@Article{CiCP-23-198,
author = {Xia Cui, Zhi-Jun Shen and Guang-Wei Yuan},
title = {Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries},
journal = {Communications in Computational Physics},
year = {2018},
volume = {23},
number = {1},
pages = {198--229},
abstract = {<p style="text-align: justify;">We study the asymptotic-preserving fully discrete schemes for non-equilibrium
radiation diffusion problem in spherical and cylindrical symmetric geometry.
The research is based on two-temperature models with Larsen&#39;s flux-limited
diffusion operators. Finite volume spatially discrete schemes are developed to circumvent
the singularity at the origin and the polar axis and assure local conservation.
Asymmetric second order accurate spatial approximation is utilized instead of
the traditional first order one for boundary flux-limiters to consummate the schemes
with higher order global consistency errors. The harmonic average approach in spherical
geometry is analyzed, and its second order accuracy is demonstrated. By formal
analysis, we prove these schemes and their corresponding fully discrete schemes with
implicitly balanced and linearly implicit time evolutions have first order asymptotic-preserving
properties. By designing associated manufactured solutions and reference
solutions, we verify the desired performance of the fully discrete schemes with numerical
tests, which illustrates quantitatively they are first order asymptotic-preserving
and basically second order accurate, hence competent for simulations of both equilibrium
and non-equilibrium radiation diffusion problems.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2016-0153},
url = {http://global-sci.org/intro/article_detail/cicp/10525.html}
}