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 (S_N) 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 S_N equations. The method is based on the use of the standard spatially discretised adjoint S_N 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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