An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits (Communications in Computational Physics, 2017)
This paper is about the construction of a unified gas-kinetic scheme (UGKS)for a coupled system of radiative transport and material heat conduction with differentdiffusive limits. Different from the previous approach, instead of including absorption/emissiononly, the current method takes both scattering and absorption/emissionmechanism into account in the radiative transport process. As a result, two asymptoticlimiting solutions will appear in the diffusive regime. In the strong absorption/emissioncase, an equilibrium diffusion limit is obtained, where the system ismainly driven by a nonlinear diffusion equation for the equilibrium radiation and materialtemperature. However, in the strong scattering case, a non-equilibrium limit canbe obtained, where coupled nonlinear diffusion system with different radiation andmaterial temperature is obtained. In addition to including the scattering term in thetransport equation, an implicit UGKS (IUGKS) will be developed in this paper as well.In the IUGKS, the numerical flux for the radiation intensity is constructed implicitly.Therefore, the conventional CFL constraint for the time step is released. With the useof a large time step for the radiative transport, it becomes possible to couple the IUGKSwith the gas dynamic equations to develop an efficient numerical method for radiativehydrodynamics. The IUGKS is a valid method for all radiative transfer regimes. A fewnumerical examples will be presented to validate the current implicit method for bothoptical thin to optical thick cases.