Immersed boundary method for unsteady kinetic model equations
Summary Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (int...
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| Veröffentlicht in: | International journal for numerical methods in fluids 2016-03, Vol.80 (8), p.453-475 |
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| container_title | International journal for numerical methods in fluids |
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| creator | Pekardan, Cem Chigullapalli, Sruti Sun, Lin Alexeenko, Alina |
| description | Summary
Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.
We present immersed boundary method formulations for the Boltzmann model kinetic equation for solution of unsteady rarefied flows. The first formulation is based on the interpolation often applied for continuum flows, whereas the relaxation method exploits locally an analytical solution of the collisionless Boltzmann equation. The third approach combines relaxation of the velocity distribution function with interpolation of macroparameters and shows the fastest convergence. |
| doi_str_mv | 10.1002/fld.4085 |
| format | Article |
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Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.
We present immersed boundary method formulations for the Boltzmann model kinetic equation for solution of unsteady rarefied flows. The first formulation is based on the interpolation often applied for continuum flows, whereas the relaxation method exploits locally an analytical solution of the collisionless Boltzmann equation. The third approach combines relaxation of the velocity distribution function with interpolation of macroparameters and shows the fastest convergence.</description><identifier>ISSN: 0271-2091</identifier><identifier>EISSN: 1097-0363</identifier><identifier>DOI: 10.1002/fld.4085</identifier><identifier>CODEN: IJNFDW</identifier><language>eng</language><publisher>Bognor Regis: Blackwell Publishing Ltd</publisher><subject>Boltzmann equation ; Boltzmann kinetic model equation ; Boundaries ; Flux ; gas damping ; immersed boundary method ; Interpolation ; Mathematical analysis ; Mathematical models ; microflows ; Navier-Stokes equations ; rarefied gas dynamics ; Unsteady</subject><ispartof>International journal for numerical methods in fluids, 2016-03, Vol.80 (8), p.453-475</ispartof><rights>Copyright © 2015 John Wiley & Sons, Ltd.</rights><rights>Copyright © 2016 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4675-cef0f5bb1b33e344e11f7d445b3db8d0142abb8fa8576649f336ff13f5b9c8313</citedby><cites>FETCH-LOGICAL-c4675-cef0f5bb1b33e344e11f7d445b3db8d0142abb8fa8576649f336ff13f5b9c8313</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Ffld.4085$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Ffld.4085$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Pekardan, Cem</creatorcontrib><creatorcontrib>Chigullapalli, Sruti</creatorcontrib><creatorcontrib>Sun, Lin</creatorcontrib><creatorcontrib>Alexeenko, Alina</creatorcontrib><title>Immersed boundary method for unsteady kinetic model equations</title><title>International journal for numerical methods in fluids</title><addtitle>Int. J. Numer. Meth. Fluids</addtitle><description>Summary
Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.
We present immersed boundary method formulations for the Boltzmann model kinetic equation for solution of unsteady rarefied flows. The first formulation is based on the interpolation often applied for continuum flows, whereas the relaxation method exploits locally an analytical solution of the collisionless Boltzmann equation. The third approach combines relaxation of the velocity distribution function with interpolation of macroparameters and shows the fastest convergence.</description><subject>Boltzmann equation</subject><subject>Boltzmann kinetic model equation</subject><subject>Boundaries</subject><subject>Flux</subject><subject>gas damping</subject><subject>immersed boundary method</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>microflows</subject><subject>Navier-Stokes equations</subject><subject>rarefied gas dynamics</subject><subject>Unsteady</subject><issn>0271-2091</issn><issn>1097-0363</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNqF0E1LxDAQgOEgCq4f4E8oePFSnWnSJD14kPUTFgVR9BbaJsGubeMmLbr_3iyKoiCecnkyw7yE7CEcIkB2ZFt9yEDma2SCUIgUKKfrZAKZwDSDAjfJVghzACgySSfk-KrrjA9GJ5Ube136ZdKZ4cnpxDqfjH0YTKmXyXPTm6Gpk85p0yZmMZZD4_qwQzZs2Qaz-_luk_vzs7vpZTq7ubianszSmnGRp7WxYPOqwopSQxkziFZoxvKK6kpqQJaVVSVtKXPBOSsspdxapPFPUUuKdJscfMx98W4xmjCorgm1aduyN24MCiUAk1gU4n8q4oq4BrNI93_RuRt9Hw-JiiNHylF-D6y9C8Ebq15808VQCkGtkquYXK2SR5p-0NemNcs_nTqfnf70Tcz89uVL_6y4oCJXD9cXSua31yAoU4_0HSELj34</recordid><startdate>20160320</startdate><enddate>20160320</enddate><creator>Pekardan, Cem</creator><creator>Chigullapalli, Sruti</creator><creator>Sun, Lin</creator><creator>Alexeenko, Alina</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QH</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>7UA</scope><scope>8FD</scope><scope>C1K</scope><scope>F1W</scope><scope>FR3</scope><scope>H8D</scope><scope>H96</scope><scope>JQ2</scope><scope>KR7</scope><scope>L.G</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20160320</creationdate><title>Immersed boundary method for unsteady kinetic model equations</title><author>Pekardan, Cem ; Chigullapalli, Sruti ; Sun, Lin ; Alexeenko, Alina</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4675-cef0f5bb1b33e344e11f7d445b3db8d0142abb8fa8576649f336ff13f5b9c8313</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Boltzmann equation</topic><topic>Boltzmann kinetic model equation</topic><topic>Boundaries</topic><topic>Flux</topic><topic>gas damping</topic><topic>immersed boundary method</topic><topic>Interpolation</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>microflows</topic><topic>Navier-Stokes equations</topic><topic>rarefied gas dynamics</topic><topic>Unsteady</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pekardan, Cem</creatorcontrib><creatorcontrib>Chigullapalli, Sruti</creatorcontrib><creatorcontrib>Sun, Lin</creatorcontrib><creatorcontrib>Alexeenko, Alina</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Aqualine</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Water Resources Abstracts</collection><collection>Technology Research Database</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</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>International journal for numerical methods in fluids</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pekardan, Cem</au><au>Chigullapalli, Sruti</au><au>Sun, Lin</au><au>Alexeenko, Alina</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Immersed boundary method for unsteady kinetic model equations</atitle><jtitle>International journal for numerical methods in fluids</jtitle><addtitle>Int. J. Numer. Meth. Fluids</addtitle><date>2016-03-20</date><risdate>2016</risdate><volume>80</volume><issue>8</issue><spage>453</spage><epage>475</epage><pages>453-475</pages><issn>0271-2091</issn><eissn>1097-0363</eissn><coden>IJNFDW</coden><abstract>Summary
Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.
We present immersed boundary method formulations for the Boltzmann model kinetic equation for solution of unsteady rarefied flows. The first formulation is based on the interpolation often applied for continuum flows, whereas the relaxation method exploits locally an analytical solution of the collisionless Boltzmann equation. The third approach combines relaxation of the velocity distribution function with interpolation of macroparameters and shows the fastest convergence.</abstract><cop>Bognor Regis</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/fld.4085</doi><tpages>23</tpages></addata></record> |
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| subjects | Boltzmann equation Boltzmann kinetic model equation Boundaries Flux gas damping immersed boundary method Interpolation Mathematical analysis Mathematical models microflows Navier-Stokes equations rarefied gas dynamics Unsteady |
| title | Immersed boundary method for unsteady kinetic model equations |
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