SP3 Limit of the 2D/1D Transport Equations with Varying Degrees of Angular Coupling

Abstract

Abstract Two-dimensional/one-dimensional (2D/1D) methods have become popular for solving the 3D Boltzmann neutron transport equation on medium-to-large computing platforms. These methods can have a wide range of accuracy that depends largely on the fidelity of the coupling between the 2D and 1D solutions in the spatial and angular variables. In general, methods with higher-order coupling are both more accurate and more computationally expensive. In order to simplify and reduce computation, an isotropic angular coupling term is frequently used. The deficiency of this approximation compared to higher-order angular coupling has been studied experimentally, but there is insufficient theoretical analysis in the literature to supplement the experimental results. In this paper, an asymptotic analysis is applied to the 2D/1D equations with varying orders of angular coupling to facilitate comparison to the simplified PN (SPN) equations. We find that the 2D/1D method with 3 angular coupling moments preserves the 3D SP3 limit, while the 2D/1D method with isotropic coupling does not. As a result, the isotropic coupling method is theoretically less accurate in problems with strong spatial gradients in both the radial and axial dimensions. This analysis provides a theoretical basis for design and optimization of the angular coupling scheme in a 2D/1D method. The results of the theoretical analysis are confirmed by using the Takeda-Ikeda benchmark to compare the accuracy of 2D/1D methods with isotropic and anisotropic coupling implemented in MPACT to SP1 and SP3 finite difference solutions.