Improvement for expansion of parabolized stability equation method in boundary layer stability analysis
An improved expansion of the parabolized stability equation (iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber α and its streamwise gradient d α /d x are unknown variables. This eigenvalue prob...
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| Veröffentlicht in: | Applied mathematics and mechanics 2018-12, Vol.39 (12), p.1737-1754 |
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| creator | Han, Yufeng Liu, Jianxin Luo, Jisheng |
| description | An improved expansion of the parabolized stability equation (iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber
α
and its streamwise gradient d
α
/d
x
are unknown variables. This eigenvalue problem is solved for the eigenvalue d
α
/d
x
with an initial
α
, and the correction of
α
is performed with the conservation relation used in the PSE. The iEPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the iEPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the iEPSE. As a local non-parallel stability analysis tool, the iEPSE has great potential application in the e
N
transition prediction in general three-dimensional boundary layers. |
| doi_str_mv | 10.1007/s10483-019-2401-9 |
| format | Article |
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α
and its streamwise gradient d
α
/d
x
are unknown variables. This eigenvalue problem is solved for the eigenvalue d
α
/d
x
with an initial
α
, and the correction of
α
is performed with the conservation relation used in the PSE. The iEPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the iEPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the iEPSE. As a local non-parallel stability analysis tool, the iEPSE has great potential application in the e
N
transition prediction in general three-dimensional boundary layers.</description><edition>English ed.</edition><identifier>ISSN: 0253-4827</identifier><identifier>EISSN: 1573-2754</identifier><identifier>DOI: 10.1007/s10483-019-2401-9</identifier><language>eng</language><publisher>Shanghai: Shanghai University</publisher><subject>Applications of Mathematics ; Boundary layer stability ; Boundary layer transition ; Classical Mechanics ; Compressibility ; Computational fluid dynamics ; Eigenvalues ; Fluid- and Aerodynamics ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Parabolized stability equations ; Partial Differential Equations ; Stability ; Stability analysis ; Wavelengths</subject><ispartof>Applied mathematics and mechanics, 2018-12, Vol.39 (12), p.1737-1754</ispartof><rights>Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><rights>Copyright © Wanfang Data Co. Ltd. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c351t-54071dd129e77fbb6f584a029c3f1021d161604f546f452101b5c2d7c9b0ffa73</citedby><cites>FETCH-LOGICAL-c351t-54071dd129e77fbb6f584a029c3f1021d161604f546f452101b5c2d7c9b0ffa73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://www.wanfangdata.com.cn/images/PeriodicalImages/yysxhlx-e/yysxhlx-e.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10483-019-2401-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10483-019-2401-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Han, Yufeng</creatorcontrib><creatorcontrib>Liu, Jianxin</creatorcontrib><creatorcontrib>Luo, Jisheng</creatorcontrib><title>Improvement for expansion of parabolized stability equation method in boundary layer stability analysis</title><title>Applied mathematics and mechanics</title><addtitle>Appl. Math. Mech.-Engl. Ed</addtitle><description>An improved expansion of the parabolized stability equation (iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber
α
and its streamwise gradient d
α
/d
x
are unknown variables. This eigenvalue problem is solved for the eigenvalue d
α
/d
x
with an initial
α
, and the correction of
α
is performed with the conservation relation used in the PSE. The iEPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the iEPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the iEPSE. As a local non-parallel stability analysis tool, the iEPSE has great potential application in the e
N
