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High‐order methods and mesh adaptation for Euler equations
Author(s) -
Alauzet F.
Publication year - 2008
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.1739
Subject(s) - classification of discontinuities , convergence (economics) , mathematics , euler's formula , norm (philosophy) , computer science , euler equations , adaptive mesh refinement , adaptation (eye) , mathematical optimization , mathematical analysis , computational science , physics , optics , political science , law , economics , economic growth
In this paper, we point out a novel contribution of mesh adaptation to high‐order methods for stationary and time‐dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint‐free method, achieves a global second‐order mesh convergence for numerical solutions with discontinuities in L p norm. To attain this result, it is mandatory to combine together all mesh adaptive methods developed in the previous work. This theoretical result is validated on 2D and 3D examples for stationary and time‐dependent simulations. Copyright © 2008 John Wiley & Sons, Ltd.