Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Strong Isotropic Scattering

In the previous works [J. Comput. Phys. 285 (2015), 265-279 and J. Comput. Phys. 302 (2015), 222-238 ], an explicit asymptotic preserving unified gas kinetic scheme (UGKS) has been constructed for the radiative transfer equations with strong absorption/emission coefficients. In the previous UGKS, for the update of the radiation intensity in all regimes, the time step is constrained by the CFL condition, which is related to the ratio of cell size over the speed of light. In order to improve the efficiency of the scheme, an implicit UGKS (IUGKS) will be developed in this paper for numerical simulation of the unsteady radiative transport with the inclusion of scattering and absorption/emission phenomena. In IUGKS, the numerical flux for the radiation intensity is constructed implicitly, and the CFL constraint can be released. As a result, a large time step can be used in the simulation of the radiative transfer. The purpose for constructing such an implicit radiative transfer method is to couple it with the gas dynamic equations in the future for the development of numerical method for radiative hydrodynamics. Theoretically, it can be proved that the current IUGKS has the asymptotic preserving (AP) property in the strong scattering regime for the capturing of non-equilibrium diffusive limiting solutions. As a result, the IUGKS can capture accurate solutions in both the photon free transport and the diffusive limit. Actually, a smooth transition of the solution from optical thin to optical thick regions can be automatically obtained through a time-dependent evolution solution for the radiative transport across a cell interface. A few numerical examples will be presented to validate the current implicit scheme.