强激光与粒子束, 2017, 29 (3): 036024, 网络出版: 2017-03-29  

JFNK在高温堆扩散计算中的应用

Application of Jacobian-free Newton-Krylov method for high temperature reactor neutron diffusion equation calculation
作者单位
清华大学 核能与新能源技术研究院, 先进核能技术协同创新中心, 先进反应堆工程与安全教育部重点实验室, 北京 100084
摘要
研究了JFNK框架下高温堆中子扩散问题的求解方法。研究结果表明,JFNK方法在求解与源迭代相同形式中子扩散方程时,相对残差下降趋势为逐渐加快并趋于稳定,有利于更高求解精度的实现。使用通量归一化附加方程可以获得更好的JFNK非线性迭代特性,但在算例中其部分牛顿修正方程求解时间偏多,总计算时间高于显式有效增殖系数附加方程法,需要研究更高效的JFNK预处理方法对线性求解环节进行改善。
Abstract
This paper studies the application of solving high temperature reactor (HTR) neutron diffusion equation with Jacobian-free Newton-Krylov (JFNK) method. Results show that when solving neutron diffusion equation, the relative residual norm of JFNK method decreases slowly at the beginning. Then the rate of convergence become faster and finally reaches a relatively stable value. This feature is conducive to a high-accuracy solution. In the test of two kinds of additional equations, the neutron diffusion equation with flux normalization condition has a better nonlinear convergence behavior. However, due to the longer computational time in solving linear equations, its total computational time is more than the one with k expression. More efficient preconditioning methods should be studied to improve linear equations.

卢佳楠, 郭炯, 李富. JFNK在高温堆扩散计算中的应用[J]. 强激光与粒子束, 2017, 29(3): 036024. Lu Jia’nan, Guo Jiong, Li Fu. Application of Jacobian-free Newton-Krylov method for high temperature reactor neutron diffusion equation calculation[J]. High Power Laser and Particle Beams, 2017, 29(3): 036024.

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