Keywords: adjoint transport problems, discrete ordinates, spectral nodal methods, source–detector problems
A numerical method for monoenergetic slab–geometry fixed–source adjoint transport problems in the discrete ordinates formulation with no spatial truncation error
A numerical method that is free of spatial truncation errors is developed for one–speed slab–geometry constant fixed–source adjoint discrete ordinates (SN) 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 SN equations. The method is based on the use of the standard spatially discretised adjoint SN 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.