Academic Journal
Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation.
| Τίτλος: | Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation. |
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| Συγγραφείς: | Fukuchi, Tsugio |
| Πηγή: | AIP Advances; Dec2020, Vol. 10 Issue 12, p1-28, 28p |
| Θεματικοί όροι: | Finite difference method, Numerical analysis, Interpolation, Equations, Poiseuille flow |
| Περίληψη: | In a previous paper, a calculation system for a high-accuracy, high-speed calculation of a one-dimensional (1D) Poisson equation based on the interpolation finite difference method was shown. Spatial high-order finite difference (FD) schemes, including a usual second-order accurate centered space FD scheme, are instantaneously derived on the equally spaced/unequally spaced grid points based on the definition of the Lagrange polynomial function. The upper limit of the higher order FD scheme is not theoretically limited but is studied up to the tenth order, following the previous paper. In the numerical analyses of the 1D Poisson equation published in the previous paper, the FD scheme setting method, SAPI (m), m = 2, 4, ..., 10, was defined. Due to specifying the value of m, the setting of FD schemes is uniquely defined. This concept is extended to the numerical analysis of two-dimensional Poisson equations. In this paper, we focus on Poiseuille flows passing through arbitrary cross sections as numerical calculation examples. Over regular and irregular domains, three types of FD methods—(i) forward time explicit method, (ii) time marching successive displacement method, and (iii) alternative direction implicit method—are formulated, and their characteristics of convergence and numerical calculation errors are investigated. The numerical calculation system of the 2D Poisson equation formulated in this paper enables high-accuracy and high-speed calculation by the high-order difference in an arbitrary domain. Especially in the alternative direction implicit method using the band diagonal matrix algorithm, convergence is remarkably accelerated, and high-speed calculation becomes possible. [ABSTRACT FROM AUTHOR] |
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| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:edb&genre=article&issn=21583226&ISBN=&volume=10&issue=12&date=20201201&spage=1&pages=1-28&title=AIP Advances&atitle=Higher%20order%20difference%20numerical%20analyses%20of%20a%202D%20Poisson%20equation%20by%20the%20interpolation%20finite%20difference%20method%20and%20calculation%20error%20evaluation.&aulast=Fukuchi%2C%20Tsugio&id=DOI:10.1063/5.0018915 Name: Full Text Finder (for New FTF UI) (ns324271) Category: fullText Text: Full Text Finder MouseOverText: Full Text Finder |
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| Items | – Name: Title Label: Title Group: Ti Data: Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Fukuchi%2C+Tsugio%22">Fukuchi, Tsugio</searchLink> – Name: TitleSource Label: Source Group: Src Data: AIP Advances; Dec2020, Vol. 10 Issue 12, p1-28, 28p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink><br /><searchLink fieldCode="DE" term="%22Poiseuille+flow%22">Poiseuille flow</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In a previous paper, a calculation system for a high-accuracy, high-speed calculation of a one-dimensional (1D) Poisson equation based on the interpolation finite difference method was shown. Spatial high-order finite difference (FD) schemes, including a usual second-order accurate centered space FD scheme, are instantaneously derived on the equally spaced/unequally spaced grid points based on the definition of the Lagrange polynomial function. The upper limit of the higher order FD scheme is not theoretically limited but is studied up to the tenth order, following the previous paper. In the numerical analyses of the 1D Poisson equation published in the previous paper, the FD scheme setting method, SAPI (m), m = 2, 4, ..., 10, was defined. Due to specifying the value of m, the setting of FD schemes is uniquely defined. This concept is extended to the numerical analysis of two-dimensional Poisson equations. In this paper, we focus on Poiseuille flows passing through arbitrary cross sections as numerical calculation examples. Over regular and irregular domains, three types of FD methods—(i) forward time explicit method, (ii) time marching successive displacement method, and (iii) alternative direction implicit method—are formulated, and their characteristics of convergence and numerical calculation errors are investigated. The numerical calculation system of the 2D Poisson equation formulated in this paper enables high-accuracy and high-speed calculation by the high-order difference in an arbitrary domain. Especially in the alternative direction implicit method using the band diagonal matrix algorithm, convergence is remarkably accelerated, and high-speed calculation becomes possible. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of AIP Advances is the property of American Institute of Physics 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.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1063/5.0018915 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 1 Subjects: – SubjectFull: Finite difference method Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Interpolation Type: general – SubjectFull: Equations Type: general – SubjectFull: Poiseuille flow Type: general Titles: – TitleFull: Higher order difference numerical analyses of a 2D Poisson equation by the interpolation finite difference method and calculation error evaluation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Fukuchi, Tsugio IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 21583226 Numbering: – Type: volume Value: 10 – Type: issue Value: 12 Titles: – TitleFull: AIP Advances Type: main |
| ResultId | 1 |