Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics
In this article, we consider exactly divergence-free H (div)-conforming finite element methods for time-dependent incompressible viscous flow problems. This is an extension of previous research concerning divergence-free H 1 -conforming methods. For the linearised Oseen case, the first semi-discrete...
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| Veröffentlicht in: | Journal of scientific computing 2018-05, Vol.75 (2), p.830-858 |
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| creator | Schroeder, Philipp W. Lube, Gert |
| description | In this article, we consider exactly divergence-free
H
(div)-conforming finite element methods for time-dependent incompressible viscous flow problems. This is an extension of previous research concerning divergence-free
H
1
-conforming methods. For the linearised Oseen case, the first semi-discrete numerical analysis for time-dependent flows is presented whereby special emphasis is put on pressure- and Reynolds-semi-robustness. For convection-dominated problems, the proposed method relies on a velocity jump upwind stabilisation which is not gradient-based. Complementing the theoretical results,
H
(div)-FEM are applied to the simulation of full nonlinear Navier–Stokes problems. Focussing on dynamic high Reynolds number examples with vortical structures, the proposed method proves to be capable of reliably handling the planar lattice flow problem, Kelvin–Helmholtz instabilities and freely decaying two-dimensional turbulence. |
| doi_str_mv | 10.1007/s10915-017-0561-1 |
| format | Article |
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H
(div)-conforming finite element methods for time-dependent incompressible viscous flow problems. This is an extension of previous research concerning divergence-free
H
1
-conforming methods. For the linearised Oseen case, the first semi-discrete numerical analysis for time-dependent flows is presented whereby special emphasis is put on pressure- and Reynolds-semi-robustness. For convection-dominated problems, the proposed method relies on a velocity jump upwind stabilisation which is not gradient-based. Complementing the theoretical results,
H
(div)-FEM are applied to the simulation of full nonlinear Navier–Stokes problems. Focussing on dynamic high Reynolds number examples with vortical structures, the proposed method proves to be capable of reliably handling the planar lattice flow problem, Kelvin–Helmholtz instabilities and freely decaying two-dimensional turbulence.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-017-0561-1</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Approximation ; Computational Mathematics and Numerical Analysis ; Error analysis ; Estimates ; Finite element method ; Fluid flow ; High Reynolds number ; Incompressible flow ; Kelvin-Helmholtz instability ; Kinematics ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Numerical analysis ; Reynolds number ; Robustness (mathematics) ; Theoretical ; Time dependence ; Velocity ; Viscosity ; Viscous flow</subject><ispartof>Journal of scientific computing, 2018-05, Vol.75 (2), p.830-858</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Springer Science+Business Media, LLC 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-3cf69fe1249f26f8910e90bbe4bb32dcff159446fe8ee68a7102a8385c732bae3</citedby><cites>FETCH-LOGICAL-c316t-3cf69fe1249f26f8910e90bbe4bb32dcff159446fe8ee68a7102a8385c732bae3</cites><orcidid>0000-0001-7644-4693</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10915-017-0561-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918312931?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,778,782,21371,27907,27908,33727,41471,42540,43788,51302,64366,64370,72220</link.rule.ids></links><search><creatorcontrib>Schroeder, Philipp W.</creatorcontrib><creatorcontrib>Lube, Gert</creatorcontrib><title>Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>In this article, we consider exactly divergence-free
H
(div)-conforming finite element methods for time-dependent incompressible viscous flow problems. This is an extension of previous research concerning divergence-free
H
1
-conforming methods. For the linearised Oseen case, the first semi-discrete numerical analysis for time-dependent flows is presented whereby special emphasis is put on pressure- and Reynolds-semi-robustness. For convection-dominated problems, the proposed method relies on a velocity jump upwind stabilisation which is not gradient-based. Complementing the theoretical results,
H
