A hexagonal geometry nodal expansion method for fast reactor calculations

Abstract

A hexagonal geometry extension of the nodal expansion diffusion theory method is presented together with solution and acceleration techniques which have proved effective for two-dimensional (2D) and three-dimensional (3D) fast reactor calculations. The method uses a radial nodal flux expansion which has hexagonal symmetry. A one-dimensional (1D) expansion is used for the axial direction. Numerical results are presented for four-group LMFBR benchmark problems and a 37-group PFR problem. A zeroth order (quadratic degree) radial expansion is found to be sufficient to permit calculations to be performed using one mesh per subassembly, whereas higher order expansions are more efficient in the axial direction because a coarser mesh can usually be used in this direction. For comparable accuracy the method is found to be a factor of 2 faster than the finite difference method for two-dimensional calculations and an order of magnitude faster for three-dimensional calculations.