Analytical Coarse-Mesh Method for Monoenergetic Slab-Geometry Reactor Kinetics using Neutron Diffusion Model

Abstract

Presented here is an analytical spectral nodal method for slab-geometry one-speed kinetics diffusion model with a given number N of groups of delayed neutron precursors. Our method is based on a spectral analysis of the nodal kinetics diffusion equations. These equations are obtained by integrating the original kinetics equations separately over a time step and over a spatial node, and then considering flat approximations for the forward difference terms. These flat approximations are the only approximations considered in the method. As a result, the present spectral nodal method for reactor kinetics generates numerical solutions for space independent problems or for time independent problems that are completely free from truncation errors, apart from computational finite arithmetic considerations. We show numerical results to a typical model problem to illustrate the method’s accuracy for space-time coarse-mesh calculations.