Title: A numerical method for monoenergetic slab-geometry fixed-source adjoint transport problems in the discrete ordinates formulation with no spatial truncation error

Authors: Damiano S. Militão; Hermes Alves Filho; Ricardo C. Barros

Addresses: Programa de Pós-graduação em Modelagem Computacional, Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Rua Bonfim 25 – parte, 28625-570 Nova Friburgo, RJ, Brazil. ' Programa de Pós-graduação em Modelagem Computacional, Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Rua Bonfim 25 – parte, 28625-570 Nova Friburgo, RJ, Brazil. ' Programa de Pós-graduação em Modelagem Computacional, Instituto Politécnico, Universidade do Estado do Rio de Janeiro, Rua Bonfim 25 – parte, 28625-570 Nova Friburgo, RJ, Brazil

Abstract: A numerical method that is free of spatial truncation errors is developed for one-speed slab-geometry constant fixed-source adjoint discrete ordinates (SN) problems. The unknowns in the method are the cell-edge and cell-average adjoint angular fluxes, and the numerical values obtained for these quantities are those of the analytic solution of the adjoint SN equations. The method is based on the use of the standard spatially discretised adjoint SN balance equations, which hold in each spatial cell and for each discrete ordinates direction, and a non-standard adjoint auxiliary equation that contains a Green's function for the cell-average adjoint angular flux in terms of the exiting cell-edge adjoint angular fluxes and the interior adjoint source. Numerical results are given to illustrate the method's accuracy.

Keywords: adjoint transport problems; discrete ordinates; spectral nodal methods; source-detector problems.

DOI: 10.1504/IJNEST.2012.048816

International Journal of Nuclear Energy Science and Technology, 2012 Vol.7 No.2, pp.151 - 165

Received: 30 Jan 2012
Accepted: 14 May 2012

Published online: 05 Dec 2014 *

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