A linear dispersive mechanism for numerical error growth: spurious caustics
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| Title: | A linear dispersive mechanism for numerical error growth: spurious caustics |
|---|---|
| Authors: | David, Cl.1 david@lmm.jussieu.fr, Sagaut, P.1, Sengupta, T.2 |
| Source: | European Journal of Mechanics B: Fluids. Jan2009, Vol. 28 Issue 1, p146-151. 6p. |
| Subjects: | Error analysis in mathematics, Dispersion (Chemistry), Caustics (Optics), Numerical analysis, Simulation methods & models |
| Abstract: | Abstract: A linear dispersive mechanism leading to a burst in the norm of the error in numerical simulation of polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity and are physically associated to interactions between rays defined by the characteristic lines of the discrete system. Several popular schemes are analyzed and are shown to admit spurious caustics. It is also observed that caustic-free schemes can be defined, like the Crank–Nicolson scheme. [Copyright &y& Elsevier] |
| Copyright of European Journal of Mechanics B: Fluids is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 35071570 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.euromechflu.2008.04.002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 6 StartPage: 146 Subjects: – SubjectFull: Error analysis in mathematics Type: general – SubjectFull: Dispersion (Chemistry) Type: general – SubjectFull: Caustics (Optics) Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Simulation methods & models Type: general Titles: – TitleFull: A linear dispersive mechanism for numerical error growth: spurious caustics Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: David, Cl. – PersonEntity: Name: NameFull: Sagaut, P. – PersonEntity: Name: NameFull: Sengupta, T. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2009 Type: published Y: 2009 Identifiers: – Type: issn-print Value: 09977546 Numbering: – Type: volume Value: 28 – Type: issue Value: 1 Titles: – TitleFull: European Journal of Mechanics B: Fluids Type: main |
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