TY - JOUR
T1 - Discrete Duality Finite Volume Discretization of the Thermal-$P_N$ Radiative Transfer Equations on General Meshes
AU - Hermeline , Francois
JO - Communications in Computational Physics
VL - 2
SP - 398
EP - 448
PY - 2022
DA - 2022/01
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2021-0084
UR - https://global-sci.org/intro/article_detail/cicp/20211.html
KW - Hybrid multiscale models, radiative transfer equation, grey $P_N$ approximation, discrete duality finite volume method.
AB - <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>