Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes

Remi Abgrall 1, 2, * Adam Larat 1, 2 Mario Ricchiuto 1, 2
* Auteur correspondant
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 : In this paper we consider the very high order approximation of solutions of the Euler equations. We present a systematic generalization of the Residual Distribution method of \cite{ENORD} to very high order of accuracy, by extending the preliminary work discussed in \cite{abgrallLarat} to systems and hybrid meshes. We present extensive numerical validation for the third and fourth order cases with Lagrange finite elements. In particular, we demonstrate that we an both have a non oscillatory behavior, even for very strong shocks and complex flow patterns, and the expected accuracy on smooth problems.
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Remi Abgrall, Adam Larat, Mario Ricchiuto. Construction of very high order residual distribution schemes for steady inviscid flow problems on hybrid unstructured meshes. [Research Report] RR-7236, INRIA. 2010, pp.60. 〈inria-00464799〉

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