【摘要】 本文利用有限无法求解二维稳态少群中子扩散方程。采用Ｇａｌｅｒｋｉｎ近似，寻找扩散方程的弱形式，最后得到求解的矩阵公式。外计算采用幂迭代法，内计算采用改进的Ｃｈｏｌｅｓｋｙ因式分解法。 本文在ＦＥＬＩＸ Ｃ－５１２计算机上用ＦＯＲＴＲＡＮ Ⅳ语言编制了在（ｘ－ｙ）、（ｒ－ｚ）几何下的二维少群中子扩散程序ＴＦＥＭ－２Ｄ（Ｔｒｉａｎｇｌｕｌａｒ Ｐａｒｔｉｔｉｏｎ； Ｆｉｎｉｔｅ Ｅｌｅｍｅｎｔ Ｍｅｔｈｏｄ Ｔｗｏ－ｄｉｍｅｎｓｉｏｎａｌ Ｐｒｏｂｌｅｍ）。列出本程序对一些简单的反应堆、四区压水堆和二维ＩＡＥＡ基准堆的数值计算结果，将粗网近似的计算结果和用细网有限差分的计算结果作了比较。结果表明用很粗的网格计算出相当好的本征值和本征向量。更多还原

【Abstract】 The time-independent, few-group, two-dimensional neutron diffusion equations are solved by using the finite element method. The matrix formulation is achieved by applying Galerkin method to the "weak" form of the neutron diffusion equation. The matrix problem is solved through the power iteration method and a modified Cholesky factorization. In this paper, a code TFEM-2D (Triangular Partition, Finite Element Method Two-dimensional Problem) for the few-group, two-dimensional (X-Y), (R-Z) geometrical neutron diffusion is implemented on the FELIX C-512 computer by using FORTRAN Ⅳ language. Numerical results are presented as evaluated through a code (TFEM-2D), for several typical problems such as the four regions PWR and the 2D-IAEA benchmark-problem. Results of using various coarse-mesh approximations are compared with finemesh finite difference calculations. The results indicate that reasonable eigenvalues and eigenvectors can be calculated by using very coarse meshes.更多还原