Analytic Basis Function Expansion Nodal Method for Neutron Diffusion Equations in Triangular Geometry

An analytic basis function expansion nodal method for directly solving the two-group neutron diffusion equation in the triangular geometry is proposed in the present paper. In this method, the distribution of neutron flux is expanded by a set of analytic basis functions. The diffusion equation is satisfied at any point in a triangular node for each group assuming that the flux within a node is flat. No transverse integration is needed. To improve the nodal coupling relations and computation accuracy, nodes are coupled with each other fulfilling both the zero- and first-order partial neutron current moments across all the three interface of the triangle mesh at the same time. Coordinate conversion is used to transform arbitrary triangle into regular triangle in order to simplify the derivation. A new sweeping scheme is developed for the triangular mesh and the response matrix technique was used to solve the nodal diffusion equation iteratively. Based on the proposed model, the code ABFEM-T is developed. Validation of code for accuracy and efficiency are carried out by calculating both rectangular and hexagonal assembly benchmark problems. Numerical results for the series of benchmark problems show that both the multiplication factor and nodal power distribution are predicted accurately. Therefore this method can be used for solving neutron diffusion problems in complex unstructured geometry.