BLACHÈRE, Florian; CHALONS, Christophe; TURPAULT, Rodolphe

doi:10.1016/j.camwa.2021.02.003

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BLACHÈRE, Florian
Automatic mesh generation and advanced methods [Gamma3]

CHALONS, Christophe
Laboratoire de Mathématiques de Versailles [LMV]

TURPAULT, Rodolphe
Institut de Mathématiques de Bordeaux [IMB]
Institut Polytechnique de Bordeaux [Bordeaux INP]

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Computers & Mathematics with Applications. 2021-04, vol. 87, p. 41-49

Elsevier

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In this paper, we consider the numerical approximation of hyperbolic systems of conservation laws with sti source terms and parabolic degeneracy in the asymptotic limit. We are more precisely interested in the design of high-order asymptotic-preserving schemes on unstructured meshes. Our approach is based on a very simple modication of the numerical ux associated with the usual HLL scheme and boils down to a sharp control of the underlying numerical diusion. The strategy allows to capture the correct asymptotic parabolic behavior and to preserve the high-order accuracy also in the asymptotic limit. Numerical experiments are proposed to illustrate these properties.< Réduire

Mots clés en anglais

asymptotic-preserving schemes

diffusion limit

nonlinear hyperbolic systems

high order finite volumes schemes

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Very high-order asymptotic-preserving schemes for hyperbolic systems of conservation laws with parabolic degeneracy on unstructured meshes

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