基于MOOSE开发的中子扩散问题求解程序

Neutron Diffusion Program Developed Based on MOOSE

基于MOOSE平台,开发了用JFNK方法求解中子扩散本征值、瞬态问题的程序。在程序中实现了反照率边界条件和真空边界条件的设置。通过基准题TWIGL对程序进行了验证,发现对于本征值和瞬态问题,模拟解和参考解都是一致的。程序中采用全隐式Newton法求解中子本征值问题,并与经典幂迭代法进行了对比,发现Newton法能极大减少非线性步的步数,大幅加快收敛速度。采用全空间时空动力学对中子瞬态问题进行求解,可精确跟踪空间中任何一点在瞬态过程中的变化,时间项处理采用向后欧拉差分,时间步长为0.01 s和0.05 s的计算结果和采用0.001 s为时间步长的参考解吻合得很好,说明程序在较大的时间步长下也能保证问题的收敛性和精度。

A program for solving multi-group neutron diffusion eigenvalue and transient problems using JFNK method was developed based on MOOSE platform. Albedo boundary condition and vacuum boundary condition were realized in this program. The program was verified by TWIGL benchmark, and the simulation results are in good agreement with the reference. In this program, full implicit Newton method was used to solve eigenvalue problem, and the results show that Newton method can greatly reduce the nonlinear steps of iteration and speed up convergence compared with classical PI(power iteration) method. Spatial-temporal dynamics was used to solve the transient problem, and any point in the domain with the change of time could be simulated. Backward Euler difference was adopted in time discretization, and the simulation results at time step 0.01 s and 0.05 s are matched very well with the reference at time step 0.001 s, so the convergence and accuracy can be ensured with a bigger time step in the program.