解析函数展开节块法的数值稳定性分析

Numerical Stability Analysis for Analytic Function Expansion Nodal Method

解析函数展开节块法是求解六角形几何堆芯中子注量率的常用方法,其核心思想是利用严格满足中子扩散方程的解析基函数,直接把节块内的各群中子注量率近似展开。研究发现,此方法在求解一些特殊问题时,出现计算发散的情况。针对此类问题,提出了两种解决方法:截断近似方法和泰勒展开方法。通过对改造后的VVER440基准题验证表明:这两种方法在保证计算精度的基础上很好地解决了解析函数展开节块法的数值不稳定性问题。

Analytic function expansion nodal method is often used to solve hexagonal geometry reactor problems w hose kernel is that the intra-nodal flux distribution is expanded in a series of analytic basic functions for each group .In some cases ,this meth-od is not convergence and two stabilization techniques are introduced to resolve the instability problem .One is truncation approximation and the other is Taylor expansion . Compared with the VVER440 benchmark results ,both techniques not only ensure the calculation accuracy but also give a good solution for numerical instability problems .