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A frame invariant and maximum principle enforcing second‐order extension for cell‐centered ALE schemes based on local convex hull preservation
Author(s) -
Hoch P.,
Labourasse E.
Publication year - 2014
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3969
Subject(s) - convex hull , mathematics , invariant (physics) , galilean , galilean invariance , regular polygon , a priori and a posteriori , limiter , hull , discretization , mathematical optimization , computer science , mathematical analysis , geometry , engineering , classical mechanics , physics , telecommunications , philosophy , epistemology , marine engineering , mathematical physics
SUMMARY Two difficulties are clearly identified for high‐order extensions of ALE schemes for Euler equations: strict respect of the maximum principle and preservation of the Galilean invariance. We deal with these two issues in this paper. Our approach is closely related to the concepts of a posteriori limiting and convex hull spanning. We introduce the notion of local convex hull preservation schemes, which embodies these two concepts. We lean on this notion to propose a fully Galilean invariant ALE scheme. Moreover, we provide a new limiter (called Apitali for A Posteriori ITerAtive LImiter) for the remap step, enforcing the local convex hull preservation property. Copyright © 2014 John Wiley & Sons, Ltd.