Matrix Method of Characteristics Based on Modular Ray Tracing

The Matrix Method of Characteristics (MOC) is an alternative to traditional MOC, in which repeatedly characteristics sweeping is needed. In the Matrix MOC, a linear algebraic equation system, which is represented by coefficient-matrix, can be formed by sweeping only once, and then solving the linear system takes the place of repeatedly characteristics sweeping. There are many linear solvers to be use, like direct LU decomposition and widely used Krylov subspace iterative methods. In the past, 2D Matrix MOC was implemented based on the long characteristics in which tremendous memory is consumed to hold the geometrical information. Then, 2D Matrix MOC based on modular ray tracing was implemented to overcome the difficulty. Modular ray tracing just holds the geometrical information of typical modules like cells or assemblies, consequently needs less memory. In this study, Filippone-type modular ray tracing in which different azimuths own the same number of characteristics lines was used, and AutoCAD VBA programing produced the geometrical information. Also, the Matrix MOC based on modular ray tracing was implemented to solve half, fourth and eighth reactor core in which additional modules, e.g. half-module, fourth-module and eighth-module were involved and need special considerations. Numerical results demonstrate that Matrix MOC based on modular ray tracing can obtain good efficiency and accuracy.