The Crank–Nicolson finite spectral element method and numerical simulations for 2D non‐stationary Navier–Stokes equations
In this paper, we first build a semi‐discretized Crank–Nicolson (CN) model about time for the two‐dimensional (2D) non‐stationary Navier–Stokes equations about vorticity–stream functions and discuss the existence, stability, and convergence of the time semi‐discretized CN solutions. And then, we bui...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2020-03, Vol.43 (5), p.2276-2288 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Luo, Zhendong Jiang, Wenrui |
| description | In this paper, we first build a semi‐discretized Crank–Nicolson (CN) model about time for the two‐dimensional (2D) non‐stationary Navier–Stokes equations about vorticity–stream functions and discuss the existence, stability, and convergence of the time semi‐discretized CN solutions. And then, we build a fully discretized finite spectral element CN (FSECN) model based on the bilinear trigonometric basic functions on quadrilateral elements for the 2D non‐stationary Navier–Stokes equations about the vorticity–stream functions and discuss the existence, stability, and convergence of the FSECN solutions. Finally, we utilize two sets of numerical experiments to check out the correctness of theoretical consequences. |
| doi_str_mv | 10.1002/mma.6039 |
| format | Article |
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And then, we build a fully discretized finite spectral element CN (FSECN) model based on the bilinear trigonometric basic functions on quadrilateral elements for the 2D non‐stationary Navier–Stokes equations about the vorticity–stream functions and discuss the existence, stability, and convergence of the FSECN solutions. Finally, we utilize two sets of numerical experiments to check out the correctness of theoretical consequences.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.6039</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>Computational fluid dynamics ; Computer simulation ; Convergence ; Discretization ; existence and stability as well as convergence ; Fluid flow ; fully discretized finite spectral element Crank–Nicolson model ; Mathematical models ; Navier-Stokes equations ; Quadrilaterals ; semi‐discretized Crank–Nicolson model ; Spectral element method ; Stability ; Two dimensional models ; two‐dimensional non‐stationary Navier–Stokes equations about vorticity‐stream functions ; Vorticity</subject><ispartof>Mathematical methods in the applied sciences, 2020-03, Vol.43 (5), p.2276-2288</ispartof><rights>2019 John Wiley & Sons, Ltd.</rights><rights>2020 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2939-e39e2ee4d5ea1cc145620f4e4835bee2f127dcf3cff1a4d15c58e722006b28e43</citedby><cites>FETCH-LOGICAL-c2939-e39e2ee4d5ea1cc145620f4e4835bee2f127dcf3cff1a4d15c58e722006b28e43</cites><orcidid>0000-0002-9469-7018</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%2Fmma.6039$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.6039$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,777,781,1412,27905,27906,45555,45556</link.rule.ids></links><search><creatorcontrib>Luo, Zhendong</creatorcontrib><creatorcontrib>Jiang, Wenrui</creatorcontrib><title>The Crank–Nicolson finite spectral element method and numerical simulations for 2D non‐stationary Navier–Stokes equations</title><title>Mathematical methods in the applied sciences</title><description>In this paper, we first build a semi‐discretized Crank–Nicolson (CN) model about time for the two‐dimensional (2D) non‐stationary Navier–Stokes equations about vorticity–stream functions and discuss the existence, stability, and convergence of the time semi‐discretized CN solutions. And then, we build a fully discretized finite spectral element CN (FSECN) model based on the bilinear trigonometric basic functions on quadrilateral elements for the 2D non‐stationary Navier–Stokes equations about the vorticity–stream functions and discuss the existence, stability, and convergence of the FSECN solutions. Finally, we utilize two sets of numerical experiments to check out the correctness of theoretical consequences.