(div)-FEM are applied to the simulation of full nonlinear Navier–Stokes problems. Focussing on dynamic high Reynolds number examples with vortical structures, the proposed method proves to be capable of reliably handling the planar lattice flow problem, Kelvin–Helmholtz instabilities and freely decaying two-dimensional turbulence.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Error analysis</subject><subject>Estimates</subject><subject>Finite element method</subject><subject>Fluid flow</subject><subject>High Reynolds number</subject><subject>Incompressible flow</subject><subject>Kelvin-Helmholtz instability</subject><subject>Kinematics</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical analysis</subject><subject>Reynolds number</subject><subject>Robustness (mathematics)</subject><subject>Theoretical</subject><subject>Time dependence</subject><subject>Velocity</subject><subject>Viscosity</subject><subject>Viscous flow</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kEtLJDEURsOgMO3jB8wu4EYX0dykHslSbNsWdAYGnW2oSt-0kaqkTKp1GvzxdtOCK1d3c8534RDyC_g5cF5fZOAaSsahZrysgMEPMoGylqyuNOyRCVeqZHVRFz_JQc7PnHOttJiQ96l_xbTEYJHNEiKdny786xmbXd9TFxN98D2yKQ4YFhhGehts7IeEOfu2Qzrr4lumb358opfD0HnbjD6GTMdI5375RP_iOsRukenvVd9iov9iGvE_na5D03ubj8i-a7qMx5_3kDzOrh-u5uzuz83t1eUdsxKqkUnrKu0QRKGdqJzSwFHztsWibaVYWOeg1EVROVSIlWpq4KJRUpW2lqJtUB6Sk93ukOLLCvNonuMqhc1LIzQoCUJL2FCwo2yKOSd0Zki-b9LaADfbyGYX2Wwim21ks3XEzskbNiwxfS1_L30ANxyABg</recordid><startdate>20180501</startdate><enddate>20180501</enddate><creator>Schroeder, Philipp W.</creator><creator>Lube, Gert</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0001-7644-4693</orcidid></search><sort><creationdate>20180501</creationdate><title>Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics</title><author>Schroeder, Philipp W. ; Lube, Gert</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-3cf69fe1249f26f8910e90bbe4bb32dcff159446fe8ee68a7102a8385c732bae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Error analysis</topic><topic>Estimates</topic><topic>Finite element method</topic><topic>Fluid flow</topic><topic>High Reynolds number</topic><topic>Incompressible flow</topic><topic>Kelvin-Helmholtz instability</topic><topic>Kinematics</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical analysis</topic><topic>Reynolds number</topic><topic>Robustness (mathematics)</topic><topic>Theoretical</topic><topic>Time dependence</topic><topic>Velocity</topic><topic>Viscosity</topic><topic>Viscous flow</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schroeder, Philipp W.</creatorcontrib><creatorcontrib>Lube, Gert</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Journal of scientific computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schroeder, Philipp W.</au><au>Lube, Gert</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2018-05-01</date><risdate>2018</risdate><volume>75</volume><issue>2</issue><spage>830</spage><epage>858</epage><pages>830-858</pages><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>In this article, we consider exactly divergence-free
H
(div)-conforming finite element methods for time-dependent incompressible viscous flow problems. This is an extension of previous research concerning divergence-free
H
1
-conforming methods. For the linearised Oseen case, the first semi-discrete numerical analysis for time-dependent flows is presented whereby special emphasis is put on pressure- and Reynolds-semi-robustness. For convection-dominated problems, the proposed method relies on a velocity jump upwind stabilisation which is not gradient-based. Complementing the theoretical results,
H
(div)-FEM are applied to the simulation of full nonlinear Navier–Stokes problems. Focussing on dynamic high Reynolds number examples with vortical structures, the proposed method proves to be capable of reliably handling the planar lattice flow problem, Kelvin–Helmholtz instabilities and freely decaying two-dimensional turbulence.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-017-0561-1</doi><tpages>29</tpages><orcidid>https://orcid.org/0000-0001-7644-4693</orcidid></addata></record> |
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| subjects | Algorithms Approximation Computational Mathematics and Numerical Analysis Error analysis Estimates Finite element method Fluid flow High Reynolds number Incompressible flow Kelvin-Helmholtz instability Kinematics Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Numerical analysis Reynolds number Robustness (mathematics) Theoretical Time dependence Velocity Viscosity Viscous flow |
| title | Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics |
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