JFNK求解高温气冷堆中子扩散问题的预处理方法研究

Preconditioning Method for JFNK on Solving HTGR Neutron Diffusion Problem

预处理方法是非线性求解方法JFNK中效率和数值收敛特性的关键。基于包括活性区、石墨反射层和外围含硼碳砖在内的高温气冷堆堆芯中子扩散本征值问题,对JFNK求解过程中的预处理环节进行了研究。根据矩阵元素的物理性质简化得到不同的近似雅克比矩阵,使用线性预处理方案ILU、SIPLU进行了预处理,并对其预处理效果、矩阵稀疏性、预处理时间等参数进行了分析。结果表明,块雅克比型近似阵是对原雅克比矩阵的较好近似,其能够在保留各中子能群内部耦合关系的前提下,构造结构简单、适用性强的近似雅克比矩阵。对于此类高温气冷堆中子扩散问题,选取SIPLU方法能获得性能良好的预处理矩阵,达到高效JFNK计算。

Preconditioning is the key to the efficiency and convergence of JFNK method.The preconditioning process of JFNK method was investigated based on an eigenvalue problem for high temperature gas-cooled reactor(HTGR)neutron diffusion,including the regions such as reactor core,graphite reflector and carbon brick.The Jacobian matrix was simplified according to the physical characteristics of matrix elements.The different preconditioners were obtained by the linear preconditioning methods such as ILU and SIPLU.The preconditioning features such as preconditioning quality,sparsity and calculation time were analyzed.The results indicate that the block Jacobian matrix is a good approximation to the original Jacobian matrix,and the former can constructe a simple and adaptive original Jacobian matrix while maintaining the coupling information inside each neutron energy group.SIPLU preconditioner can reach a high preconditioning quality and efficient simulation in solving this kind of HTGR neutron diffusion problem.