Time Implicit Unified Gas Kinetic Scheme for 3D Multi-Group Neutron Transport Simulation (Communications in Computational Physics, 2020)
In this paper, a time implicit unified gas kinetic scheme (IUGKS) for 3Dmulti-group neutron transport equation with delayed neutron is developed. Theexplicit scheme, implicit 1st-order backward Euler scheme, and 2nd-order Crank-Nicholson scheme, become the subsets of the current IUGKS. In neutron transport,the microscopic angular flux and the macroscopic scalar flux are fully coupled in animplicit way with the combination of dual-time step technique for the convergence acceleration of unsteady evolution. In IUGKS, the computational time step is no longerlimited by the Courant-Friedrichs-Lewy (CFL) condition, which improves the computational efficiency in both steady and unsteady simulations with a large time step.Mathematically, the current scheme has the asymptotic preserving (AP) property inrecovering automatically the diffusion solution in the continuum regime. Since theexplicit scanning along neutron traveling direction within the computational domainis not needed in IUGKS, the scheme can be easily extended to multi-dimensional andparallel computations. The numerical tests demonstrate that the IUGKS has high computational efficiency, high accuracy, and strong robustness when compared with otherschemes, such as the explicit UGKS, the commonly used finite difference, and finitevolume methods. This study shows that the IUGKS can be used faithfully to studyneutron transport in practical engineering applications.
Keywords: UGKS; neutron transport; time implicit scheme.