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Numerical approximation of parabolic problems by means of residual distribution schemes

Remi Abgrall 1, 2 Guillaume Baurin 1 Arnaud Krust 1 Dante de Santis 1, 2 Mario Ricchiuto 1, 2 
1 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : We are interested in the numerical approximation of steady scalar convection diffusion problems by mean of high order schemes called Residual Distribution (RD). In the inviscid case, one can develop non linear RD that are non oscillatory, even in the case of very strong shocks, while having the most possible compact stencil, on hybrid unstructured meshes. This paper proposes and compare several extension of these schemes for the convection diffusion problem. This methodology, in particular in term of accuracy, is evaluated on several problems, some of which having exact solutions.
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Submitted on : Wednesday, December 14, 2011 - 12:34:07 PM
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Remi Abgrall, Guillaume Baurin, Arnaud Krust, Dante de Santis, Mario Ricchiuto. Numerical approximation of parabolic problems by means of residual distribution schemes. [Research Report] RR-7824, INRIA. 2011, pp.21. ⟨hal-00647999v2⟩

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