基于中子扩散方程的JFNK方法研究

Research of JFNK Method Based on Neutron Diffusion Equation

将中子扩散方程采用有限差分法离散成广义特征值问题,采用JFNK方法进行求解,同时采用LRA基准题和无限平板基准题对JFNK方法进行了验证,并基于单棒例题对JFNK方法的微扰量、预处理矩阵等关键技术进行了研究,结果表明:JFNK方法求解中子扩散方程具有良好的精度和收敛效率;在差分构造雅阁比向量时,微扰量在10-5附近时与解析构造雅阁比向量的效果相当;采用中子扩散方程对应的完整雅阁比矩阵作为预处理矩阵的加速效果更好;源迭代次数超过一定值后,源迭代计算结果作为初值带来的加速效果逐渐减弱。

The neutron diffusion equation is discretized into a generalized eigenvalue problem by finite difference method and solved by JFNK method.The LRA benchmark and the infinite plate benchmark are used to verify the JFNK method for solving neutron diffusion equation.Based on the single fuel pin example,the perturbation and preprocessing matrices of JFNK method are studied.The results show that:JFNK method is with good accuracy in solving neutron diffusion equation;when Jacobian vector is constructed by difference method and the perturbation is near 10-5,the computational efficiency is comparable to the analytical method,using the complete Jacobian matrix corresponding to the neutron diffusion equation as the pretreatment matrix has better acceleration effect;and when the number of source iterations exceeds some value,the acceleration effect caused by the initial value is gradually weakened.