3D Nodal Expansion Method HEXNEM for Solution of the Neutron Diffusion Equation in Hexagonal Geometry

The nodal expansion method (NEM) used in the hexagonal version of the code DYN3D is based on the node averaged values of fluxes in the node volume and averaged values of fluxes and currents at the interfaces of the nodes [1]. The 3-dimensional neutron diffusion equation for two energy groups is split into a 2-dimensional equation in the hexagonal plane solved with the help of Bessel functions and a 1-dimensional equation in axial direction solved by polynomial expansion. The two equation systems are coupled by the transversal bucklings. The accuracy of this method is sufficient for the VVER-440 where the assembly pitch is 14.7 cm. The assemblies of the VVER-1000 have a larger pitch of 24.1 cm. Comparing with mathematical benchmarks for the VVER-1000 the maximal deviation of powers is in the order of 5%. The new nodal expansion method HEXNEM presented here uses a different flux expansion in the nodes. In addition to the average values at the interfaces of the hexagon the values at the corner points are included, too. It is shown that the accuracy is improved for the VVER-1000 problems.