Geodesic
Finite volume method in curvilinear coordinates for hyperbolic conservation laws
A. Bonnement1 ; T. Fajraoui2 ; H. Guillard1 ; M. Martin3 ; A. Mouton4 ; B. Nkonga3 ; A. Sangam3
1 INRIA Sophia-Antipolis & Université Nice Sophia-Antipolis, UMR CNRS 6621, France
2 Université Valenciennes, FR CNRS 2956, France
3 Université Nice Sophia-Antipolis, UMR CNRS 6621 & INRIA Sophia-Antipolis, France
4 Université Toulouse 3, UMR CNRS 5219, France
ESAIM. Proceedings, Tome 32 (2011), pp. 163-176.

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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.
DOI : 10.1051/proc/2011019

A. Bonnement 1 ; T. Fajraoui 2 ; H. Guillard 1 ; M. Martin 3 ; A. Mouton 4 ; B. Nkonga 3 ; A. Sangam 3

1 INRIA Sophia-Antipolis & Université Nice Sophia-Antipolis, UMR CNRS 6621, France
2 Université Valenciennes, FR CNRS 2956, France
3 Université Nice Sophia-Antipolis, UMR CNRS 6621 & INRIA Sophia-Antipolis, France
4 Université Toulouse 3, UMR CNRS 5219, France 
@article{EP_2011_32_a12,
     author = {A. Bonnement and T. Fajraoui and H. Guillard and M. Martin and A. Mouton and B. Nkonga and A. Sangam},
     title = {Finite volume method in curvilinear coordinates for hyperbolic conservation laws},
     journal = {ESAIM. Proceedings},
     pages = {163--176},
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     volume = {32},
     year = {2011},
     doi = {10.1051/proc/2011019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2011019/}
}
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A. Bonnement; T. Fajraoui; H. Guillard; M. Martin; A. Mouton; B. Nkonga; A. Sangam. Finite volume method in curvilinear coordinates for hyperbolic conservation laws. ESAIM. Proceedings, Tome 32 (2011), pp. 163-176. doi : 10.1051/proc/2011019. http://geodesic.mathdoc.fr/articles/10.1051/proc/2011019/

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