种方法都采用相同的内部迭代方案（即行-列迭代策略）来求解界面电流方程。通常认为，NEM比NGFM快一些。但是，通过新实施的NGFM和NEM对IAEA3D基准问题进行的计算表明，在笛卡尔几何上，NGFM的准确性和性能均优于NEM。 NGFM和NEM都被扩展为求解圆柱几何中的中子扩散方程。由于传统的横向积分无法在θ方向上生成一维横向积分方程，因此引入了一种简单的方法来在θ方向上获得该方程。分别通过NEM使用特殊多项式来求解一维横向积分方程，并使用基于修正贝塞尔函数的格林函数通过NGFM来求解一维横向积分方程。用于笛卡尔几何的相同迭代方案可以很容易地应用于圆柱几何案例。开发了圆柱节点扩展方法（CNEM）和圆柱节点格林函数方法（CNGFM）代码，并将其应用于Dodd的r-z基准问题。结果表明，CNEM和CNGFM都具有非常好的性能和圆柱几何形状的精度。同时，本文证明了节点方法在笛卡尔几何和圆柱几何方面都比传统的有限差分法具有明显的优势。

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