Asymptotic Approximant for the Falkner-Skan Boundary-Layer equation
We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl. Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the Falkner-Skan boundary layer equation for flow over a wedge having angle $\beta\...
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Belden, Elizabeth R Dickman, Zachary A Weinstein, Steven J Archibee, Alex D Burroughs, Ethan Barlow, Nathaniel S |
| description | We demonstrate that the asymptotic approximant applied to the Blasius
boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl.
Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the
Falkner-Skan boundary layer equation for flow over a wedge having angle
$\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying
$\beta\in[-0.198837735, 1]$ are considered, and the previously established
non-unique solutions for $\beta |
| doi_str_mv | 10.48550/arxiv.1907.09912 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1907_09912</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1907_09912</sourcerecordid><originalsourceid>FETCH-LOGICAL-a672-c62aa2d97165bd8c8e71d6f53aa350594f43cc43b8102a3b11070de85cb9d49c3</originalsourceid><addsrcrecordid>eNotz71OwzAYhWEvHVDLBTDhG3Dwb2yPIaKAFImB7tEX2xFRWzu4LmruHihMZ3t1HoTuGK2kUYo-QL5MXxWzVFfUWsZvUNucluNcUpkcbuY5p8t0hFjwmDIuHwFv4bCPIZP3PUT8mM7RQ15IB0vIOHyeoUwpbtBqhMMp3P7vGu22T7v2hXRvz69t0xGoNSeu5gDcW81qNXjjTNDM16MSAEJRZeUohXNSDIZRDmJgjGrqg1FusF5aJ9bo_i97VfRz_nmal_5X01814htDIkUi</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Asymptotic Approximant for the Falkner-Skan Boundary-Layer equation</title><source>arXiv.org</source><creator>Belden, Elizabeth R ; Dickman, Zachary A ; Weinstein, Steven J ; Archibee, Alex D ; Burroughs, Ethan ; Barlow, Nathaniel S</creator><creatorcontrib>Belden, Elizabeth R ; Dickman, Zachary A ; Weinstein, Steven J ; Archibee, Alex D ; Burroughs, Ethan ; Barlow, Nathaniel S</creatorcontrib><description>We demonstrate that the asymptotic approximant applied to the Blasius
boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl.
Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the
Falkner-Skan boundary layer equation for flow over a wedge having angle
$\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying
$\beta\in[-0.198837735, 1]$ are considered, and the previously established
non-unique solutions for $\beta<0$ having positive and negative shear rates
along the wedge are accurately represented. The approximant is used to
determine the singularities in the complex plane that prescribe the radius of
convergence of the power series solution to the Falkner-Skan equation. An
attractive feature of the approximant is that it may be constructed quickly by
recursion compared with traditional Pad\'e approximants that require a matrix
inversion. The accuracy of the approximant is verified by numerical solutions,
and benchmark numerical values are obtained that characterize the asymptotic
behavior of the Falkner-Skan solution at large distances from the wedge.</description><identifier>DOI: 10.48550/arxiv.1907.09912</identifier><language>eng</language><subject>Physics - Computational Physics</subject><creationdate>2019-07</creationdate><rights>http://creativecommons.org/licenses/by-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1907.09912$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1907.09912$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Belden, Elizabeth R</creatorcontrib><creatorcontrib>Dickman, Zachary A</creatorcontrib><creatorcontrib>Weinstein, Steven J</creatorcontrib><creatorcontrib>Archibee, Alex D</creatorcontrib><creatorcontrib>Burroughs, Ethan</creatorcontrib><creatorcontrib>Barlow, Nathaniel S</creatorcontrib><title>Asymptotic Approximant for the Falkner-Skan Boundary-Layer equation</title><description>We demonstrate that the asymptotic approximant applied to the Blasius
boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl.
Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the
Falkner-Skan boundary layer equation for flow over a wedge having angle
$\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying
$\beta\in[-0.198837735, 1]$ are considered, and the previously established
non-unique solutions for $\beta<0$ having positive and negative shear rates
along the wedge are accurately represented. The approximant is used to
determine the singularities in the complex plane that prescribe the radius of
convergence of the power series solution to the Falkner-Skan equation. An
attractive feature of the approximant is that it may be constructed quickly by
recursion compared with traditional Pad\'e approximants that require a matrix
inversion. The accuracy of the approximant is verified by numerical solutions,
and benchmark numerical values are obtained that characterize the asymptotic
behavior of the Falkner-Skan solution at large distances from the wedge.</description><subject>Physics - Computational Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAYhWEvHVDLBTDhG3Dwb2yPIaKAFImB7tEX2xFRWzu4LmruHihMZ3t1HoTuGK2kUYo-QL5MXxWzVFfUWsZvUNucluNcUpkcbuY5p8t0hFjwmDIuHwFv4bCPIZP3PUT8mM7RQ15IB0vIOHyeoUwpbtBqhMMp3P7vGu22T7v2hXRvz69t0xGoNSeu5gDcW81qNXjjTNDM16MSAEJRZeUohXNSDIZRDmJgjGrqg1FusF5aJ9bo_i97VfRz_nmal_5X01814htDIkUi</recordid><startdate>20190717</startdate><enddate>20190717</enddate><creator>Belden, Elizabeth R</creator><creator>Dickman, Zachary A</creator><creator>Weinstein, Steven J</creator><creator>Archibee, Alex D</creator><creator>Burroughs, Ethan</creator><creator>Barlow, Nathaniel S</creator><scope>GOX</scope></search><sort><creationdate>20190717</creationdate><title>Asymptotic Approximant for the Falkner-Skan Boundary-Layer equation</title><author>Belden, Elizabeth R ; Dickman, Zachary A ; Weinstein, Steven J ; Archibee, Alex D ; Burroughs, Ethan ; Barlow, Nathaniel S</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-c62aa2d97165bd8c8e71d6f53aa350594f43cc43b8102a3b11070de85cb9d49c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Physics - Computational Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Belden, Elizabeth R</creatorcontrib><creatorcontrib>Dickman, Zachary A</creatorcontrib><creatorcontrib>Weinstein, Steven J</creatorcontrib><creatorcontrib>Archibee, Alex D</creatorcontrib><creatorcontrib>Burroughs, Ethan</creatorcontrib><creatorcontrib>Barlow, Nathaniel S</creatorcontrib><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Belden, Elizabeth R</au><au>Dickman, Zachary A</au><au>Weinstein, Steven J</au><au>Archibee, Alex D</au><au>Burroughs, Ethan</au><au>Barlow, Nathaniel S</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic Approximant for the Falkner-Skan Boundary-Layer equation</atitle><date>2019-07-17</date><risdate>2019</risdate><abstract>We demonstrate that the asymptotic approximant applied to the Blasius
boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl.
Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the
Falkner-Skan boundary layer equation for flow over a wedge having angle
$\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying
$\beta\in[-0.198837735, 1]$ are considered, and the previously established
non-unique solutions for $\beta<0$ having positive and negative shear rates
along the wedge are accurately represented. The approximant is used to
determine the singularities in the complex plane that prescribe the radius of
convergence of the power series solution to the Falkner-Skan equation. An
attractive feature of the approximant is that it may be constructed quickly by
recursion compared with traditional Pad\'e approximants that require a matrix
inversion. The accuracy of the approximant is verified by numerical solutions,
and benchmark numerical values are obtained that characterize the asymptotic
behavior of the Falkner-Skan solution at large distances from the wedge.</abstract><doi>10.48550/arxiv.1907.09912</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.1907.09912 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_1907_09912 |
| source | arXiv.org |
| subjects | Physics - Computational Physics |
| title | Asymptotic Approximant for the Falkner-Skan Boundary-Layer equation |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T21%3A33%3A52IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Asymptotic%20Approximant%20for%20the%20Falkner-Skan%20Boundary-Layer%20equation&rft.au=Belden,%20Elizabeth%20R&rft.date=2019-07-17&rft_id=info:doi/10.48550/arxiv.1907.09912&rft_dat=%3Carxiv_GOX%3E1907_09912%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |