Construction, analysis and implementation of two nodal finite volume schemes for the $P_N$ model for particle transport in 2D

Christophe Buet (1) , Stéphane Delpino (1) , Victor Fournet (2)

1 LIHPC - Laboratoire en Informatique Haute Performance pour le Calcul et la simulation
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

In this paper, we present two new nodal finite volume schemes for the PN 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.

Domaines: Analyse numérique [math.NA]

Christophe Buet, Stéphane Delpino, Victor Fournet. Construction, analysis and implementation of two nodal finite volume schemes for the $P_N$ model for particle transport in 2D. 2024. ⟨cea-04519862v2⟩