Abstract The Continuous Galerkin Virtual Element Method (CG-VEM) is a recent innovation in spatial discretisation methods that can solve partial differential equations (PDEs) using polygonal (2D) and polyhedral (3D) meshes. This paper presents the first application of VEM to the field of nuclear reactor physics, specifically to the steady-state, multigroup, neutron diffusion equation (NDE). In this paper the theoretical convergence rates of the CG-VEM are verified using the Method of Manufactured Solutions (MMS) for a reaction-diffusion problem in the presence of both highly distorted and non-convex elements and also in the presence of discontinuous material data. Finally, numerical results for the 2D IAEA and the 2D C5G7 industrial nuclear reactor physics benchmarks are presented using both block-Cartesian and general polygonal meshes.

中文翻译：

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用于核反应堆物理应用的多边形网格上多群中子扩散方程空间离散化的虚拟元方法

摘要 连续伽辽金虚拟元法 (CG-VEM) 是空间离散化方法的最新创新，它可以使用多边形 (2D) 和多面体 (3D) 网格求解偏微分方程 (PDE)。本文介绍了 VEM 在核反应堆物理领域的首次应用，特别是稳态、多群、中子扩散方程 (NDE)。在本文中，CG-VEM 的理论收敛率使用制造解法 (MMS) 验证，用于在存在高度扭曲和非凸元素的情况下以及存在不连续材料数据的情况下的反应扩散问题. 最后，2D IAEA 和 2D C5G7 工业核反应堆物理基准的数值结果使用块笛卡尔网格和一般多边形网格呈现。