The ADO-nodal method for solving two-dimensional discrete ordinates transport problems

In this work, recent results on the solution of fixed-source two-dimensional transport problems, in Cartesian geometry, are reported. Homogeneous and heterogeneous media problems are considered in order to incorporate the idea of arbitrary number of domain division into regions (nodes) when applying the ADO method, which is a method of analytical features, to those problems. The ADO-nodal formulation is developed, for each node, following previous work devoted to heterogeneous media problem. Here, however, the numerical procedure is extended to higher number of domain divisions. Such extension leads, in some cases, to the use of an iterative method for solving the general linear system which defines the arbitrary constants of the general solution. In addition to solve alternative heterogeneous media configurations than reported in previous works, the present approach allows comparisons with results provided by other metodologies generated with refined meshes. Numerical results indicate the ADO solution may achieve a prescribed accuracy using coarser meshes than other schemes.