采用空间区域分解并行IRAM算法求解中子输运/扩散方程及其共轭方程的高阶谐波

Calculation of Higher Eigenmodes of Neutron Transport/Diffusion Forward and Adjoint Equations Using IRAM Algorithm Based on Domain Decomposition

中子输运/扩散方程及其共轭方程的高阶谐波在堆芯功率扩展、稳定性分析、敏感性与不确定性分析等方面具有较为广泛的应用前景。基于空间区域分解并行计算及多群多区域耦合PGMRES算法,应用隐式再启动Arnoldi算法求解中子输运/扩散方程及其共轭方程的高阶谐波,采用IAEA3D扩散基准题、一维两群两区平板输运问题以及二维C5G7基准题进行数值验证。数值结果显示,中子输运/扩散方程与其共轭方程具有相同的特征值谱,高阶谐波与共轭高阶谐波满足F正交性;数值结果与理论分析吻合良好。

For the higher eigenmodes of neutron transport/diffusion forward and adjoint equations, there are various application perspectives for engineering purposes, such as core power distribution reconstruction, stability analysis, and uncertainty and sensitivity analysis. In this paper, the higher eigenmodes of both forward and adjoint equations are calculated using implicitly restarted Arnoldi method(IRAM) based on domain decomposition parallel computation and multi-group multi-domain coupled PGMRES accelerating algorithm. The IAEA3 D diffusion benchmark, a 1 D 2-group 2-domain transport problem and 2 D C5 G7 benchmark are used for verification. Numerical results demonstrate that the forward equations and the adjoint equations keep the same eigenvalue spectrum, and the obtained higher eigenfunctions are F-orthogonal or biorthogonal. These numerical results agree well with the expectations of theory analysis.