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Interface model coupling via prescribed local flux balance

Published online by Cambridge University Press:  24 April 2014

Annalisa Ambroso ,
Christophe Chalons ,
Frédéric Coquel  and
Thomas Galié
Annalisa Ambroso
Affiliation:
UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
Christophe Chalons
Affiliation:
Laboratoire de Mathématiques de Versailles, UMR 8100, Université de Versailles Saint-Quentin-en-Yvelines UFR des Sciences, bâtiment Fermat, 45 avenue des Etats-Unis, 78035 Versailles Cedex, France. [email protected]
Frédéric Coquel
Affiliation:
CNRS & Centre de Mathématiques Appliquées, U.M.R. 7641 Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France; [email protected]
Thomas Galié
Affiliation:
UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
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Abstract

This paper deals with the non-conservative coupling of two one-dimensional barotropic Euler systems at an interface at x = 0. The closure pressure laws differ in the domains x < 0 and x > 0, and a Dirac source term concentrated at x = 0 models singular pressure losses. We propose two numerical methods. The first one relies on ghost state reconstructions at the interface while the second is based on a suitable relaxation framework. Both methods satisfy a well-balanced property for stationary solutions. In addition, the second method preserves mass conservation and exactly restores the prescribed singular pressure drops for both unsteady and steady solutions.

Keywords

Gas dynamics equationsinterfacial couplingmeasure valued loadrelaxation methodcoupled Riemann problem
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 3 , May 2014 , pp. 895 - 918
Copyright
© EDP Sciences, SMAI, 2014

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