Extension of the Discrete-Ordinates Transport Solver IDT to Regular Two-Dimensional Triangular Meshes

In this work, the Integro-Differential Transport solver (IDT), which is one of the transport solvers available in the APOLLO3(R) lattice code, has been extended to handle 2D unstructured meshes. In particular, the previously implemented method of short characteristics (MoSC) used to solve for the spatial variable in the framework of an SN approach has been extended to triangular cells which represent the natural discretization for calculating the hexagonal lattices present in fast reactors. The coefficients of the collision-probability matrices have been evaluated by means of a split-cell algorithm, specialized for dealing with different orientations of the triangle with respect to each discrete ordinate of the SN sweeping. A new sweeping routine for unstructured meshes has been added to IDT. The correct implementation of the method and its robustness with respect to the skewness and the optical thickness of the triangle has been verified. The method of manufactured solutions has been employed to obtain a numerical estimate of the spatial convergence order of the method. The same version of the MoSC has then been implemented in MINARET, another solver available in APOLLO3(R). Finally, the modified IDT applied to an unstructured mesh for the C5G7 benchmark has been successfully benchmarked against MC calculations, and the modified MINARET has been applied to a neutron transport calculation for the RJH research reactor.