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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
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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 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.
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