Long‐time behavior of shape design solutions for the Navier–Stokes equations
We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Mechanik 2023-02, Vol.103 (2), p.n/a |
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| container_title | Zeitschrift für angewandte Mathematik und Mechanik |
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| creator | Simon, John Sebastian H. |
| description | We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the L∞$L^\infty$‐topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property. As a consequence, we show that the asymptotic convergence of shape solutions for parabolic/elliptic problems is a particular case of our analysis. Last, a numerical example is provided to show the occurrence of the convergence of shape design solutions of time‐dependent problems with different values of the terminal time T to a shape design solution of the stationary problem.
We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the L∞$L^\infty$‐topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property.… |
| doi_str_mv | 10.1002/zamm.202100441 |
| format | Article |
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We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the L∞$L^\infty$‐topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property.…</description><identifier>ISSN: 0044-2267</identifier><identifier>EISSN: 1521-4001</identifier><identifier>DOI: 10.1002/zamm.202100441</identifier><language>eng</language><publisher>Weinheim: Wiley Subscription Services, Inc</publisher><subject>Characteristic functions ; Convergence ; Domains ; Fluid dynamics ; Fluid flow ; Navier-Stokes equations ; Shape optimization ; Time dependence ; Topology</subject><ispartof>Zeitschrift für angewandte Mathematik und Mechanik, 2023-02, Vol.103 (2), p.n/a</ispartof><rights>2022 Wiley‐VCH GmbH.</rights><rights>2023 Wiley‐VCH GmbH.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2021-5a7f2a0e32c18c2bad9fb6b2f45d8d352eb18c43d25fbaea69128973ccd8fc83</cites><orcidid>0000-0002-7711-9582</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fzamm.202100441$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fzamm.202100441$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>315,781,785,1418,27929,27930,45579,45580</link.rule.ids></links><search><creatorcontrib>Simon, John Sebastian H.</creatorcontrib><title>Long‐time behavior of shape design solutions for the Navier–Stokes equations</title><title>Zeitschrift für angewandte Mathematik und Mechanik</title><description>We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the L∞$L^\infty$‐topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property. As a consequence, we show that the asymptotic convergence of shape solutions for parabolic/elliptic problems is a particular case of our analysis. Last, a numerical example is provided to show the occurrence of the convergence of shape design solutions of time‐dependent problems with different values of the terminal time T to a shape design solution of the stationary problem.
We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the L∞$L^\infty$‐topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property.…</description><subject>Characteristic functions</subject><subject>Convergence</subject><subject>Domains</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Navier-Stokes equations</subject><subject>Shape optimization</subject><subject>Time dependence</subject><subject>Topology</subject><issn>0044-2267</issn><issn>1521-4001</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNqFkMtOwzAQRS0EEqWwZW2JdYo9cV7LquIltYBEV2wsx7HblCZu7QRUVv0EJP6wX4JDESxZjebOuTOji9A5JQNKCFy-i6oaAAHfMEYPUI9GQANGCD1EvU4LAOLkGJ04tyBezWjYQ49jU89224-mrBTO1Vy8lsZio7Gbi5XChXLlrMbOLNumNLXD2k-bucL3HlR2t_18asyLclitW_FNnKIjLZZOnf3UPppeX01Ht8H44eZuNBwHsnsxiESiQRAVgqSphFwUmc7jHDSLirQII1C511lYQKRzoUScUUizJJSySLVMwz662K9dWbNulWv4wrS29hc5JAnLYsYYeGqwp6Q1zlml-cqWlbAbTgnvQuNdaPw3NG_I9oa3cqk2_9D8eTiZ_Hm_ABUcc8c</recordid><startdate>202302</startdate><enddate>202302</enddate><creator>Simon, John Sebastian H.</creator><general>Wiley Subscription Services, Inc</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/0000-0002-7711-9582</orcidid></search><sort><creationdate>202302</creationdate><title>Long‐time behavior of shape design solutions for the Navier–Stokes equations</title><author>Simon, John Sebastian H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2021-5a7f2a0e32c18c2bad9fb6b2f45d8d352eb18c43d25fbaea69128973ccd8fc83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Characteristic functions</topic><topic>Convergence</topic><topic>Domains</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Navier-Stokes equations</topic><topic>Shape optimization</topic><topic>Time dependence</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Simon, John Sebastian H.</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>Zeitschrift für angewandte Mathematik und Mechanik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Simon, John Sebastian H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Long‐time behavior of shape design solutions for the Navier–Stokes equations</atitle><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle><date>2023-02</date><risdate>2023</risdate><volume>103</volume><issue>2</issue><epage>n/a</epage><issn>0044-2267</issn><eissn>1521-4001</eissn><abstract>We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the L∞$L^\infty$‐topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property. As a consequence, we show that the asymptotic convergence of shape solutions for parabolic/elliptic problems is a particular case of our analysis. Last, a numerical example is provided to show the occurrence of the convergence of shape design solutions of time‐dependent problems with different values of the terminal time T to a shape design solution of the stationary problem.
We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that the solution of the former approaches a neighborhood of that of the latter. The convergence of domains is based on the L∞$L^\infty$‐topology of their corresponding characteristic functions, which is closed under the set of domains satisfying the cone property.…</abstract><cop>Weinheim</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/zamm.202100441</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-7711-9582</orcidid></addata></record> |
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| subjects | Characteristic functions Convergence Domains Fluid dynamics Fluid flow Navier-Stokes equations Shape optimization Time dependence Topology |
| title | Long‐time behavior of shape design solutions for the Navier–Stokes equations |
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