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Commun. Comput. Phys., 31 (2022), pp. 398-448.
Published online: 2022-01
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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.
}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0084}, url = {http://global-sci.org/intro/article_detail/cicp/20211.html} }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.