Abstract We present the new iterative method lpCMFD-SOR, which combines the linear prolongation coarse-mesh finite difference (lpCMFD) scheme with the method of successive overrelaxation (SOR) for neutron transport source iteration (SI). The lpCMFD method is the latest coarse-mesh finite difference (CMFD)–type acceleration scheme and is unconditionally stable and more effective than the standard CMFD method. The SOR method is a variant of the Gauss-Seidel method for solving a linear system of equations, resulting in faster convergence. The idea is to update the scattering source with overrelaxation to speed up the coupled transport-diffusion SI. Fourier analysis shows that the lpCMFD-SOR method converges for a relaxation parameter in the range of . It becomes less effective when underrelaxed (i.e., ) and increasingly more effective as increases above 1 until reaching the optimal overrelaxation value, which is, however, problem dependent. The optimal overrelaxation parameter increases with both the scattering ratio and the optical thickness of the problem. Numerical experiments have confirmed the Fourier analysis results. In general, the SOR method can further enhance the convergence rate of the lpCMFD method by more than 40% for neutron transport problems.

中文翻译：

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通过中子传输源迭代的连续过松弛增强 lpCMFD 加速

摘要 我们提出了一种新的迭代方法lpCMFD-SOR，它结合了线性延长粗网格有限差分（lpCMFD）方案和中子输运源迭代（SI）的连续过松弛（SOR）方法。lpCMFD 方法是最新的粗网格有限差分 (CMFD) 型加速方案，比标准 CMFD 方法无条件稳定且更有效。SOR 方法是用于求解线性方程组的 Gauss-Seidel 方法的变体，从而可以更快地收敛。这个想法是用过松弛来更新散射源，以加速耦合传输扩散 SI。傅立叶分析表明，lpCMFD-SOR 方法收敛于 范围内的松弛参数。当放松不足时（即，) 并且随着增加到 1 以上变得越来越有效，直到达到最佳过松弛值，然而，这取决于问题。最佳过松弛参数随着散射比和问题的光学厚度而增加。数值实验证实了傅立叶分析的结果。总的来说，SOR方法对于中子输运问题可以进一步提高lpCMFD方法40%以上的收敛速度。