Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/57481

Titlea posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations
Author(s)Clain, Stéphane
Loubère, Raphaël
Machado, Gaspar J.
KeywordsFinite volume
MOOD
Very high order
Hyperbolic equations
Steady-state
Issue date2018
PublisherSpringer
JournalAdvances in Computational Mathematics
Abstract(s)We propose a new family of high order accurate finite volume schemes devoted to solve one-dimensional steady-state hyperbolic systems. High-accuracy (up to the sixth-order presently) is achieved thanks to polynomial reconstructions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. Such a procedure demands the determination of a detector chain to discriminate between troubled and valid cells, a cascade of polynomial degrees to be successively tested when oscillations are detected, and a parachute scheme cor- responding to the last, viscous, and robust scheme of the cascade. Experimented on linear, Burgers’, and Euler equations, we demonstrate that the schemes manage to retrieve smooth solutions with optimal order of accuracy but also irregular solutions without spurious oscillations.
TypeArticle
URIhttp://hdl.handle.net/1822/57481
DOI10.1007/s10444-017-9556-6
ISSN1019-7168
e-ISSN1572-9044
Peer-Reviewedyes
AccessEmbargoed access (6 Months)
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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