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Article Dans Une Revue Numerische Mathematik Année : 2012

Design of asymptotic preserving schemes for the hyperbolic heat equation on unstructured meshes

Résumé

The transport equation, in highly scattering regimes, has a limit in which the dominant behavior is given by the solution of a diffusion equation. The simplified models like SN, PN or the nonlinear models MN have the same property. For such systems it would be interesting to construct finite volume schemes on unstructured meshes which have the same dominant behavior even if the meshes are coarse. Such schemes are called diffusion asymptotic preserving (AP) schemes and are designed presently at most on Cartesian meshes. In this work we give some answers for unstructured meshes, when considering the most simplify model, that is the P1 model also refereed to as the hyperbolic heat equation. We start from the modified upwind AP scheme proposed by Jin and Levermore for this equation in 1-D. We show that extended in 2-D on unstructured meshes, the classical edge formulation of this scheme is no longer asymptotic preserving. To solve this problem, we propose new schemes built on a node formulation of the Jin and Levermore's scheme which use the analogy between P1 model and acoustic equations for which schemes with corner's fluxes have been built in the context of gas dynamics.
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Dates et versions

hal-00523809 , version 1 (06-10-2010)

Identifiants

Citer

Christophe Buet, Bruno Després, Emmanuel Franck. Design of asymptotic preserving schemes for the hyperbolic heat equation on unstructured meshes. Numerische Mathematik, 2012, http://www.springer.com/alert/urltracking.do?id=Lbe18b9M9c40acSaff211f. ⟨10.1007/s00211-012-0457-9⟩. ⟨hal-00523809⟩
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