A Three-Dimensional Flux Expansion Nodal Method for Hexagonal Geometry Application

In this paper, a new flux expansion nodal method for hexagonal-z geometry is presented to solve multi-group neutron diffusion equations. In each three dimensional node and each group, the intra-nodal flux is approximated by the linear combination of exponential functions and orthogonal polynomials up to the second order. The coefficients are obtained by the weighted residual methods and the coupling conditions of the nodes, which satisfy the continuity of both the zero- and first-order moments of fluxes and currents across the nodal surfaces. A series of benchmark problems including the three dimensional cases are used to test this method. The numerical results verify that it is a rather accurate and efficient for the estimation of the eigenvalue and power distribution.