A second order anti-diffusive Lagrange-remap scheme for two-component flows

Marie Billaud Friess; Benjamin Boutin; Filipa Caetano; Gloria Faccanoni; Samuel Kokh; Frédéric Lagoutière; Laurent Navoret

doi:10.1051/proc/2011018

Geodesic

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A second order anti-diffusive Lagrange-remap scheme for two-component flows

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

ESAIM. Proceedings, Tome 32 (2011), pp. 149-162.

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Résumé

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

Affiliations des auteurs :

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

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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},
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     doi = {10.1051/proc/2011018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2011018/}
}

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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. http://geodesic.mathdoc.fr/articles/10.1051/proc/2011018/

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