基于一阶中子输运方程的杂交间断有限元方法研究  

Investigation on Hybrid Discontinuous Galerkin Method Based on First-Order Neutron Transport Equation

作　　者：孙启政 刘晓晶[1] 张滕飞 Sun Qizheng;Liu Xiaojing;Zhang Tengfei(School of Nuclear Science and Engineering,Shanghai Jiao Tong University,Shanghai,200240,China)

机构地区：[1]上海交通大学核科学与工程学院,上海200240

出　　处：《核动力工程》2024年第6期248-253,共6页Nuclear Power Engineering

基　　金：国家自然科学基金(12175138、U20B2011)。

摘　　要：复杂构型先进反应堆的不断提出对中子学数值方法提出了更高的要求,为实现对复杂问题的准确、高效模拟,本文提出一种基于一阶双曲型中子输运方程(NTE)的杂交间断有限元(HDG)方法。该方法在角度上采用了离散纵标(S_(N))的格式将原始的方程解耦为各个角度方向的相互独立的方程;在空间上采用迎风格式对方程进行离散,整个问题的全局矩阵耦合系统呈现分块下三角的形式,更加适合网格数目较多的复杂几何非均匀中子输运问题场景。选取了TAKEDA1基准题与非均匀组件问题作为分析对象,对所提出的HDG方法的计算性能进行了分析。数值结果表明,HDG在上述算例中均实现稳定收敛,有效增殖系数k_(eff)与参考解的最大误差为108pcm(1pcm=10^(−5))。此外,与传统二阶偶对称形式方法相比,一阶HDG方法空间扫描更为高效,在上述算例中实现了约2倍的加速比。因此,本文研究的HDG方法能够为复杂构型反应堆问题提供可选的解决方案。The development of advanced reactor designs imposes higher demands on neutronic numerical methods.To achieve accurate and efficient simulation of complex problems,this paper introduces a hybrid discontinuous Galerkin(HDG)method based on the first-order hyperbolic neutron transport equation(NTE).The method decouples the original equation into independent equations for each angular direction using the discrete-ordinates(S_(N))method in angular space.In spatial discretization,this paper employs an upwind scheme that results in a blocked-lowertriangular global matrix coupling system,making it well-suited for complex,geometrically heterogeneous neutron transport scenarios with a large number of meshes.The study evaluates the performance of the proposed HDG method using the TAKEDA1 benchmark and a heterogeneous assembly problem.The results demonstrate that the HDG method achieves stable convergence for the aforementioned problems,with a maximum error between the effective multiplication coefficient k_(eff) and the reference solution of 108 pcm(1pcm=10^(−5)).In addition,compared with the traditional second-order even-parity method,the first-order HDG method is more efficient in spatial scanning,and the acceleration ratio is about 2 times in the above examples.Therefore,the proposed HDG method can provide an alternative solution for complex reactor problems.

关 键 词：杂交间断有限元(HDG) 中子输运方程(NTE) 迎风格式 离散纵标(SN) 

分 类 号：TL329[核科学技术—核技术及应用]