Finite volume method in curvilinear coordinates for hyperbolic conservation laws Article - Novembre 2011

Herve Guillard, Audrey Bonnement, Martin Marie, T. Fajraoui, Alexandre Mouton, Boniface Nkonga, Afeintou Sangam

Marie Martin
Herve Guillard, Audrey Bonnement, Martin Marie, T. Fajraoui, Alexandre Mouton, Boniface Nkonga, Afeintou Sangam, « Finite volume method in curvilinear coordinates for hyperbolic conservation laws  », ESAIM : Proceedings, novembre 2011, pp. 163-176. ISSN 1270-900X. 〈http://dx.doi.org/10.1051/proc/2011019〉

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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