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Interface model coupling via prescribed local flux balance
Annalisa Ambroso, Christophe Chalons, Frédéric Coquel, Thomas Galié
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 48 / Issue 3 / May 2014

Published online by Cambridge University Press:

24 April 2014, pp. 895-918

Print publication:

May 2014
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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.