Polar Parity for Efficient Evaluation of Anisotropic Transverse Leakage in the 2D/1D Transport Method

Abstract

A new method for calculating anisotropic radial transverse leakage (TL) in a two-dimensional (2D)/one-dimensional (1D) transport method is derived and implemented in MPACT. This method makes use of parity in the polar angle only to form the 2D transport equations for the 2D/1D method. The even-parity component is solved on a fine mesh using the method of characteristics (MOC), while the odd-parity component is solved on a coarse mesh using S${ }_N$. The anisotropic radial TL on the coarse cell boundaries is calculated by combining the even- and odd-parity components. The new method is faster than a similar previous method because it delegates half of the work required to calculate the solution of the 2D transport problem to a coarse-mesh S${ }_N$ solver, which is more than ten times faster than the fine-mesh MOC solver. The results show that the accuracy of the new method is equivalent to that of the previously implemented method for anisotropic TL, with a significant speedup. With azimuthally isotropic TL, the new method reduces the computational overhead compared to the standard method from 58% to 5% for the three-dimensional (3D) C5G7 benchmark problems. With azimuthally anisotrop\ic TL using Fourier expansion, the new method reduces the overhead from 84% to 37%. This is important because the accuracy of the 2D/1D method is limited by the isotropic TL approximation. With anisotropic TL, the accuracy of 2D/1D is equivalent or comparable to 3D transport, but there is a significant computational cost associated with calculating the anisotropic TL. The method presented provides a faster way to calculate the anisotropic TL, giving the 2D/1D method significantly increased accuracy with only a modest increase in computational requirements compared to isotropic 2D/1D.

Keywords:

• Transverse leakage
• 2D/1D transport method, MPACT

Acknowledgments

This research was supported by the Consortium for Advanced Simulation of Light Water Reactors (www.casl.gov), an Energy Innovation Hub (http://www.energy.gov/hubs) for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy Contract No. DE-AC05-00OR22725.