Geodesic
A second order anti-diffusive Lagrange-remap scheme for two-component flows
Marie Billaud Friess1 ; Benjamin Boutin2 ; Filipa Caetano3 ; Gloria Faccanoni4 ; Samuel Kokh5 ; Frédéric Lagoutière3, 6 ; Laurent Navoret7
1Université de Bordeaux, CEA, CNRS, CELIA, 351 Cours de la Libération, 33405 Talence, France
2IRMAR - Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France
3Université Paris-Sud 11, Département de Mathématiques, CNRS UMR 8628, Bâtiment 425, 91405 Orsay, France
4IMATH, Université du Sud Toulon-Var, Bâtiment U, 83957 La Garde, France
5DEN/DANS/DM2S/SFME/LETR, CEA Saclay, 91191 Gif-sur-Yvette, France
6Équipe-Projet SIMPAF, Centre de Recherche INRIA Futurs, Parc Scientifique de la Haute Borne, 40 Avenue Halley B.P. 70478, F-59658 Villeneuve d’Ascq, France
7Laboratoire MAP (UMR CNRS 8145), Université Paris Descartes, 45 rue des Saints Pères, 75270 Paris, France
ESAIM. Proceedings, Tome 32 (2011), pp. 149-162
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We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that preserves sharp interfaces. Numerical results reported at the end of the paper are very encouraging, showing the interest of the second order accuracy for genuinely non-linear waves.
DOI : 10.1051/proc/2011018

Marie Billaud Friess  1   ; Benjamin Boutin  2   ; Filipa Caetano  3   ; Gloria Faccanoni  4   ; Samuel Kokh  5   ; Frédéric Lagoutière  3 , 6   ; Laurent Navoret  7

1 Université de Bordeaux, CEA, CNRS, CELIA, 351 Cours de la Libération, 33405 Talence, France
2 IRMAR - Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France
3 Université Paris-Sud 11, Département de Mathématiques, CNRS UMR 8628, Bâtiment 425, 91405 Orsay, France
4 IMATH, Université du Sud Toulon-Var, Bâtiment U, 83957 La Garde, France
5 DEN/DANS/DM2S/SFME/LETR, CEA Saclay, 91191 Gif-sur-Yvette, France
6 Équipe-Projet SIMPAF, Centre de Recherche INRIA Futurs, Parc Scientifique de la Haute Borne, 40 Avenue Halley B.P. 70478, F-59658 Villeneuve d’Ascq, France
7 Laboratoire MAP (UMR CNRS 8145), Université Paris Descartes, 45 rue des Saints Pères, 75270 Paris, France 
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     author = {Marie Billaud Friess and Benjamin Boutin and Filipa Caetano and Gloria Faccanoni and Samuel Kokh and Fr\'ed\'eric Lagouti\`ere and Laurent Navoret},
     title = {A second order anti-diffusive {Lagrange-remap} scheme for two-component flows},
     journal = {ESAIM. Proceedings},
     pages = {149--162},
     year = {2011},
     volume = {32},
     doi = {10.1051/proc/2011018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2011018/}
}
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%A Benjamin Boutin
%A Filipa Caetano
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%A Frédéric Lagoutière
%A Laurent Navoret
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%J ESAIM. Proceedings
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Marie Billaud Friess; Benjamin Boutin; Filipa Caetano; Gloria Faccanoni; Samuel Kokh; Frédéric Lagoutière; Laurent Navoret. A second order anti-diffusive Lagrange-remap scheme for two-component flows. ESAIM. Proceedings, Tome 32 (2011), pp. 149-162. doi: 10.1051/proc/2011018

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