An analytical discrete ordinates nodal solution to the two-dimensional adjoint transport problem

A solution to the one-group discrete ordinates approximation of the adjoint to the transport equation in two-dimensional Cartesian geometry is developed in this work. Starting from an integration process over a region (node) of the domain, the model is reduced to one-dimensional transverse-integrated equations in the x and y variables which are then solved by the Analytical Discrete Ordinates Method (ADO Method). Particular attention is given to the effect of non-homogeneous boundary conditions in the formulation. Explicit expressions are derived and used for evaluating, in a fast way, absorption rates of internal detectors from the adjoint formulation. Excellent agreement was found between numerical results obtained for the absorption rates evaluated from the forward and adjoint problems. (C) 2019 Elsevier Ltd. All rights reserved.