求解中子扩散方程的半解析节块方法

Semi-analytic Nodal Methods for Neutron Diffusion Calculation

为快速、精确实现反应堆堆芯多群中子扩散计算,采用基于横向积分技术的半解析节块方法(SANM)求解中子扩散方程,并结合解析粗网有限差分(ACMFD)方法,导出了基于半解析节块方法的粗网有限差分方程(CMFD)耦合系数。在半解析节块方法中,散射源和裂变源采用勒让德多项式,并在此假设下解析求解中子扩散横向积分方程。分别采用了零次、二次和四次勒让德多项式展开,以适应粗网和细网的计算。数值计算结果表明,所提出的方法具有很高的计算精度和计算效率。

A fast and established for reactor accurate multigroup core, and the semi neutron diffusion calculation method was analytic nodal method （SANM） based on transverse-integrated diffusion equation was introduced within the framework of the analytic coarse mesh finite difference （ACMFD） formulation. Additionally, the ACMFD coupling coefficients were determined analytically from the SANM. In the SANM, the Legendre polynomials were employed to approximate the fission and scattering sources so that the analytic solution of transverse-integrated diffusion equation can be obtained. Furthermore, the 0th, 2nd and 4th-order Legendre polynomial representations were used respectively in order to perform fine-mesh and coarse-mesh calculations. The mumerical results show that the method possesses high accuracy and efficiency.