This research extends MATLAB PDE Toolbox to model nuclear reactors by solving the 2-D and 3-D multigroup neutron diffusion equations using the finite element method. The developed scripts can simulate reactors with rectangular and hexagonal lattices and have the potential to handle complex core configurations, benefitting from the constructive solid geometry. The meshing subroutine decomposes the domain into unstructured triangular or tetrahedral elements that are either linear or quadratic. With many versatile MATLAB functions, data analysis and visualization can be accomplished within the same software environment. The proposed toolbox provides a graphical user interface for novices and simple models and a programmatic workflow for experienced users and complex problems. Multiple benchmark tests show that the developed framework produces accurate results with acceptable computation speed. The developed MATLAB reactor simulation engine is license friendly and readily accessible by researchers and students, making it an ideal research and educational tool.

本研究通过使用有限元方法求解 2-D 和 3-D 多群中子扩散方程，将 MATLAB PDE Toolbox 扩展到模拟核反应堆。开发的脚本可以模拟具有矩形和六边形晶格的反应堆，并有可能处理复杂的核心配置，受益于建设性的实体几何。网格划分子程序将域分解为线性或二次的非结构化三角形或四面体元素。借助许多通用的 MATLAB 函数，可以在同一个软件环境中完成数据分析和可视化。建议的工具箱为新手和简单模型提供图形用户界面，为有经验的用户和复杂问题提供程序化工作流程。多个基准测试表明，开发的框架以可接受的计算速度产生准确的结果。开发的 MATLAB 反应堆仿真引擎许可证友好，研究人员和学生可以轻松访问，使其成为理想的研究和教育工具。