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Finite volume method in curvilinear coordinates for hyperbolic conservation laws

2011; EDP Sciences; Volume: 32; Linguagem: Inglês

10.1051/proc/2011019

1270-900X

Audrey Bonnement, Tarek Fajraoui, H. Guillard, Marie Martin, Alexandre Mouton, Boniface Nkonga, Afeintou Sangam,

Computational Fluid Dynamics and Aerodynamics

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.