Simultaneous pseudo-time stepping for 3D aerodynamic shape optimization
Identifieur interne : 001A75 ( Istex/Corpus ); précédent : 001A74; suivant : 001A76Simultaneous pseudo-time stepping for 3D aerodynamic shape optimization
Auteurs : S. B. Hazra ; V. Schulz ; J. BrezillonSource :
- Journal of Numerical Mathematics [ 1570-2820 ] ; 2008-06.
Abstract
This paper presents a numerical method for aerodynamic shape optimization problems with state constraint. It uses a simultaneous semi-iterative technique to solve the equations arising from the first order necessary optimality conditions. Although there is no theoretical proof of convergence of this algorithm so far, in our numerical experiments the method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simulation runs.
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DOI: 10.1515/JNUM.2008.007
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Although there is no theoretical proof of convergence of this algorithm so far, in our numerical experiments the method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simulation runs.</div></front></TEI><istex><corpusName>degruyter-journals</corpusName><author><json:item><name>S. B. Hazra</name><affiliations><json:string>Department of Mathematics, University of Trier, D-54286 Trier, Germany</json:string></affiliations></json:item><json:item><name>V. Schulz</name><affiliations><json:string>Department of Mathematics, University of Trier, D-54286 Trier, Germany</json:string></affiliations></json:item><json:item><name>J. 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It uses a simultaneous semi-iterative technique to solve the equations arising from the first order necessary optimality conditions. Although there is no theoretical proof of convergence of this algorithm so far, in our numerical experiments the method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simulation runs.</abstract><qualityIndicators><score>8.224</score><pdfVersion>1.3</pdfVersion><pdfPageSize>595 x 842 pts (A4)</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>6</keywordCount><abstractCharCount>707</abstractCharCount><pdfWordCount>5680</pdfWordCount><pdfCharCount>32878</pdfCharCount><pdfPageCount>23</pdfPageCount><abstractWordCount>102</abstractWordCount></qualityIndicators><title>Simultaneous pseudo-time stepping for 3D aerodynamic shape optimization</title><refBibs><json:item><host><author><json:item><name>W,K Anderson</name></json:item><json:item><name>V Venkatakrishnan</name></json:item></author><title>Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation</title><publicationDate>1997</publicationDate></host></json:item><json:item><author><json:item><name>A Battermann</name></json:item><json:item><name>M Heinkenschloss</name></json:item></author><host><pages><last>32</last><first>15</first></pages><author></author><title>Optimal Control of PDE</title><publicationDate>1996</publicationDate></host><title>Preconditioners for Karush-Kuhn-Tucker systems arising in the optimal control of distributed systems</title><publicationDate>1996</publicationDate></json:item><json:item><host><pages><last>18</last><first>1</first></pages><author><json:item><name>A Battermann</name></json:item><json:item><name>E,W Sachs</name></json:item></author><title>Block preconditioners for KKT systems in PDE-governed optimal control problems</title><publicationDate>2001</publicationDate></host></json:item><json:item><author><json:item><name>G Biros</name></json:item><json:item><name>O Ghattas</name></json:item></author><host><pages><last>713</last><first>687</first></pages><issue>27</issue><author></author><title>SIAM J. 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B.</forename><surname>Hazra</surname></persName><affiliation>Department of Mathematics, University of Trier, D-54286 Trier, Germany</affiliation></author><author xml:id="author-2"><persName><forename type="first">V.</forename><surname>Schulz</surname></persName><affiliation>Department of Mathematics, University of Trier, D-54286 Trier, Germany</affiliation></author><author xml:id="author-3"><persName><forename type="first">J.</forename><surname>Brezillon</surname></persName><affiliation>Institute of Aerodynamics and Flow Technology, German Aerospace Center, D-38108 Braunschweig, Germany</affiliation></author></analytic><monogr><title level="j">Journal of Numerical Mathematics</title><title level="j" type="abbrev">Journal of Numerical Mathematics</title><idno type="pISSN">1570-2820</idno><idno type="eISSN">1569-3953</idno><imprint><publisher>Walter de Gruyter GmbH & Co. KG</publisher><date type="published" when="2008-06"></date><biblScope unit="volume">16</biblScope><biblScope unit="issue">2</biblScope><biblScope unit="page" from="139">139</biblScope><biblScope unit="page" to="161">161</biblScope></imprint></monogr><idno type="istex">3BFB757C5EE485B8374867A81CE32C613A91B4B1</idno><idno type="DOI">10.1515/JNUM.2008.007</idno><idno type="ArticleID">JNMA.16.2.139</idno><idno type="pdf">jnum.2008.007.pdf</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2008-06-25</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>This paper presents a numerical method for aerodynamic shape optimization problems with state constraint. It uses a simultaneous semi-iterative technique to solve the equations arising from the first order necessary optimality conditions. Although there is no theoretical proof of convergence of this algorithm so far, in our numerical experiments the method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simulation runs.