On a Response Matrix Solver for Slab-Geometry Neutral Particle Transport Problems in the Discrete Ordinates and Energy Multigroup Formulations Considering Non-Uniform Interior Sources

Abstract

We present in this work an extension of the Response Matrix (RM) method for the numerical solution of slab-geometry neutral particle transport equation in the discrete ordinates (S) and energy multigroup formulations considering non-uniform sources. By using the term non-uniform we mean that the particle source is not spatially uniform inside the regions that compose the domain. The extended RM method, differently from the conventional RM method, is based on the solution of “source-independent” auxiliary problems (Green’s functions). The solution of these auxiliary problems is used in conjunction with the given non-uniform source to generate the sweeping matrices for the extended RM method. Numerical results with respect to both uniform and non-uniform source problems are given to illustrate the efficiency of the offered extended RM method.