Abstract The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry.

中文翻译：

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用于对中子扩散方程进行积分的模态方法的自适应时间步长控制

摘要 瞬变中子扩散方程的解可以使用准静态方法近似求解，该方法将中子通量分解为时变函数乘以与空间和时间相关的形状函数的乘积。这种技术的推广是更新的模态方法。该策略假设中子通量可以分解为幅度之和乘以一些形状函数。这些函数，称为模式，来自与静态中子扩散方程相关的特征值问题的解决方案，这些方程正在沿瞬态更新。在以前的工作中，用于更新模式的时间步长设置为固定值，这意味着需要使用小时间步长来获得准确的结果，因此计算成本很高。在这项工作中，我们建议使用自适应控制时间步长，当算法检测到大错误时自动减少时间步长，并在不需要使用小步长时增加该值。提出了几种计算模式更新时间步长的策略，并在具有矩形和六边形几何形状的基准反应器中针对不同瞬态测试了它们的性能。