Nodal Integral method for multi-group neutron diffusion equation in three dimensional cylindrical coordinate system

Abstract

Due to their high accuracy, the nodal methods are quite extensively used for solving neutron diffusion and transport equations. However, their use is mainly restricted to the geometries which can be mapped by rectangular (cuboidal in 3D) or hexagonal cells. For several Generation IV reactors the equations are solved in cylindrical geometries, needing fine meshing near the boundaries if traditional nodal methods are used. Therefore, a Nodal Integral Method (NIM) for one group neutron diffusion in 2D polar coordinates was developed recently. Here, the method is extended to multi-group neutron diffusion in 3D cylindrical coordinates. Unlike the Cartesian geometries, each direction needs separate treatment in case of the cylindrical geometries. Therefore, the extension is neither trivial nor straightforward. The developed method is tested by solving three different problems for which analytical or benchmark solutions exist. It is observed that the methodology preserves its high accuracy for multi-group 3D problems.