NURBS-enhanced control volume finite element spatial discretisation methods for the steady-state multigroup neutron diffusion equation

The paper describes a novel spatial discretisation termed the NURBS-enhanced control volume finite element Method (NECVFEM) and applies it to the solution of the steady-state multigroup neutron diffusion equation. The NECVFEM combines the geometric flexibility of FEM with the local, and global, conservation properties of finite volumes and the exact geometric representation associated with Non-Uniform Rational B-Splines (NURBS). In this paper, the NECVFEM and CVFEM discretisations are used to solve three nuclear reactor physics benchmark verification test cases. The numerical accuracy, and computational efficiency, of the NECVFEM and CVFEM have been compared to standard Lagrangian FEM. The Lagrangian FEM has utilised both volume and surface preserving approaches for curvilinear computational domains. The NECVFEM method has been shown to be highly effective in reducing the geometric errors associated with modelling curvilinear computational domains. It has achieved lower numerical errors than the CVFEM across all spatial refinements and benchmark verification test cases. In addition, the NURBS-enhanced methods have been shown to produce geometric errors that are lower, or of similar magnitude, to that of the volume and surface preserving methods while avoiding the need for complex mesh modification steps. A comparison of computational solution times associated with each discretisation method showed that the NECVFEM was more computationally efficient than the CVFEM and comparable to the FEM, particularly for linear spatial discretisations.