Title: Analytical adjoint discrete ordinates formulation for monoenergetic slab-geometry source-detector calculations

Authors: Cássio B. Pazinatto; Ricardo C. Barros; Liliane B. Barichello

Addresses: Programa de Pós-graduação em Matemática Aplicada, Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, Cx. Postal 15080, 91509-900, Porto Alegre, RS, 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 ' Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500, Cx. Postal 15080, 91509-900, Porto Alegre, RS, Brazil

Abstract: The adjoint to the neutral-particle transport equation in discrete ordinates formulation is solved by the Analytical Discrete Ordinates (ADO) method. A concise and accurate solution is derived for anisotropic scattering problems in multilayer slab geometry with generalised boundary conditions. The derived adjoint discrete ordinates solution is used to compute the absorption rate of neutral particles for source-detector problems. Numerical results for two typical model problems are given to illustrate the efficiency and accuracy of the offered method.

Keywords: source detector problems; adjoint transport equations; analytical discrete ordinates; multilayer slab geometry; neutral particles; particle transport; anisotropic scattering.

DOI: 10.1504/IJNEST.2016.077478

International Journal of Nuclear Energy Science and Technology, 2016 Vol.10 No.2, pp.107 - 122

Received: 28 Nov 2015
Accepted: 12 Apr 2016
Published online: 03 Jul 2016 *

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