@Article{CiCP-31-2,
author = {Hermeline, Francois},
title = {Discrete Duality Finite Volume Discretization of the Thermal-$P_N$ Radiative Transfer Equations on General Meshes},
journal = {Communications in Computational Physics},
year = {2022},
volume = {31},
number = {2},
pages = {398--448},
abstract = {<p style="text-align: justify;">The discrete duality finite volume method has proven to be a practical tool
for discretizing partial differential equations coming from a wide variety of areas of
physics on nearly arbitrary meshes. The main ingredients of the method are: (1) use
of three meshes, (2) use of the Gauss-Green theorem for the approximation of derivatives, (3) discrete integration by parts. In this article we propose to extend this method
to the coupled grey thermal-$P_N$ radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation. The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are
proved while the experimental second-order accuracy is observed with manufactured
solutions. Several numerical experiments are reported which show the good behavior
of the method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0084},
url = {https://global-sci.com/article/79517/discrete-duality-finite-volume-discretization-of-the-thermal-p-n-radiative-transfer-equations-on-general-meshes}
}