中子输运问题源项反演的反幂法

Inverse Power Method for Source Term Inversion in Neutron Transport Equation

对于包括裂变反应在内的中子输运源项反演问题,研究关于源项有效倍增因子的k-特征值问题的求解.基于球谐函数展开和有限差分离散,给出了中子输运方程的源项反演逼近的反幂算法,该方法的优势是在适当的初值条件下可以显著提高计算速度.计算结果表明,在对有效倍增因子有较好的预先估计值的情况下,反幂法迭代3步,误差就为0.045 45%,而乘幂法迭代20步,误差为0.109%,由此可以看出反幂法计算速度更快,计算结果更精确.

Considering the inversion of the source term for neutron transport in such as fission reaction, the numerical solution of the effective multiplication factor related to k-eigenvalue problem is investigated. Based on the spherical harmonic functions expansion and finite difference for discretization of transport equation, an inverse power scheme is presented for calculation of the k-eigenvalue problem. This scheme can obviously speed up convergence rate under the proper initial value condition. The numerical results show that the error of the inverse power method gets only 0. 045 45% at 3rd iterative step while the error of the standard power method is still reaching to 0. 109% after 20 iterative steps, therefore the inverse power algorithm is endowed with higher computing rate and accuracy than the standard power method if an available estimate of the effective multiplication factor is pre-provided.