transition prediction in general three-dimensional boundary layers.</description><subject>Applications of Mathematics</subject><subject>Boundary layer stability</subject><subject>Boundary layer transition</subject><subject>Classical Mechanics</subject><subject>Compressibility</subject><subject>Computational fluid dynamics</subject><subject>Eigenvalues</subject><subject>Fluid- and Aerodynamics</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Parabolized stability equations</subject><subject>Partial Differential Equations</subject><subject>Stability</subject><subject>Stability analysis</subject><subject>Wavelengths</subject><issn>0253-4827</issn><issn>1573-2754</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAURS0EEqXwA9gssSEF3nPsuBlRxZdUiQVmy0nsNlVqFzuFhl-PqyDBwvSWc6_uO4RcItwggLyNCHyWZ4BlxjhgVh6RCQqZZ0wKfkwmwESe8RmTp-QsxjUAcMn5hCyfN9vgP8zGuJ5aH6jZb7WLrXfUW7rVQVe-a79MQ2Ovq7Zr-4Ga953uD8TG9Cvf0NbRyu9co8NAOz2Y8IfVTndDbOM5ObG6i-bi507J28P96_wpW7w8Ps_vFlmdC-wzwUFi0yArjZS2qgorZlwDK-vcIjBssMACuBW8sFwwBKxEzRpZlxVYq2U-Jddj76d2VrulWvtdSBuiGoa4X3V7ZRjgDBlAnuCrEU4K3ncm9r80w2SxEFBgonCk6uBjDMaqbWg36VmFoA7y1ShfJfnqIF-VKcPGTEysW5rw2_x_6Bvs94hR</recordid><startdate>20181201</startdate><enddate>20181201</enddate><creator>Han, Yufeng</creator><creator>Liu, Jianxin</creator><creator>Luo, Jisheng</creator><general>Shanghai University</general><general>Springer Nature B.V</general><general>Department of Mechanics, Tianjin University, Tianjin 300072, China%Department of Mechanics, Tianjin University, Tianjin 300072, China</general><general>Tianjin Key Laboratory of Modern Engineering Mechanics, Tianjin 300072, China</general><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20181201</creationdate><title>Improvement for expansion of parabolized stability equation method in boundary layer stability analysis</title><author>Han, Yufeng ; Liu, Jianxin ; Luo, Jisheng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c351t-54071dd129e77fbb6f584a029c3f1021d161604f546f452101b5c2d7c9b0ffa73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Applications of Mathematics</topic><topic>Boundary layer stability</topic><topic>Boundary layer transition</topic><topic>Classical Mechanics</topic><topic>Compressibility</topic><topic>Computational fluid dynamics</topic><topic>Eigenvalues</topic><topic>Fluid- and Aerodynamics</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Parabolized stability equations</topic><topic>Partial Differential Equations</topic><topic>Stability</topic><topic>Stability analysis</topic><topic>Wavelengths</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Han, Yufeng</creatorcontrib><creatorcontrib>Liu, Jianxin</creatorcontrib><creatorcontrib>Luo, Jisheng</creatorcontrib><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Applied mathematics and mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Han, Yufeng</au><au>Liu, Jianxin</au><au>Luo, Jisheng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Improvement for expansion of parabolized stability equation method in boundary layer stability analysis</atitle><jtitle>Applied mathematics and mechanics</jtitle><stitle>Appl. Math. Mech.-Engl. Ed</stitle><date>2018-12-01</date><risdate>2018</risdate><volume>39</volume><issue>12</issue><spage>1737</spage><epage>1754</epage><pages>1737-1754</pages><issn>0253-4827</issn><eissn>1573-2754</eissn><abstract>An improved expansion of the parabolized stability equation (iEPSE) method is proposed for the accurate linear instability prediction in boundary layers. It is a local eigenvalue problem, and the streamwise wavenumber
α
and its streamwise gradient d
α
/d
x
are unknown variables. This eigenvalue problem is solved for the eigenvalue d
α
/d
x
with an initial
α
, and the correction of
α
is performed with the conservation relation used in the PSE. The iEPSE is validated in several compressible and incompressible boundary layers. The computational results show that the prediction accuracy of the iEPSE is significantly higher than that of the ESPE, and it is in excellent agreement with the PSE which is regarded as the baseline for comparison. In addition, the unphysical multiple eigenmode problem in the EPSE is solved by using the iEPSE. As a local non-parallel stability analysis tool, the iEPSE has great potential application in the e
N
transition prediction in general three-dimensional boundary layers.</abstract><cop>Shanghai</cop><pub>Shanghai University</pub><doi>10.1007/s10483-019-2401-9</doi><tpages>18</tpages><edition>English ed.</edition></addata></record> |
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| subjects | Applications of Mathematics Boundary layer stability Boundary layer transition Classical Mechanics Compressibility Computational fluid dynamics Eigenvalues Fluid- and Aerodynamics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Parabolized stability equations Partial Differential Equations Stability Stability analysis Wavelengths |
| title | Improvement for expansion of parabolized stability equation method in boundary layer stability analysis |
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