Analytic function expansion nodal method for hexagonal geometry

A new hexagonal nodal method that directly solves the multidimensional diffusion equation without the transverse integration procedure is described. The new method expands the homogeneous flux distributions within a node in nonseparable analytic basis functions satisfying the neutron diffusion equations at any point of the node. Because the new method does not use the transverse integration, it does not suffer from the need of approximating the transverse leakage shape and the nonphysical singular terms occurring in hexagonal nodes. And, because of the use of analytical basis functions and the corner-point flux included in the nodal coupling equations, the method accurately models large localized flux gradients in the vicinity of nodal corner points as well as nodal interfaces. The new method was tested on two hexagonal benchmark problems consisting of uranium-oxide and mixed-oxide fuel assemblies to demonstrate its accuracy and applicability to realistic problems. The results show that the new method accurately predicts the nodal flux distribution and the core multiplication factor.