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

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。

This paper studies the application of solving high temperature reactor （HTR） neutron diffusion equation with Ja- cobian-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 rela- tively stable value. This feature is conducive to a high-accuracy solution. In the test of two kinds of additional equations, the neu- tron 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.