</p></abstract><textClass><keywords scheme="keyword"><list><head>Keywords</head><item><term>shape optimization</term></item><item><term>simultaneous pseudo-time stepping</term></item><item><term>Euler equations</term></item><item><term>preconditioner</term></item><item><term>reduced SQP methods</term></item><item><term>supersonic aircraft</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2008-06-25">Created</change><change when="2008-06">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-17">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/3BFB757C5EE485B8374867A81CE32C613A91B4B1/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus degruyter-journals" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Atypon//DTD Atypon Systems Archival NLM DTD Suite v2.2.0 20090301//EN" URI="nlm-dtd/archivearticle.dtd" name="istex:docType"></istex:docType><istex:document><article article-type="research-article" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">JNMA</journal-id><abbrev-journal-title abbrev-type="full">Journal of Numerical Mathematics</abbrev-journal-title><issn pub-type="ppub">1570-2820</issn><issn pub-type="epub">1569-3953</issn><publisher><publisher-name>Walter de Gruyter GmbH & Co. KG</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">JNMA.16.2.139</article-id><article-id pub-id-type="doi">10.1515/JNUM.2008.007</article-id><title-group><article-title>Simultaneous pseudo-time stepping for 3D aerodynamic shape optimization</article-title></title-group><contrib-group><contrib contrib-type="author"><name><given-names>S. B.</given-names><x> </x><surname>Hazra</surname></name><x>, </x><aff>Department of Mathematics, University of Trier, D-54286 Trier, Germany</aff></contrib><contrib contrib-type="author"><name><given-names>V.</given-names><x> </x><surname>Schulz</surname></name><x>, and </x><aff>Department of Mathematics, University of Trier, D-54286 Trier, Germany</aff></contrib><contrib contrib-type="author"><name><given-names>J.</given-names><x> </x><surname>Brezillon</surname></name><aff>Institute of Aerodynamics and Flow Technology, German Aerospace Center, D-38108 Braunschweig, Germany</aff></contrib></contrib-group><pub-date pub-type="ppub"><month>June</month><year>2008</year></pub-date><pub-date pub-type="epub"><day>25</day><month>06</month><year>2008</year></pub-date><volume>16</volume><issue>2</issue><fpage>139</fpage><lpage>161</lpage><history><date date-type="received"><day>14</day><month>07</month><year>2006</year><string-date>Received July 14, 2006.</string-date></date><date date-type="rev-recd"><day>20</day><month>11</month><year>2007</year><string-date>Received in revised form November 20, 2007.</string-date></date></history><copyright-statement>© de Gruyter 2008</copyright-statement><copyright-year>2008</copyright-year><related-article related-article-type="pdf" xlink:href="jnum.2008.007.pdf"></related-article><abstract><title>Abstract</title><p>This paper presents a numerical method for aerodynamic shape optimization problems with state constraint. It uses a simultaneous semi-iterative technique to solve the equations arising from the first order necessary optimality conditions. Although there is no theoretical proof of convergence of this algorithm so far, in our numerical experiments the method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simulation runs.</p></abstract><kwd-group><title>Keywords:</title><kwd>shape optimization</kwd><x>, </x><kwd>simultaneous pseudo-time stepping</kwd><x>, </x><kwd>Euler equations</kwd><x>, </x><kwd>preconditioner</kwd><x>, </x><kwd>reduced SQP methods</kwd><x>, </x><kwd>supersonic aircraft</kwd></kwd-group></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Simultaneous pseudo-time stepping for 3D aerodynamic shape optimization</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>Simultaneous pseudo-time stepping for 3D aerodynamic shape optimization</title></titleInfo><name type="personal"><namePart type="given">S. B.</namePart><namePart type="family">Hazra</namePart><affiliation>Department of Mathematics, University of Trier, D-54286 Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">V.</namePart><namePart type="family">Schulz</namePart><affiliation>Department of Mathematics, University of Trier, D-54286 Trier, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">J.</namePart><namePart type="family">Brezillon</namePart><affiliation>Institute of Aerodynamics and Flow Technology, German Aerospace Center, D-38108 Braunschweig, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><originInfo><publisher>Walter de Gruyter GmbH & Co. KG</publisher><dateIssued encoding="w3cdtf">2008-06</dateIssued><dateCreated encoding="w3cdtf">2008-06-25</dateCreated><copyrightDate encoding="w3cdtf">2008</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract lang="en">This paper presents a numerical method for aerodynamic shape optimization problems with state constraint. It uses a simultaneous semi-iterative technique to solve the equations arising from the first order necessary optimality conditions. Although there is no theoretical proof of convergence of this algorithm so far, in our numerical experiments the method converges without additional globalization in the design space. A reduced SQP method based preconditioner is used for convergence acceleration. Design examples of drag reduction with constant lift for wing and body of a Supersonic Commercial Transport (SCT) aircraft are included. The overall cost of computation is about 8 forward simulation runs.</abstract><subject><genre>Keywords</genre><topic>shape optimization</topic><topic>simultaneous pseudo-time stepping</topic><topic>Euler equations</topic><topic>preconditioner</topic><topic>reduced SQP methods</topic><topic>supersonic aircraft</topic></subject><relatedItem type="host"><titleInfo><title>Journal of Numerical Mathematics</title></titleInfo><titleInfo type="abbreviated"><title>Journal of Numerical Mathematics</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">1570-2820</identifier><identifier type="eISSN">1569-3953</identifier><identifier type="PublisherID">JNMA</identifier><part><date>2008</date><detail type="volume"><caption>vol.</caption><number>16</number></detail><detail type="issue"><caption>no.</caption><number>2</number></detail><extent unit="pages"><start>139</start><end>161</end></extent></part></relatedItem><identifier type="istex">3BFB757C5EE485B8374867A81CE32C613A91B4B1</identifier><identifier type="DOI">10.1515/JNUM.2008.007</identifier><identifier type="ArticleID">JNMA.16.2.139</identifier><identifier type="pdf">jnum.2008.007.pdf</identifier><accessCondition type="use and reproduction" contentType="copyright">© de Gruyter 2008, 2008</accessCondition><recordInfo><recordContentSource>De Gruyter</recordContentSource></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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