The modified spectral deterministic method applied to fixed–source discrete ordinates problems in X,Y–geometry

Jesús Pérez Curbelo,Ricardo Carvalho Barros,Rafael Barbosa Libotte,Hermes Alves Filho,Amaury Muñoz Oliva

doi:10.15392/bjrs.v8i3a.1268

Abstract

A new approach for the application of the coarse–mesh Modified Spectral Deterministic method to numerically solve the two–dimensional neutron transport equation in the discrete ordinates (Sn) formulation is presented in this work. The method is based on within node general solution of the conventional one–dimensional Sn transverse integrated equations considering constant approximations for the transverse leakage terms and obtaining the Sn spatial balance equations. The discretized equations are solved by using a modified Source Iteration scheme without additional approximations since the average angular fluxes are computed analytically in each iteration. The numerical algorithm of the method presented here is algebraically simpler than other spectral nodal methods in the literature for the type of problems we have considered. Numerical results to two typical model problems are presented to test the accuracy of the offered method.

Highlights

Over the past 30 years, several spectral nodal methods have been developed for numerically solving the time–independent, slab–geometry Boltzmann transport equation in the discrete ordinates (SN) formulation with no spatial truncation error
One can point out the spectral Green's function (SGF) [1; 2], the spectral Response Matrix (RM) [3] and the Analytical Discrete Ordinates (ADO) [4] analytical numerical methods, which generate numerical values for the node–edge angular fluxes that exactly agree with the analytical solution of the SN transport equations
We present the application of the modified Spectral Deterministic Method (SDM) to X, Y–geometry SN problems

Summary

Introduction

Over the past 30 years, several spectral nodal methods have been developed for numerically solving the time–independent, slab–geometry Boltzmann transport equation in the discrete ordinates (SN) formulation with no spatial truncation error Among these methods, one can point out the spectral Green's function (SGF) [1; 2], the spectral Response Matrix (RM) [3] and the Analytical Discrete Ordinates (ADO) [4] analytical numerical methods, which generate numerical values for the node–edge angular fluxes that exactly agree with the analytical solution of the SN transport equations. This method shows to be algebraically and computationally simpler than other spectral–nodal methods and was termed the Spectral Deterministic Method (SDM)

Methods

Results

Conclusion