中子扩散方程三棱柱节块解析基函数展开方法的应用

The application of the analytic basis function expansion triangular-z nodal method for neutron diffusion calculation

将中子通量密度在三棱柱节块内用一组完全满足中子扩散方程的解析基函数近似展开,节块之间采用面偏流零次矩阵和一次矩阵进行耦合,从而获得了中子扩散方程的解析基函数展开方法。基于此方法,研制了TABFEN程序,并将此程序应用到复杂几何中子扩散方程的求解当中。另外,中子共轭方程是表征中子价值守恒的方程,通过数值推导,可以将共轭中子扩散方程写成形如中子扩散方程的矩阵形式,进而可以通过解析基函数展开方法求解,在求解的过程中,采用从低能群到高能群的扫描方式以提高计算效率。为了验证该方法的可行性,选取了一系列问题进行测试,并将计算结果和细网差分程序CITATION及参考解对比,结果表明,该方法计算精度较高,切实可行。

The distributions of homogeneous neutron flux within a node are expanded into a set of analytic basis functions which satisfies the diffusion equation at any point in a triangular-z node for each energy group, and among the nodes are coupled with both the zero- and first-order partial neutron current moments across all the interfaces of the triangular prism at the same time. Based on this method, a code TABFEN has been developed and applied to solve the neutron diffusion equation in a complicated geometry. In addition, after a series of numerical derivation, one can get the neutron adjoint diffusion equations in matrix form, which is the same with the neutron diffusion equation, therefore, it can be solved by TABFEN, and the low-high scan strategy is adopted to improve the efficiency. In order to verify the feasibility of this method, a series of problems are calculated by TABFEN, the results show that a good agreement with the references which demonstrates the high efficiency and feasibility of this method.