Isogeometric Analysis for Neutron Diffusion Problems

摘要

Isogeometric analysis can be viewed as a generalisation of the finite element method. It permits the exact representation of a wider range of geometries including conic sections. This is possible due to the use of concepts employed in computer-aided design. The underlying mathematical representations from computer-aided design are used to capture both the geometry and approximate the solution. In this paper the neutron diffusion equation is solved using isogeometric analysis. The practical advantages are highlighted by looking at the problem of a circular fuel pin in a square moderator. For this problem the finite element method requires the geometry to be approximated. This leads to errors in the shape and size of the interface between the fuel and the moderator. In contrast to this isogeometric analysis allows the interface to be represented exactly. It is found that, due to a cancellation of errors, the finite element method converges more quickly than isogeometric analysis for this problem. A fuel pin in a vacuum was then considered as this problem is highly sensitive to the leakage across the interface. In this case isogeometric analysis greatly outperforms the finite element method. Due to the improvement in the representation of the geometry isogeometric analysis can outperform traditional finite element methods. It is proposed that the use of isogeometric analysis on neutron transport problems will allow deterministic solutions to be obtained for exact geometries. Something that is only currently possible with Monte Carlo techniques.