Polygonal Virtual Element Spatial Discretisation Methods for the Neutron Diffusion Equation With Applications in Nuclear Reactor Physics

Abstract

In this paper the application of the virtual element method (VEM) to the multigroup, neutron diffusion equation will be presented. The VEM is a recently developed Bubnov-Galerkin spatial discretisation method based largely on the mimetic finite difference method (MFD) that preserves the properties of the underlying vector operators. It can discretise elliptic partial differential equations (PDEs) on arbitrary polygonal/polyhedral meshes with arbitrary order and regularity. Deterministic, geometry conforming methods, used to solve multigroup, neutron diffusion, nuclear reactor physics problems have historically used the finite element method (FEM). However, FEM requires high-quality meshes with few highly distorted elements (elements with a poor aspect ratio) or it may may experience convergence problems. The process of creating high quality meshes, even with automated mesh generation algorithms, such as the advancing front and Delaunay methods, is often very time consuming. For these reasons VEM is being studied in this paper as a possible alternative to FEM in the numerical solution of neutron diffusion problems in nuclear reactor physics. A C5G7 UOX pincell problem is presented to demonstrate the application of VEM to mutligroup diffusion problem. The method of manufactured solutions (MMS) is used to determine the order of convergence.