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Finite volume method in curvilinear coordinates for hyperbolic conservation laws

Herve Guillard Audrey Bonnement 1 Martin Marie 2 T. Fajraoui Alexandre Mouton 3, 4 Boniface Nkonga 1 Afeintou Sangam 2
1 PUMAS - Plasma, tUrbulence, Modeling, Approximation and Simulation
CRISAM - Inria Sophia Antipolis - Méditerranée
3 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : This paper deals with the design of finite volume approximation of hyperbolic conservation laws in curvilinear coordinates. Such coordinates are encountered naturally in many problems as for instance in the analysis of a large number of models coming from magnetic confinement fusion in tokamaks. In this paper we derive a new finite volume method for hyperbolic conservation laws in curvilinear coordinates. The method is first described in a general setting and then is illustrated in 2D polar coordinates. Numerical experiments show its advantages with respect to the use of Cartesian coordinates.
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https://hal.inria.fr/hal-00914822
Contributor : Herve Guillard <>
Submitted on : Friday, December 6, 2013 - 10:46:54 AM
Last modification on : Friday, June 19, 2020 - 9:22:04 AM

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  • HAL Id : hal-00914822, version 1

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Herve Guillard, Audrey Bonnement, Martin Marie, T. Fajraoui, Alexandre Mouton, et al.. Finite volume method in curvilinear coordinates for hyperbolic conservation laws. ESAIM: Proceedings, EDP Sciences, 2011, 32, pp.163-176. ⟨hal-00914822⟩

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