An Adjoint Technique Applied to Slab-Geometry Source-Detector Problems Using the Generalized Spectral Green’s Function Nodal Method

Abstract

Presented here is the application of an adjoint technique for solving source-detector discrete ordinates (S_N) transport problems by using a spectral nodal method. For slab-geometry adjoint S_N model, the adjoint spectral Green’s function method (SGF^†) is extended to multigroup problems considering arbitrary L′th order of scattering anisotropy, and the possibility of nonzero prescribed boundary conditions for the forward S_N transport problem. The SGF^† method converges numerical solutions that are completely free from spatial truncation errors. In order to generate numerical solutions of the SGF^† equations, we use the partial adjoint one-region block inversion (RBI) iterative scheme. Partial adjoint RBI scheme uses the most recent estimates for the region-edge adjoint angular fluxes in the outgoing directions of a given region, to solve the resulting adjoint S_N problem in that region for all the adjoint angular fluxes in the incoming directions, which constitute the outgoing adjoint angular fluxes for the adjacent region in the sweeping direction. Numerical results are given to illustrate the present spectral nodal method’s features and some advantages of using the adjoint technique in source-detector problems.

Keywords:

• Adjoint transport problem
• discrete ordinates
• spectral nodal method
• energy multigroup
• source-detector problem

Additional information

Funding

The authors acknowledge the partial financial support of Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq – Brazil) and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ – Brazil). The work by the first author was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES – Brazil).