Discrete Duality Finite Volume Discretization of the Thermal-$P_N$ Radiative Transfer Equations on General Meshes (Communications in Computational Physics, 2022)
The discrete duality finite volume method has proven to be a practical toolfor discretizing partial differential equations coming from a wide variety of areas ofphysics on nearly arbitrary meshes. The main ingredients of the method are: (1) useof 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 methodto 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 areproved while the experimental second-order accuracy is observed with manufacturedsolutions. Several numerical experiments are reported which show the good behaviorof the method.