Application of an adjoint technique to one-speed X,Y-geometry source-detector transport problems in the discrete ordinates formulation using a spectral nodal method

Described here is an application of an adjoint technique for solving source-detector discrete ordinates (SN) transport problems by using a spectral nodal method. For one-speed X,Y-geometry adjoint SN transport problems, considering linearly anisotropic scattering in non-multiplying media, the coarse-mesh adjoint spectral Green's function-constant nodal (SGF†-CN) method is presented. The discretized SGF†-CN equations are solved by using the adjoint partial one-node block inversion (NBI) iterative scheme. The partial adjoint NBI scheme performs SN transport sweeps from the four corners of the rectangular domain. One uses the most recent estimates for the adjoint node-edge average fluxes in the outgoing directions, to solve the resulting adjoint SN problem in that node for all the incoming adjoint node-edge average fluxes, which constitute the outgoing adjoint node-edge average fluxes for the adjacent nodes in the direction of the transport sweep. Numerical results are given to illustrate the method's accuracy in coarse-mesh adjoint SN calculations and some advantages of using the adjoint technique in source-detector problems.