@Article{CiCP-22-4,
author = {},
title = {An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits},
journal = {Communications in Computational Physics},
year = {2017},
volume = {22},
number = {4},
pages = {889--912},
abstract = {<p style="text-align: justify;">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 different
diffusive limits. Different from the previous approach, instead of including absorption/emission
only, the current method takes both scattering and absorption/emission
mechanism into account in the radiative transport process. As a result, two asymptotic
limiting solutions will appear in the diffusive regime. In the strong absorption/emission
case, an equilibrium diffusion limit is obtained, where the system is
mainly driven by a nonlinear diffusion equation for the equilibrium radiation and material
temperature. However, in the strong scattering case, a non-equilibrium limit can
be obtained, where coupled nonlinear diffusion system with different radiation and
material temperature is obtained. In addition to including the scattering term in the
transport 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 use
of a large time step for the radiative transport, it becomes possible to couple the IUGKS
with the gas dynamic equations to develop an efficient numerical method for radiative
hydrodynamics. The IUGKS is a valid method for all radiative transfer regimes. A few
numerical examples will be presented to validate the current implicit method for both
optical thin to optical thick cases.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0261},
url = {https://global-sci.com/article/80165/an-implicit-unified-gas-kinetic-scheme-for-radiative-transfer-with-equilibrium-and-non-equilibrium-diffusive-limits}
}