a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations
| hal.structure.identifier | Centro de Matemática [Minho] [CMAT] | |
| dc.contributor.author | CLAIN, Stéphane | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Centre National de la Recherche Scientifique [CNRS] | |
| dc.contributor.author | LOUBÈRE, Raphaël | |
| hal.structure.identifier | Centro de Matemática [Minho] [CMAT] | |
| dc.contributor.author | MACHADO, Gaspar | |
| dc.date.accessioned | 2024-04-04T03:12:04Z | |
| dc.date.available | 2024-04-04T03:12:04Z | |
| dc.date.created | 2016-12-17 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193831 | |
| dc.description.abstractEn | We propose a new family of finite volume high-accurate numerical 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 control the cell polynomial degree for eliminating non-physical oscillations in the vicinity of discontinuities. Such a procedure demands the determination of a chain detector to discriminate between troubled and valid cells, a cascade of polynomial degrees to be successively tested when oscillations are detected, and a parachute scheme corresponding 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. | |
| dc.language.iso | en | |
| dc.subject.en | steady-state | |
| dc.subject.en | hyperbolic equations | |
| dc.subject.en | finite volume | |
| dc.subject.en | high-order | |
| dc.subject.en | MOOD | |
| dc.title.en | a posteriori stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Analyse numérique [math.NA] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01418899 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01418899v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=CLAIN,%20St%C3%A9phane&LOUB%C3%88RE,%20Rapha%C3%ABl&MACHADO,%20Gaspar&rft.genre=preprint |
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