An Azimuthal, Fourier Moment-Based Axial SN Solver for the 2D/1D Scheme.

Abstract

Despite the incredible advancements in computing power in recent decades, using explicitly three-dimensional neutron transport methods is still very computationally expensive. Several alternative methods have been developed to make computation more tractable, such as the “2D/1D” scheme, which decomposes three-dimensional geometries into an axial stack of radial planes. In this scheme, one common approximation is to assume that the radial and axial transverse leakages that couple the axial and radial solvers are isotropic, which means that all angular dependence of the leakage is neglected. For more complicated problems, such as those with control rods or mixed oxide (MOX) fuels, higher fidelity treatment of the axial and radial leakages is needed to better capture the relationship between the solvers.

The first objective of the work presented here investigates incorporating full angular dependence of both the azimuthal and polar angles into the transverse leakages. Fully explicit angular dependence is shown to be particularly burdensome, both in terms of memory and run time requirements. The second, more novel objective uses a Fourier series expansion to account for the azimuthal dependence, requiring the formulation of a new axial SN solver to generate angular fluxes for the axial transverse leakage construction.

In several test cases analyzed, which include cases with both control rods and MOX fuels, noteworthy accuracy gains are observed by including the angular dependence of the leakages. The Fourier moment-based approach performs very well, accurately capturing the azimuthal dependence with only a few moments. Overall, the Fourier moment-based approach reduces the run time by roughly a factor of 1.5, the aggregate memory footprint by a factor of 3 to 4, and angle-dependent variables by an order of magnitude.

Other test problems highlight one of the remaining sources of error relating to the spatial distribution of the axial transverse leakage, which is introduced because the axial solver operates on a coarse radial grid. The results suggest that by including a more accurate angular representation, some cancellation of error between the spatial and angular treatments is removed, indicating that future work focusing on improving the spatial distribution should be pursued.