Adjoint-based optimal control of incompressible flows with convective-like energy-stable open boundary conditions
•The adjoint system for the incompressible Navier-Stokes equations with stabilized open boundary conditions is derived.•The primal and adjoint systems are solved using the least-squares finite element method.•Example problems are solved, including the drag reduction of a cylinder in a severely trunc...
Gespeichert in:
| Veröffentlicht in: | Computers & mathematics with applications (1987) 2022-01, Vol.106, p.40-56 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 56 |
|---|---|
| container_issue | |
| container_start_page | 40 |
| container_title | Computers & mathematics with applications (1987) |
| container_volume | 106 |
| creator | Gałecki, Jakub Szumbarski, Jacek |
| description | •The adjoint system for the incompressible Navier-Stokes equations with stabilized open boundary conditions is derived.•The primal and adjoint systems are solved using the least-squares finite element method.•Example problems are solved, including the drag reduction of a cylinder in a severely truncated domain.
This paper describes an open-loop optimal control strategy for flow problems governed by the incompressible Navier-Stokes equations with convective-like energy-stable boundary conditions. A quasi-Newton optimization procedure is employed, and the required objective sensitivities are computed using the continuous adjoint method. The adjoint equations for the corresponding system are derived and discussed. Both the primal and adjoint systems are solved using the least-squares finite element method. This choice circumvents the LBB condition and leads to symmetric positive-definite algebraic systems. Numerical examples are provided to show the stability and accuracy of the proposed approach. |
| doi_str_mv | 10.1016/j.camwa.2021.12.004 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2637399211</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0898122121004302</els_id><sourcerecordid>2637399211</sourcerecordid><originalsourceid>FETCH-LOGICAL-c246t-8fee0ab65cab0f26817be99451d3deaf68fee4c7e6ed36822d849754598ae9f73</originalsourceid><addsrcrecordid>eNp90M9PwyAUwHFiNHFO_wIvJJ5bgXaUHjwsi7-SJV70TCi8KrWDDtiW_fe2zrOnd_k8yPsidEtJTgnl912u1eagckYYzSnLCSnP0IyKqsgqzsU5mhFRi4wyRi_RVYwdGUXByAxtl6bz1qWsUREM9kOyG9Vj7V0Kvse-xdZpvxkCxGibHnDb-0PEB5u-JrQHnewest5-AwYH4fOYxaQm6AdwuPE7Z1Q4TtbYZL2L1-iiVX2Em785Rx9Pj--rl2z99vy6Wq4zzUqeMtECENXwhVYNaRkXtGqgrssFNYUB1fIJlLoCDqbggjEjyrpalItaKKjbqpiju9O7Q_DbHcQkO78LbvxSMl5URV0zSkdVnJQOPsYArRzCWCAcJSVyais7-dtWTm0lZXIqN0cPpy0YD9hbCDJqC06DsWEsIo23_-7_AGSehoM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2637399211</pqid></control><display><type>article</type><title>Adjoint-based optimal control of incompressible flows with convective-like energy-stable open boundary conditions</title><source>Elsevier ScienceDirect Journals</source><creator>Gałecki, Jakub ; Szumbarski, Jacek</creator><creatorcontrib>Gałecki, Jakub ; Szumbarski, Jacek</creatorcontrib><description>•The adjoint system for the incompressible Navier-Stokes equations with stabilized open boundary conditions is derived.•The primal and adjoint systems are solved using the least-squares finite element method.•Example problems are solved, including the drag reduction of a cylinder in a severely truncated domain.
This paper describes an open-loop optimal control strategy for flow problems governed by the incompressible Navier-Stokes equations with convective-like energy-stable boundary conditions. A quasi-Newton optimization procedure is employed, and the required objective sensitivities are computed using the continuous adjoint method. The adjoint equations for the corresponding system are derived and discussed. Both the primal and adjoint systems are solved using the least-squares finite element method. This choice circumvents the LBB condition and leads to symmetric positive-definite algebraic systems. Numerical examples are provided to show the stability and accuracy of the proposed approach.</description><identifier>ISSN: 0898-1221</identifier><identifier>EISSN: 1873-7668</identifier><identifier>DOI: 10.1016/j.camwa.2021.12.004</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Backflow instability ; Boundary conditions ; Continuous adjoint method ; Finite element method ; Fluid flow ; Incompressible flow ; Least-squares finite element method ; Mathematical analysis ; Open boundary conditions ; Optimal control ; Optimal flow control ; Optimization</subject><ispartof>Computers & mathematics with applications (1987), 2022-01, Vol.106, p.40-56</ispartof><rights>2021 Elsevier Ltd</rights><rights>Copyright Elsevier BV Jan 15, 2022</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c246t-8fee0ab65cab0f26817be99451d3deaf68fee4c7e6ed36822d849754598ae9f73</citedby><cites>FETCH-LOGICAL-c246t-8fee0ab65cab0f26817be99451d3deaf68fee4c7e6ed36822d849754598ae9f73</cites><orcidid>0000-0003-1176-106X ; 0000-0002-8263-9996</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0898122121004302$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids></links><search><creatorcontrib>Gałecki, Jakub</creatorcontrib><creatorcontrib>Szumbarski, Jacek</creatorcontrib><title>Adjoint-based optimal control of incompressible flows with convective-like energy-stable open boundary conditions</title><title>Computers & mathematics with applications (1987)</title><description>•The adjoint system for the incompressible Navier-Stokes equations with stabilized open boundary conditions is derived.•The primal and adjoint systems are solved using the least-squares finite element method.•Example problems are solved, including the drag reduction of a cylinder in a severely truncated domain.
