Tort solutions for the 3D radiation transport benchmarks for simple geometries with void region

We present the solutions for the set of three-dimensional radiation transport Benchmark problems obtained with the TORT transport code using its three optional methods: Theta Weighted (θW), Linear Nodal (LN), and Linear Characteristic (LC). Only the cases with 50% scattering are presented in this paper since the nonscattering cases are bound to suffer severe ray effects. By solving the problems on a sequence of refined meshes we illustrate that for some points defined in the benchmark the solution converges with mesh refinement. However, the solution at most points does not converge with mesh refinement, and we illustrate that this is a consequence of ray effects in the void region. Also, we compare TORT's solutions to the Monte Carlo reference solution and observe that even when TORT's solution converges with mesh refinement, it usually does not converge to the Monte Carlo reference. This behavior also results from ray effects, and therefore we conjecture it will appear in varying degrees in all discrete ordinates accurate solutions because ray effects exist in the exact solution of the discrete ordinates equations. While this result is disappointing from the benchmarking point of view, it bodes well for TORT's ability to produce highly accurate solutions to the discrete ordinates approximation. Eliminating ray effects requires extensions of the solution algorithm, e.g. via a first collision source, while preserving the desirable features of the discrete ordinates methodology.