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Kinetic schemes on staggered grids for barotropic Euler models: entropy-stability analysis


Authors: Florent Berthelin, Thierry Goudon and Sebastian Minjeaud
Journal: Math. Comp. 84 (2015), 2221-2262
MSC (2010): Primary 65M08; Secondary 35L05
DOI: https://doi.org/10.1090/S0025-5718-2015-02957-3
Published electronically: March 18, 2015
MathSciNet review: 3356025
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Abstract: We introduce, in the one-dimensional framework, a new scheme of finite volume type for barotropic Euler equations. The numerical unknowns, namely densities and velocities, are defined on staggered grids. The numerical fluxes are defined by using the framework of kinetic schemes. We can consider general (convex) pressure laws. We justify that the density remains non-negative and the total physical entropy does not increase, under suitable stability conditions. Performances of the scheme are illustrated through a set of numerical experiments.


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Additional Information

Florent Berthelin
Affiliation: Inria, Sophia Antipolis Méditerranée Research Centre, Project COFFEE & Univ. Nice Sophia Antipolis, CNRS, Labo J. A. Dieudonné, UMR 7351 Parc Valrose, F-06108 Nice, France
Email: Florent.Berthelin@unice.fr

Thierry Goudon
Affiliation: Inria, Sophia Antipolis Méditerranée Research Centre, Project COFFEE & Univ. Nice Sophia Antipolis, CNRS, Labo J. A. Dieudonné, UMR 7351 Parc Valrose, F-06108 Nice, France
Email: thierry.goudon@inria.fr

Sebastian Minjeaud
Affiliation: Inria, Sophia Antipolis Méditerranée Research Centre, Project CASTOR & Univ. Nice Sophia Antipolis, CNRS, Labo J. A. Dieudonné, UMR 7351 Parc Valrose, F-06108 Nice, France
Email: minjeaud@unice.fr

DOI: https://doi.org/10.1090/S0025-5718-2015-02957-3
Received by editor(s): September 3, 2013
Received by editor(s) in revised form: February 5, 2014
Published electronically: March 18, 2015
Article copyright: © Copyright 2015 American Mathematical Society