This paper describes an open-loop optimal control strategy for flow problems governed by the incompressible Navier-Stokes equations with convective-like energy-stable boundary conditions. A quasi-Newton optimization procedure is employed, and the required objective sensitivities are computed using the continuous adjoint method. The adjoint equations for the corresponding system are derived and discussed. Both the primal and adjoint systems are solved using the least-squares finite element method. This choice circumvents the LBB condition and leads to symmetric positive-definite algebraic systems. Numerical examples are provided to show the stability and accuracy of the proposed approach.</description><subject>Backflow instability</subject><subject>Boundary conditions</subject><subject>Continuous adjoint method</subject><subject>Finite element method</subject><subject>Fluid flow</subject><subject>Incompressible flow</subject><subject>Least-squares finite element method</subject><subject>Mathematical analysis</subject><subject>Open boundary conditions</subject><subject>Optimal control</subject><subject>Optimal flow control</subject><subject>Optimization</subject><issn>0898-1221</issn><issn>1873-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp90M9PwyAUwHFiNHFO_wIvJJ5bgXaUHjwsi7-SJV70TCi8KrWDDtiW_fe2zrOnd_k8yPsidEtJTgnl912u1eagckYYzSnLCSnP0IyKqsgqzsU5mhFRi4wyRi_RVYwdGUXByAxtl6bz1qWsUREM9kOyG9Vj7V0Kvse-xdZpvxkCxGibHnDb-0PEB5u-JrQHnewest5-AwYH4fOYxaQm6AdwuPE7Z1Q4TtbYZL2L1-iiVX2Em785Rx9Pj--rl2z99vy6Wq4zzUqeMtECENXwhVYNaRkXtGqgrssFNYUB1fIJlLoCDqbggjEjyrpalItaKKjbqpiju9O7Q_DbHcQkO78LbvxSMl5URV0zSkdVnJQOPsYArRzCWCAcJSVyais7-dtWTm0lZXIqN0cPpy0YD9hbCDJqC06DsWEsIo23_-7_AGSehoM</recordid><startdate>20220115</startdate><enddate>20220115</enddate><creator>Gałecki, Jakub</creator><creator>Szumbarski, Jacek</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-1176-106X</orcidid><orcidid>https://orcid.org/0000-0002-8263-9996</orcidid></search><sort><creationdate>20220115</creationdate><title>Adjoint-based optimal control of incompressible flows with convective-like energy-stable open boundary conditions</title><author>Gałecki, Jakub ; Szumbarski, Jacek</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c246t-8fee0ab65cab0f26817be99451d3deaf68fee4c7e6ed36822d849754598ae9f73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Backflow instability</topic><topic>Boundary conditions</topic><topic>Continuous adjoint method</topic><topic>Finite element method</topic><topic>Fluid flow</topic><topic>Incompressible flow</topic><topic>Least-squares finite element method</topic><topic>Mathematical analysis</topic><topic>Open boundary conditions</topic><topic>Optimal control</topic><topic>Optimal flow control</topic><topic>Optimization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gałecki, Jakub</creatorcontrib><creatorcontrib>Szumbarski, Jacek</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Computers & mathematics with applications (1987)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gałecki, Jakub</au><au>Szumbarski, Jacek</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adjoint-based optimal control of incompressible flows with convective-like energy-stable open boundary conditions</atitle><jtitle>Computers & mathematics with applications (1987)</jtitle><date>2022-01-15</date><risdate>2022</risdate><volume>106</volume><spage>40</spage><epage>56</epage><pages>40-56</pages><issn>0898-1221</issn><eissn>1873-7668</eissn><abstract>•The adjoint system for the incompressible Navier-Stokes equations with stabilized open boundary conditions is derived.•The primal and adjoint systems are solved using the least-squares finite element method.•Example problems are solved, including the drag reduction of a cylinder in a severely truncated domain.
This paper describes an open-loop optimal control strategy for flow problems governed by the incompressible Navier-Stokes equations with convective-like energy-stable boundary conditions. A quasi-Newton optimization procedure is employed, and the required objective sensitivities are computed using the continuous adjoint method. The adjoint equations for the corresponding system are derived and discussed. Both the primal and adjoint systems are solved using the least-squares finite element method. This choice circumvents the LBB condition and leads to symmetric positive-definite algebraic systems. Numerical examples are provided to show the stability and accuracy of the proposed approach.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.camwa.2021.12.004</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0003-1176-106X</orcidid><orcidid>https://orcid.org/0000-0002-8263-9996</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0898-1221 |
| ispartof | Computers & mathematics with applications (1987), 2022-01, Vol.106, p.40-56 |
| issn | 0898-1221 1873-7668 |
| language | eng |
| recordid | cdi_proquest_journals_2637399211 |
| source | Elsevier ScienceDirect Journals |
| subjects | Backflow instability Boundary conditions Continuous adjoint method Finite element method Fluid flow Incompressible flow Least-squares finite element method Mathematical analysis Open boundary conditions Optimal control Optimal flow control Optimization |
| title | Adjoint-based optimal control of incompressible flows with convective-like energy-stable open boundary conditions |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-24T06%3A43%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Adjoint-based%20optimal%20control%20of%20incompressible%20flows%20with%20convective-like%20energy-stable%20open%20boundary%20conditions&rft.jtitle=Computers%20&%20mathematics%20with%20applications%20(1987)&rft.au=Ga%C5%82ecki,%20Jakub&rft.date=2022-01-15&rft.volume=106&rft.spage=40&rft.epage=56&rft.pages=40-56&rft.issn=0898-1221&rft.eissn=1873-7668&rft_id=info:doi/10.1016/j.camwa.2021.12.004&rft_dat=%3Cproquest_cross%3E2637399211%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2637399211&rft_id=info:pmid/&rft_els_id=S0898122121004302&rfr_iscdi=true |