Recent Studies on the Asymptotic Convergence of the Spatial Discretization for Two-Dimensional Discrete Ordinates Solutions

ABSTRACT

In this work, four types of quadrature schemes are used to define discrete directions in the solution of a two-dimensional fixed-source discrete ordinates problem in Cartesian geometry. Such schemes enable generating numerical results for averaged scalar fluxes over specified regions of the domain with high number (up to 105) of directions per octant. Two different nodal approaches, the ADO and AHOT-N0 methods, are utilized to obtain the numerical results of interest. The AHOT-N0 solutions on a sequence of refined meshes are then used to develop an asymptotic analysis of the spatial discretization error in order to derive a reference solution. It was more clearly observed that the spatial discretization error converges asymptotically with second order for the source region with all four quadratures employed, while for the other regions refined meshes along with tighter convergence criterion must be applied to evidence the same behavior. However, in that case, some differences among the four quadrature schemes results were found.

KEYWORDS:

• Discrete ordinates
• Two-dimensional geometry
• Asymptotic Spatial Convergence

Funding

All authors would like to thank CNPq and CAPES of Brazil and one of them (YYA) would like to thank also CNEC, for partial financial support of this work. The work of the last author (YYA) is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number(s) DE-NA0002576. In addition, (LBB) would like to thank the kind hospitality of CNEC during a recent visit when this work was written.