A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows
Purpose – The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems. Design/methodology/approach – The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solve...
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| Veröffentlicht in: | International journal of numerical methods for heat & fluid flow 2014-01, Vol.24 (3), p.735-759 |
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| container_title | International journal of numerical methods for heat & fluid flow |
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| creator | Younes, Anis Makradi, Ahmed Zidane, Ali Shao, Qian Bouhala, Lyazid |
| description | Purpose
– The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems.
Design/methodology/approach
– The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error.
Findings
– Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity.
Originality/value
– The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel. |
| doi_str_mv | 10.1108/HFF-07-2012-0156 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_emera</sourceid><recordid>TN_cdi_emerald_primary_10_1108_HFF-07-2012-0156</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1541432281</sourcerecordid><originalsourceid>FETCH-LOGICAL-c377t-a16147ab4bb0c2e713bac0845c7721e1cbbc255b5b116fadba681eb435311c553</originalsourceid><addsrcrecordid>eNqFkb1P3DAYh60KpB7QvaMllg415zeO7dx4OgggHQIhOlu246iGxKZ2cu31r2-i61JUieldnt_79SD0GegFAK2WN3VNqCQFhYJQ4OIDWoDkFRG84kdoQVcCCOds9RGd5PxMKeWiFAvUrLGNvfFBDz4GHFu8SXH87fwv8qh3XqfhK7702cYw-DDGMeNr3bn04gPWocF3D_Ua9274HpuM25iwGeNeB7snTfI7F3DbxZ_5DB23usvu0996ir7VV0-bG7K9v77drLfEMikHokFAKbUpjaG2cBKY0ZZWJbdSFuDAGmMLzg03AKLVjdGiAmdKxhmAnY47RV8OfV9T_DG6PKh-Wt11nQ5uWl2BlJSx-S3vo7yEkhVFBRN6_gZ9jmMK0yETVVDByhXMs-mBsinmnFyrXpPvddoroGo2pCZDiko1G1KzoSmyPERc75Lumv8l_nHK_gClNZDT</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1520634915</pqid></control><display><type>article</type><title>A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows</title><source>Emerald Journals</source><creator>Younes, Anis ; Makradi, Ahmed ; Zidane, Ali ; Shao, Qian ; Bouhala, Lyazid</creator><creatorcontrib>Younes, Anis ; Makradi, Ahmed ; Zidane, Ali ; Shao, Qian ; Bouhala, Lyazid</creatorcontrib><description>Purpose
– The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems.
Design/methodology/approach
– The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error.
Findings
– Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity.
Originality/value
– The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel.</description><identifier>ISSN: 0961-5539</identifier><identifier>EISSN: 1758-6585</identifier><identifier>DOI: 10.1108/HFF-07-2012-0156</identifier><identifier>CODEN: INMFEM</identifier><language>eng</language><publisher>Bradford: Emerald Group Publishing Limited</publisher><subject>Algorithms ; Approximation ; Buoyancy ; Convection ; Engineering ; Finite element analysis ; Finite volume method ; Fluid flow ; Heat ; Holes ; Mathematical analysis ; Mathematical models ; Mechanical engineering ; Navier-Stokes equations ; Numerical analysis ; Partial differential equations ; Problems ; Reynolds number ; Studies ; Temperature gradients ; Truncation errors ; Velocity</subject><ispartof>International journal of numerical methods for heat & fluid flow, 2014-01, Vol.24 (3), p.735-759</ispartof><rights>Emerald Group Publishing Limited</rights><rights>Copyright Emerald Group Publishing Limited 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c377t-a16147ab4bb0c2e713bac0845c7721e1cbbc255b5b116fadba681eb435311c553</citedby><cites>FETCH-LOGICAL-c377t-a16147ab4bb0c2e713bac0845c7721e1cbbc255b5b116fadba681eb435311c553</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.emerald.com/insight/content/doi/10.1108/HFF-07-2012-0156/full/pdf$$EPDF$$P50$$Gemerald$$H</linktopdf><linktohtml>$$Uhttps://www.emerald.com/insight/content/doi/10.1108/HFF-07-2012-0156/full/html$$EHTML$$P50$$Gemerald$$H</linktohtml><link.rule.ids>314,776,780,961,11615,27903,27904,52664,52667</link.rule.ids></links><search><creatorcontrib>Younes, Anis</creatorcontrib><creatorcontrib>Makradi, Ahmed</creatorcontrib><creatorcontrib>Zidane, Ali</creatorcontrib><creatorcontrib>Shao, Qian</creatorcontrib><creatorcontrib>Bouhala, Lyazid</creatorcontrib><title>A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows</title><title>International journal of numerical methods for heat & fluid flow</title><description>Purpose
– The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems.
Design/methodology/approach
– The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error.
Findings
– Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity.
