Numerical methods to solve the fuel depletion equations for a nuclear reactor

Abstract

Different numerical methods for solving the fuel depletion equations in the depletion module of a reactor core analysis system are compared with each other, in order to find the best method and the best implementation of this method to be used in NECSA's OSCAR system. It is assumed that the neutron flux is constant with time over each burnup step, giving a linear system of first order differential equations with constant coefficients that has to be solved. Using the special properties of the fuel depletion equations of stiffness, sparseness and essential-nonnegativity, it is shown how the various methods can be optimally implemented. By using a sample global reactor depletion and an assembly depletion problem, it is then shown that the Taylor expansion method, using a generalised uniformization technique, performs the best under most circumstances.