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

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.