Volume 48, Number 3, May-June 2014
|Page(s)||895 - 918|
|Published online||24 April 2014|
Interface model coupling via prescribed local flux balance
UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions,
2 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
3 CNRS & Centre de Mathématiques Appliquées, U.M.R. 7641 Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France
Received: 15 February 2012
Revised: 6 July 2013
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.
Mathematics Subject Classification: 35L50 / 35L60 / 35L65 / 35L67 / 35L81 / 76M12
Key words: Gas dynamics equations / interfacial coupling / measure valued load / relaxation method / coupled Riemann problem
© EDP Sciences, SMAI, 2014
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