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Construction, analysis and implementation of two nodal finite volume schemes for the $P_N$ model for particle transport in 2D
Christophe Buet1; Stéphane Del Pino1; Victor Fournet2
1 CEA, DAM, DIF, F-91297, Arpajon, France and Université Paris-Saclay, CEA, Laboratoire en Informatique Haute Performance pour le Calcul et la simulation, 91297 Arpajon, France
2 Laboratoire Jacques Louis Lions, Sorbonne Université, 4 place Jussieu, 75005 Paris, France, CEA, DAM, DIF, F-91297, Arpajon, France
The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 39-84.

In this paper, we present two new nodal finite volume schemes for the $P_N$ model on arbitrary polygonal meshes in 2D. We show that these schemes are well-defined, conservative and stable, finally we prove their convergence. We also present some numerical results.

Published online:
DOI: 10.5802/smai-jcm.119
Classification: 65M08, 65M12
Keywords: nodal solver, $P_N$ approximation, transport equation, hyperbolic

Christophe Buet 1; Stéphane Del Pino 1; Victor Fournet 2

1 CEA, DAM, DIF, F-91297, Arpajon, France and Université Paris-Saclay, CEA, Laboratoire en Informatique Haute Performance pour le Calcul et la simulation, 91297 Arpajon, France
2 Laboratoire Jacques Louis Lions, Sorbonne Université, 4 place Jussieu, 75005 Paris, France, CEA, DAM, DIF, F-91297, Arpajon, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     author = {Christophe Buet and St\'ephane Del Pino and Victor Fournet},
     title = {Construction, analysis and implementation of two nodal finite volume schemes for the $P_N$ model for particle transport {in~2D}},
     journal = {The SMAI Journal of computational mathematics},
     pages = {39--84},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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     year = {2025},
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Christophe Buet; Stéphane Del Pino; Victor Fournet. Construction, analysis and implementation of two nodal finite volume schemes for the $P_N$ model for particle transport in 2D. The SMAI Journal of computational mathematics, Volume 11 (2025), pp. 39-84. doi : 10.5802/smai-jcm.119. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.119/

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