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Conservativity and weak consistency of a class of staggered finite volume methods for the Euler equations


Authors: R. Herbin, J.-C. Latché, S. Minjeaud and N. Therme
Journal: Math. Comp. 90 (2021), 1155-1177
MSC (2010): Primary 65M08
DOI: https://doi.org/10.1090/mcom/3575
Published electronically: December 29, 2020
MathSciNet review: 4232220
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Abstract: We address here a class of staggered schemes for the compressible Euler equations; this scheme was introduced in recent papers and possesses the following features: upwinding is performed with respect to the material velocity only and the internal energy balance is solved, with a correction term designed on consistency arguments. These schemes have been shown in previous works to preserve the convex of admissible states and have been extensively tested numerically. The aim of the present paper is twofold: we derive a local total energy equation satisfied by the solutions, so that the schemes are in fact conservative, and we prove that they are consistent in the Lax-Wendroff sense.


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Additional Information

R. Herbin
Affiliation: I2M, CNRS and Université d’Aix-Marseille
MR Author ID: 244425
ORCID: 0000-0003-0937-1900
Email: raphaele.herbin@univ-amu.fr

J.-C. Latché
Affiliation: Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES/SA2I, Cadarache, St-Paul-lez-Durance, 13115, France
MR Author ID: 715367
Email: jean-claude.latche@irsn.fr

S. Minjeaud
Affiliation: Laboratoire Jean Dieudonné, Université de Nice-Sophia Antipolis
MR Author ID: 889818
Email: sebastian.minjeaud@unice.fr

N. Therme
Affiliation: CEA/CESTA 33116, Le Barp, France
MR Author ID: 1088061
Email: nicolas.therme@cea.fr

Keywords: Finite volumes, consistency
Received by editor(s): December 8, 2019
Received by editor(s) in revised form: June 6, 2020
Published electronically: December 29, 2020
Article copyright: © Copyright 2020 American Mathematical Society