Abstract
Presented here is the application of an adjoint technique for solving source-detector discrete ordinates (SN) transport problems by using a spectral nodal method. For slab-geometry adjoint SN 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 SN 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 SN 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.