We propose and study a family of formally second-order accurate schemes to approximate weak solutions of hyperbolic systems of conservation laws. Theses schemes are based on a dissipative property satisfied by the second-order discretization in space. They are proven to satisfy a global entropy inequality for a generic strictly convex entropy. These schemes do not involve limitation techniques. Numerical results are provided to illustrate their accuracy and stability.
DOI: 10.5802/smai-jcm.94
Keywords: Systems of conservation laws, Second-order finite Volume schemes, Explicit schemes, Global entropy inequality.
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@article{SMAI-JCM_2023__9__31_0,
author = {Mehdi Badsi and Christophe Berthon and Ludovic Martaud},
title = {A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws},
journal = {The SMAI Journal of computational mathematics},
pages = {31--60},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {9},
year = {2023},
doi = {10.5802/smai-jcm.94},
zbl = {1507.65221},
mrnumber = {4573691},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.94/}
}
TY - JOUR AU - Mehdi Badsi AU - Christophe Berthon AU - Ludovic Martaud TI - A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws JO - The SMAI Journal of computational mathematics PY - 2023 SP - 31 EP - 60 VL - 9 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.94/ DO - 10.5802/smai-jcm.94 LA - en ID - SMAI-JCM_2023__9__31_0 ER -
%0 Journal Article %A Mehdi Badsi %A Christophe Berthon %A Ludovic Martaud %T A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws %J The SMAI Journal of computational mathematics %D 2023 %P 31-60 %V 9 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.94/ %R 10.5802/smai-jcm.94 %G en %F SMAI-JCM_2023__9__31_0
Mehdi Badsi; Christophe Berthon; Ludovic Martaud. A family of second-order dissipative finite volume schemes for hyperbolic systems of conservation laws. The SMAI Journal of computational mathematics, Volume 9 (2023), pp. 31-60. doi : 10.5802/smai-jcm.94. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.94/
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