Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition
Calculating Time Eigenvalues of the Neutron Transport Equation with Dynamic Mode Decomposition
复制标题
用动模分解计算中子输运方程的时间特征值
DOI：
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发表时间：
2018
影响因子：
1.2
通讯作者：
R. McClarren
中科院分区：
文献类型：
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作者：
R. McClarren
摘要基于含时输运方程的解，提出了一种计算中子输运问题时间本征值的新方法。使用这些解决方案，我们使用动态模式分解，形成一个近似的运输运营商。该近似算子具有与中子输运方程的时间本征值在数学上相关的本征值。这种方法适用于任何临界水平的系统，并且不需要用户对特征值进行估计。数值结果均质和非均质介质。数值结果表明，该方法在给定的时间范围内找到了对解的变化贡献最大的特征值，而具有最大真实的部分的特征值在短时间和中间时间对系统演化并不一定重要.
Abstract A novel method to compute time eigenvalues of neutron transport problems is presented based on solutions to the time-dependent transport equation. Using these solutions, we use the dynamic mode decomposition to form an approximate transport operator. This approximate operator has eigenvalues that are mathematically related to the time eigenvalues of the neutron transport equation. This approach works for systems of any level of criticality and does not require the user to have estimates for the eigenvalues. Numerical results are presented for homogeneous and heterogeneous media. The numerical results indicate that the method finds the eigenvalues that contribute the most to the change in the solution over a given time range, and the eigenvalue with the largest real part is not necessarily important to the system evolution at short and intermediate times.