Originality/value
– The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Buoyancy</subject><subject>Convection</subject><subject>Engineering</subject><subject>Finite element analysis</subject><subject>Finite volume method</subject><subject>Fluid flow</subject><subject>Heat</subject><subject>Holes</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mechanical engineering</subject><subject>Navier-Stokes equations</subject><subject>Numerical analysis</subject><subject>Partial differential equations</subject><subject>Problems</subject><subject>Reynolds number</subject><subject>Studies</subject><subject>Temperature gradients</subject><subject>Truncation errors</subject><subject>Velocity</subject><issn>0961-5539</issn><issn>1758-6585</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqFkb1P3DAYh60KpB7QvaMllg415zeO7dx4OgggHQIhOlu246iGxKZ2cu31r2-i61JUieldnt_79SD0GegFAK2WN3VNqCQFhYJQ4OIDWoDkFRG84kdoQVcCCOds9RGd5PxMKeWiFAvUrLGNvfFBDz4GHFu8SXH87fwv8qh3XqfhK7702cYw-DDGMeNr3bn04gPWocF3D_Ua9274HpuM25iwGeNeB7snTfI7F3DbxZ_5DB23usvu0996ir7VV0-bG7K9v77drLfEMikHokFAKbUpjaG2cBKY0ZZWJbdSFuDAGmMLzg03AKLVjdGiAmdKxhmAnY47RV8OfV9T_DG6PKh-Wt11nQ5uWl2BlJSx-S3vo7yEkhVFBRN6_gZ9jmMK0yETVVDByhXMs-mBsinmnFyrXpPvddoroGo2pCZDiko1G1KzoSmyPERc75Lumv8l_nHK_gClNZDT</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Younes, Anis</creator><creator>Makradi, Ahmed</creator><creator>Zidane, Ali</creator><creator>Shao, Qian</creator><creator>Bouhala, Lyazid</creator><general>Emerald Group Publishing Limited</general><scope>AAYXX</scope><scope>CITATION</scope><scope>0U~</scope><scope>1-H</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F1W</scope><scope>FR3</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>H96</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K6~</scope><scope>KR7</scope><scope>L.-</scope><scope>L.0</scope><scope>L.G</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQBIZ</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope><scope>7UA</scope><scope>C1K</scope></search><sort><creationdate>20140101</creationdate><title>A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows</title><author>Younes, Anis ; Makradi, Ahmed ; Zidane, Ali ; Shao, Qian ; Bouhala, Lyazid</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c377t-a16147ab4bb0c2e713bac0845c7721e1cbbc255b5b116fadba681eb435311c553</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Buoyancy</topic><topic>Convection</topic><topic>Engineering</topic><topic>Finite element analysis</topic><topic>Finite volume method</topic><topic>Fluid flow</topic><topic>Heat</topic><topic>Holes</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mechanical engineering</topic><topic>Navier-Stokes equations</topic><topic>Numerical analysis</topic><topic>Partial differential equations</topic><topic>Problems</topic><topic>Reynolds number</topic><topic>Studies</topic><topic>Temperature gradients</topic><topic>Truncation errors</topic><topic>Velocity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Younes, Anis</creatorcontrib><creatorcontrib>Makradi, Ahmed</creatorcontrib><creatorcontrib>Zidane, Ali</creatorcontrib><creatorcontrib>Shao, Qian</creatorcontrib><creatorcontrib>Bouhala, Lyazid</creatorcontrib><collection>CrossRef</collection><collection>Global News & ABI/Inform Professional</collection><collection>Trade PRO</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Technology Research 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Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Business</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><collection>Water Resources Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><jtitle>International journal of numerical methods for heat & fluid flow</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Younes, Anis</au><au>Makradi, Ahmed</au><au>Zidane, Ali</au><au>Shao, Qian</au><au>Bouhala, Lyazid</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows</atitle><jtitle>International journal of numerical methods for heat & fluid flow</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>24</volume><issue>3</issue><spage>735</spage><epage>759</epage><pages>735-759</pages><issn>0961-5539</issn><eissn>1758-6585</eissn><coden>INMFEM</coden><abstract>Purpose
– The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems.
Design/methodology/approach
– The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error.
Findings
– Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity.
Originality/value
– The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel.</abstract><cop>Bradford</cop><pub>Emerald Group Publishing Limited</pub><doi>10.1108/HFF-07-2012-0156</doi><tpages>25</tpages></addata></record> |
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| identifier | ISSN: 0961-5539 |
| ispartof | International journal of numerical methods for heat & fluid flow, 2014-01, Vol.24 (3), p.735-759 |
| issn | 0961-5539 1758-6585 |
| language | eng |
| recordid | cdi_emerald_primary_10_1108_HFF-07-2012-0156 |
| source | Emerald Journals |
| subjects | Algorithms Approximation Buoyancy Convection Engineering Finite element analysis Finite volume method Fluid flow Heat Holes Mathematical analysis Mathematical models Mechanical engineering Navier-Stokes equations Numerical analysis Partial differential equations Problems Reynolds number Studies Temperature gradients Truncation errors Velocity |
| title | A combination of Crouzeix-Raviart, Discontinuous Galerkin and MPFA methods for buoyancy-driven flows |
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