A parallel unified gas kinetic scheme for three-dimensional multi-group neutron transport

Abstract

In this paper, a parallel unified gas kinetic scheme (UGKS) is developed to simulate 3D multi-group neutron transport. The physical processes of neutron absorption, scattering, fission are included in the scheme. In order to design a multiscale method for capturing the physics in different regimes, the scheme is composed of solving coupled equations of microscopic neutron transport and macroscopic moment equation. As a result, a time accurate numerical fluxes for the neutron transport can be uniquely formulated and used in the construction of the multiscale method. The isotropic scattering neutron transport is studied in this paper, and it can be proved mathematically that this extended UGKS for multi-group neutron transport equation is an asymptotic preserving scheme. The scheme can be used effectively to capture the diffusion limit even with the mesh size being much larger than the neutron's transport characteristic scale, i.e., the so-called mean free path. Thus, the computation efficiency is greatly improved in comparison with the conventional single-scale scheme. In order to further speed up the computation, a parallelized UGKS has been developed for 3D neutron transport simulation as well. The newly developed scheme is verified through many numerical tests and shows high accuracy and strong robustness in the simulations under a large variation of transport condition.