</description><subject>Computational fluid dynamics</subject><subject>Computer simulation</subject><subject>Convergence</subject><subject>Discretization</subject><subject>existence and stability as well as convergence</subject><subject>Fluid flow</subject><subject>fully discretized finite spectral element Crank–Nicolson model</subject><subject>Mathematical models</subject><subject>Navier-Stokes equations</subject><subject>Quadrilaterals</subject><subject>semi‐discretized Crank–Nicolson model</subject><subject>Spectral element method</subject><subject>Stability</subject><subject>Two dimensional models</subject><subject>two‐dimensional non‐stationary Navier–Stokes equations about vorticity‐stream functions</subject><subject>Vorticity</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kEtOwzAQhi0EEqUgcQRLbNik2I7zWlblKbVlQVlHrjNW3SZ2ayegrugRkLhhT0LasGU10sw382s-hK4pGVBC2F1ViUFMwuwE9SjJsoDyJD5FPUITEnBG-Tm68H5JCEkpZT30NVsAHjlhVvvdz1RLW3prsNJG14D9GmTtRImhhApMjSuoF7bAwhTYNBU4Lduh11VTilpb47GyDrN7bKzZ7759fewKt8VT8aHBtRFvtV2Bx7Bpuo1LdKZE6eHqr_bR--PDbPQcjF-fXkbDcSBZFmYBhBkwAF5EIKiUlEcxI4oDT8NoDsAUZUkhVSiVooIXNJJRCgljhMRzlgIP--imu7t2dtOAr_OlbZxpI3MWxllCWRRGLXXbUdJZ7x2ofO101T6QU5If9Oat3vygt0WDDv3UJWz_5fLJZHjkfwH3M4D3</recordid><startdate>20200330</startdate><enddate>20200330</enddate><creator>Luo, Zhendong</creator><creator>Jiang, Wenrui</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0002-9469-7018</orcidid></search><sort><creationdate>20200330</creationdate><title>The Crank–Nicolson finite spectral element method and numerical simulations for 2D non‐stationary Navier–Stokes equations</title><author>Luo, Zhendong ; Jiang, Wenrui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2939-e39e2ee4d5ea1cc145620f4e4835bee2f127dcf3cff1a4d15c58e722006b28e43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computational fluid dynamics</topic><topic>Computer simulation</topic><topic>Convergence</topic><topic>Discretization</topic><topic>existence and stability as well as convergence</topic><topic>Fluid flow</topic><topic>fully discretized finite spectral element Crank–Nicolson model</topic><topic>Mathematical models</topic><topic>Navier-Stokes equations</topic><topic>Quadrilaterals</topic><topic>semi‐discretized Crank–Nicolson model</topic><topic>Spectral element method</topic><topic>Stability</topic><topic>Two dimensional models</topic><topic>two‐dimensional non‐stationary Navier–Stokes equations about vorticity‐stream functions</topic><topic>Vorticity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Luo, Zhendong</creatorcontrib><creatorcontrib>Jiang, Wenrui</creatorcontrib><collection>CrossRef</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><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Luo, Zhendong</au><au>Jiang, Wenrui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Crank–Nicolson finite spectral element method and numerical simulations for 2D non‐stationary Navier–Stokes equations</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2020-03-30</date><risdate>2020</risdate><volume>43</volume><issue>5</issue><spage>2276</spage><epage>2288</epage><pages>2276-2288</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>In this paper, we first build a semi‐discretized Crank–Nicolson (CN) model about time for the two‐dimensional (2D) non‐stationary Navier–Stokes equations about vorticity–stream functions and discuss the existence, stability, and convergence of the time semi‐discretized CN solutions. And then, we build a fully discretized finite spectral element CN (FSECN) model based on the bilinear trigonometric basic functions on quadrilateral elements for the 2D non‐stationary Navier–Stokes equations about the vorticity–stream functions and discuss the existence, stability, and convergence of the FSECN solutions. Finally, we utilize two sets of numerical experiments to check out the correctness of theoretical consequences.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.6039</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0002-9469-7018</orcidid></addata></record> |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Computational fluid dynamics Computer simulation Convergence Discretization existence and stability as well as convergence Fluid flow fully discretized finite spectral element Crank–Nicolson model Mathematical models Navier-Stokes equations Quadrilaterals semi‐discretized Crank–Nicolson model Spectral element method Stability Two dimensional models two‐dimensional non‐stationary Navier–Stokes equations about vorticity‐stream functions Vorticity |
| title | The Crank–Nicolson finite spectral element method and numerical simulations for 2D non‐stationary Navier–Stokes equations |
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