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Article Dans Une Revue Communications in Applied Mathematics and Computational Science Année : 2016

An Asymptotic-Preserving Scheme for Systems of Conservation Laws with Source Terms on 2D Unstructured Meshes

Résumé

In this paper, finite volumes numerical schemes are developed for hyperbolic systems of conservation laws with source terms. The systems under consideration degenerate into parabolic systems in large times when the source terms become stiff. In this framework, it is crucial that the numerical schemes are asymptotic-preserving ı.e. that they degenerate accordingly. Here, an asymptotic-preserving numerical scheme is proposed for any system within the aforementioned class on 2D unstructured meshes. This scheme is proved to be consistent and stable under a suitable CFL condition. Moreover, we show that it is also possible to prove that it preserves the set of (physically) admissible states under a geometrical property on the mesh. Finally, numerical examples are given to illustrate its behavior.
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Dates et versions

hal-01255899 , version 1 (14-01-2016)

Identifiants

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C Berthon, G Moebs, C Sarazin-Desbois, Rodolphe Turpault. An Asymptotic-Preserving Scheme for Systems of Conservation Laws with Source Terms on 2D Unstructured Meshes. Communications in Applied Mathematics and Computational Science, 2016, ⟨10.1007/978-3-319-05684-5_9⟩. ⟨hal-01255899⟩
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