HEXNEM - A Nodal Method for the Solution of the Neutron Diffusion Equation in Hexagonal Geometry

The nodal expansion method HEXNEM presented here bases on the transverse integration in axial direction and over the hexagonal plane of the nodes. For that, the 3-dimensional problem is split into a 2-dimensional problem in the hexagonal plane and a 1-dimensional problem in the z-direction. The 2-dimensional hexagonal problem is solved by an expansion of the neutron flux using two-dimensional polynomials and exponential functions being the solutions of the homogeneous equation. The transversal leakage term and the fission and scattering sources are approximated by the polynomials. To improve the accuracy, the method is not only based on the side averaged fluxes and currents but also on the corner point values. An analogous flux expansion is used for the solution of the 1-dimensional equation in axial direction. An inner and outer iteration procedure is applied to the solution of the problem. This method leads to an improvement of the accuracy against the simpler method implemented in the code DYN3D. It is shown by comparing the results with reference solutions of 2- and 3-dimensional benchmark problems.