Interface model coupling via prescribed local flux balance
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, p. 895-918
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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.

DOI : https://doi.org/10.1051/m2an/2013125
Classification:  35L50,  35L60,  35L65,  35L67,  35L81,  76M12
Keywords: gas dynamics equations, interfacial coupling, measure valued load, relaxation method, coupled Riemann problem
@article{M2AN_2014__48_3_895_0,
     author = {Ambroso, Annalisa and Chalons, Christophe and Coquel, Fr\'ed\'eric and Gali\'e, Thomas},
     title = {Interface model coupling via prescribed local flux balance},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     pages = {895-918},
     doi = {10.1051/m2an/2013125},
     zbl = {1292.35166},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_3_895_0}
}
Ambroso, Annalisa; Chalons, Christophe; Coquel, Frédéric; Galié, Thomas. Interface model coupling via prescribed local flux balance. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, pp. 895-918. doi : 10.1051/m2an/2013125. http://www.numdam.org/item/M2AN_2014__48_3_895_0/

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