对称性及多群中子扩散方程数值解

SYMMETRIES AND NUMERICAL SOLUTION TO THE MULTIGROUP NEUTRON DIFFUSION EQUATION

在多群中子扩散方程解析解的基础上 ,利用方程及求解域的对称性建立了新的数值求解中子扩散方程的理论模型 .该模型显著的优点是适用于各种对称区域 (二维、三维区域 )尤其是非正方形区域中子扩散方程的求解 ,它彻底避免了常规节块法应用于非正方形几何时所出现的奇异性问题 ,且所得的解在求解域内任意点上均满足扩散方程 .以二、三维六角形几何为例建立了数学模型 ,并用基准问题校核了模型的正确性 .

The neutron diffusion equation is usually solved in a symmetric region.For a non\|rectangular symmetric region,the nonphysical singular problem arises when the conventional method of deriving nodal solution is employed.In this paper,a new method based on both symmetries of the problem and an analytic representation of the nodal flux distribution is presented.The method is effective for the solution of multigroup diffusion equation in the symmetric region,especially for the non\|rectangular problem.It can be applied in 2\|D or 3\|D problems and its application in hexagonal geometry is introduced as an example.The only approximations used in deriving the method are the treatment of unknown functions.The efficiency of the proposed method is demonstrated by results of various 2\|D and 3\|D benchmark problems using the GTDIF\|H code.