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A simple construction of very high order non oscillatory compact schemes on unstructured meshes.

Remi Abgrall 1, 2 Adam Larat 2, 1 Mario Ricchiuto 2, 1 C. Tavé 2, 1 
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 \cite{abgrall-roe} have been constructed very high order residual distribution schemes for scalar problems. They were using triangle unstructured meshes. However, the construction was quite involved and was not very flexible. Here, following \cite{abgrall}, we develop a systematic way of constructing very high order non oscillatory schemes for such meshes. Applications to scalar and systems problems are given.
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Remi Abgrall, Adam Larat, Mario Ricchiuto, C. Tavé. A simple construction of very high order non oscillatory compact schemes on unstructured meshes.. Computers and Fluids, Elsevier, 2009, 38 (7), pp.1314-1323. ⟨10.1016/j.compfluid.2008.01.031⟩. ⟨inria-00333756⟩

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