Numerical analysis of spatial discretization schemes in ARES transport code for shielding calculation

The discrete ordinates method (SN) is one of the mainstream methods for radiation shielding calculation of nuclear systems. The accuracy of spatial discretization in the SN equations has a significant effect on the accuracy of the shielding calculations. This work numerically examines the error behavior of various spatial discretization schemes implemented in the ARES transport code for shielding calculations. The numerical diffusion effect, encountered when the uncollided flux component is significant, such as in fast neutron groups or multi-dimensional void regions, is studied by investigating the ray propagation problem and glancing void problem. Positivity is investigated in optically thick cells and multi-dimensional void regions using spatial discretization schemes that cannot preserve non-negativity. In addition, the local accuracy is examined through a series of one-cell problems with various exact flux smoothness conditions in the cell. The results indicate that local accuracy depends not only on the spatial discretization but also the smoothness of the exact flux. Globally, severe unphysical flux representations arise in the diamond difference (DD) scheme. Other zero-order schemes inhibit oscillation but present significant numerical diffusion, whereas finite element methods damp the oscillation quickly near the flux discontinuity and present better resilience against negativity than DD. All these results can provide guidelines on selection of spatial discretization in realistic applications.