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求解两群多维中子扩散方程的稳态非线性解析节块方法是基于非线性迭代技术与解析节块方法而建立的,并在计算程序NODAN中实现。使用了粗网有限差分方法(CMFD)作为整体耦合计算方法,同时引入耦合修正因子对低阶近似中的耦合关系加以修正。利用解析方法求解局部两节块问题,用以确定耦合修正因子,并在计算过程中通过周期地更新修正因子,迫使CMFD近似中的表面流与高阶方法解得的表面流相等。建立了一种稳定技术,用于克服在解析求解两节块问题中可能遇到的数值不稳定问题。这种非线性方法与有效的数值方法和稳定技术相结合,为求解节块方程提供了一条高效的途径。使用程序NODAN对几种轻水堆基准问题进行了计算,数值结果表明,这种节块方法可以得到精确的结果,与常规节块方法NEMC相比,计算效率显著提高。
The steady-state nonlinear analytical nodal method for solving two groups of multidimensional neutron diffusion equations is based on the nonlinear iterative technique and analytical nodal method and is implemented in the computational program NODAN. The coarse mesh finite difference method (CMFD) is used as the integral coupling calculation method, and the coupling correction factor is introduced to correct the coupling relation in low-order approximation. The analytical method is used to solve the local two-block problem to determine the coupling correction factor. During the calculation, the correction factor is periodically updated to force the surface flow in the CMFD approximation to be equal to the surface flow obtained by the higher-order method. A stabilization technique was developed to overcome the numerical instability problems that may be encountered in solving two block problems analytically. This non-linear method combined with efficient numerical methods and stabilization techniques provides an efficient way to solve the nodal equation. Using the program NODAN, several LWR benchmarking problems were calculated. The numerical results show that this nodal method can obtain accurate results, and the computational efficiency is significantly improved compared with the conventional nodal method NEMC.