Analytic basis function expansion method for neutron diffusion calculation in the arbitrary triangular nodes

A new nodal method for directly solving the neutron diffusion equation in the arbitrary triangular nodes was proposed. The neutron flux distributions within a node were expanded in a series of analytic basis functions for each group. Nodes were coupled each other with both the zero- and first-order partial neutron current moments simultaneously. The relationships between a regular triangle and an arbitrary triangle are utilized to describe the neutron current moments. With a new sweeping scheme developed for arbitrary triangular node, the response matrix technique was used to solve the nodal diffusion equations iteratively. Based on the proposed model, the code ABFEM-T was developed. The numerical results for a series of benchmark problems show that the core multiplication factor and nodal powers are predicted accurately using this model for unstructured neutron diffusion problems.