The Implicit Unified Gas Kinetic Scheme for Neutron Transport with Arbitrary Anisotropic Scattering Model

Abstract

In previous work, we developed the unified gas dynamics scheme (UGKS) and its corresponding time-implicit variant (IUGKS) for neutron transport. The multi-scale characteristics of these schemes are particularly well-suited for transport equations, which show good performances in large-scale conditions. However, only the isotropic scattering model equation was considered in these studies, which does not meet the application requirements in complex engineering cases. In this paper, we extend our studies of isotropic neutron IUGKS to encompass the transport equation with arbitrary anisotropic scattering. We first clarify the construction principle of IUGKS-PN scheme according to the general form of anisotropic scattering models. However, the construction of the scheme is complex and the versatility is not strong. To address these challenges, a more concise scheme IUGKS-AM is proposed based on the isotropic IUGKS framework, in which the higher-order moments of the neutron distribution function are estimated. We theoretically analyze the asymptotic property of IUGKS-AM, and verify the numerical performances in anisotropic model by numerical experiments. Finally, several complex anisotropic scattering models are computed by using the numerical scheme, demonstrating its general applicability. This study significantly enhances the practical utility of multi-scale neutron transport UGKS in engineering applications.