We develop and validate node homogenization methods, based on one and three-dimensional node equivalent problems, that improve the volume weighted method for the treatment of the rod cusping effect. The numerical implementation of these techniques in a numerical approach based on general spherical harmonics, nodal collocation method, for arbitrary odd order $L$, and fully implicit time discretization, is verified on the AECL-7236 PHWR benchmark transient, showing the validity and convergence of the $P_1$ and $P_3$ approximations and the ability of the method to give accurate results for the relative power and scalar flux when a coarse spatial mesh combined with advanced homogenization techniques is used.

我们基于一维和三维节点等效问题，开发并验证了节点均质化方法，该方法改进了体积加权方法来处理杆卡套效应。这些技术的数值实现是基于通用球谐函数的数值方法，节点配点法（对于任意奇数阶）$\mathrm{大号}$，并在AECL-7236 PHWR基准瞬态上验证了完全隐式时间离散化，显示了 $P_{\mathrm{1个}}$ 和 $P_3$ 当使用粗糙的空间网格与先进的均质技术相结合时，该方法的近似值和方法能够给出相对功率和标量通量的准确结果的能力。