An Asymptotic Preserving Implicit Unified Gas Kinetic Scheme for Frequency-dependent Radiative Transfer Equations

In this paper, an asymptotic preserving implicit unified gas kinetic scheme (IUGKS) is constructed for the frequency-dependent radiative transfer equations. Different from the asymptotic preserving unified gas kinetic scheme (UGKS) which uses the explicit initial value of the radiation intensity in the construction of the boundary fluxes as in the previous works [Sun et al., J. Comput. Phys. 285 (2015), pp. 265-279 and J. Comput. Phys. 302 (2015), pp. 222-238], here we construct the boundary fluxes by a back-time discretization so that they depend implicitly on the radiation intensity. Thus, the time step constraint by the Courant-Friedrichs-Lewy (CFL) condition is not needed anymore for IUGKS. It is shown that IUGKS is asymptotic preserving uniformly with the small Knudsen parameter. A number of numerical tests have been carried out and the numerical results show that large time steps can be used for the current scheme, and the computational efficiency can be improved greatly in comparison with UGKS and the implicit Monte Carlo scheme.