Abstract
Isogeometric Analysis (IGA) has been applied to heterogeneous reactor physics problems using the multigroup neutron diffusion equation. IGA uses a computer-aided design (CAD) description of the geometry commonly built from Non-Uniform Rational B-Splines (NURBS), which can exactly represent complicated curved shapes such as circles and cylinders, common features in reactor design. This work has focused on comparing IGA to finite element analysis (FEA) for heterogeneous reactor physics problems, including the OECD/NEA C5G7 LWR benchmark. The exact geometry and increased basis function continuity contribute to the accuracy of IGA and an improvement over comparable FEA calculations has been observed.
Highlights
Development of efficient computational methods to solve reactor physics and shielding problems is an ongoing area of research
A comparative study of finite element analysis (FEA) and Isogeometric analysis (IGA) applied to a series of single group pincell test cases and a seven group UOX pincell using the diffusion approximation has been performed
Our results showed that the C0 Non-Uniform Rational B-Splines (NURBS) isogeometric analysis can provide improvements in accuracy compared to both mass preserved, polygonal finite elements and non-mass preserved high-order finite element meshes of the same polynomial order
Summary
Development of efficient computational methods to solve reactor physics and shielding problems is an ongoing area of research. A linearised version of the Boltzmann transport equation, the neutron transport equation is solved on a seven-dimensional phase space This high dimensionality combined with complicated reactor geometries makes solving threedimensional, heterogeneous, full core problems infeasible, even with high-performance computing (HPC) resources. The principal aim of IGA is to unify the fields of design and analysis using a common mathematical description of the geometry in both processes, eliminating the costly finite element (FE) mesh generation step while providing an exact geometrical description as opposed to the approximate polygonal or polyhedral meshes used for FEA (Hughes et al, 2005).
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