A new mathematical model for traveling sand dunes: analysis and approximation.
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| Title: | A new mathematical model for traveling sand dunes: analysis and approximation. |
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| Authors: | Falcone, M.1 (AUTHOR) falcone@mat.uniroma1.it, Finzi Vita, S.1 (AUTHOR) finzi@mat.uniroma1.it |
| Source: | Applied Numerical Mathematics. Sep2020, Vol. 155, p208-225. 18p. |
| Subjects: | Mathematical models, Finite differences, Sand dunes, Erosion |
| Abstract: | We present a new two-layer closed form model for the dynamics of desert dunes under the effect of a horizontal wind blowing in an arbitrary direction. This model is an extension of a very simplified model previously introduced by Hadeler and Kuttler [12]. Our extension, inspired by the sandpile dynamics approach, includes the effects of gravity on both sides (upwind and downwind) of the dune, and allows to describe erosion and deposition in a more accurate way. After a discussion of the model and its properties we present a numerical scheme based on finite differences in 1D and we prove its consistency and stability. Some numerical tests show a good qualitative behavior and a realistic shape for the evolving dunes. Finally, we discuss the preliminary steps of a possible extension of this model to the 2D case. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Numerical Mathematics 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: 142792639 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A new mathematical model for traveling sand dunes: analysis and approximation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Falcone%2C+M%2E%22">Falcone, M.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> falcone@mat.uniroma1.it</i><br /><searchLink fieldCode="AR" term="%22Finzi+Vita%2C+S%2E%22">Finzi Vita, S.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> finzi@mat.uniroma1.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Sep2020, Vol. 155, p208-225. 18p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+differences%22">Finite differences</searchLink><br /><searchLink fieldCode="DE" term="%22Sand+dunes%22">Sand dunes</searchLink><br /><searchLink fieldCode="DE" term="%22Erosion%22">Erosion</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We present a new two-layer closed form model for the dynamics of desert dunes under the effect of a horizontal wind blowing in an arbitrary direction. This model is an extension of a very simplified model previously introduced by Hadeler and Kuttler [12]. Our extension, inspired by the sandpile dynamics approach, includes the effects of gravity on both sides (upwind and downwind) of the dune, and allows to describe erosion and deposition in a more accurate way. After a discussion of the model and its properties we present a numerical scheme based on finite differences in 1D and we prove its consistency and stability. Some numerical tests show a good qualitative behavior and a realistic shape for the evolving dunes. Finally, we discuss the preliminary steps of a possible extension of this model to the 2D case. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Numerical Mathematics 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.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.apnum.2019.12.017 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 208 Subjects: – SubjectFull: Mathematical models Type: general – SubjectFull: Finite differences Type: general – SubjectFull: Sand dunes Type: general – SubjectFull: Erosion Type: general Titles: – TitleFull: A new mathematical model for traveling sand dunes: analysis and approximation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Falcone, M. – PersonEntity: Name: NameFull: Finzi Vita, S. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2020 Type: published Y: 2020 Identifiers: – Type: issn-print Value: 01689274 Numbering: – Type: volume Value: 155 Titles: – TitleFull: Applied Numerical Mathematics Type: main |
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