An implicit simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible isothermal flows
•An implicit simplified SGKS is presented for simulation of 3D incompressible isothermal flows.•The formulations for numerical fluxes at the cell interface can be given explicitly and concisely.•The implicit LU-SGS method is introduced to further improve the computational efficiency and numerical st...
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| Veröffentlicht in: | Computers & fluids 2018-01, Vol.160, p.204-218 |
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| creator | Yang, L.M. Shu, C. Yang, W.M. Wang, Y. Lee, C.B. |
| description | •An implicit simplified SGKS is presented for simulation of 3D incompressible isothermal flows.•The formulations for numerical fluxes at the cell interface can be given explicitly and concisely.•The implicit LU-SGS method is introduced to further improve the computational efficiency and numerical stability.•The computational efficiency of present scheme is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS).
In this work, an implicit simplified sphere function-based gas kinetic scheme (SGKS) is presented for simulation of 3D incompressible isothermal flows. At first, the numerical fluxes of governing equations are reconstructed by the local solution of Boltzmann equation with sphere function distribution. Due to incompressible limit, the sphere at cell interface can be approximately considered to be symmetric as shown in the work. Besides that, the energy equation is usually not needed for simulation of incompressible isothermal flows. With all these simplifications, the formulations of the simplified SGKS can be expressed concisely and explicitly. Secondly, the commonly-used implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method is adopted to further improve the computational efficiency and numerical stability of present scheme. In LU-SGS method, only a forward and a backward sweep are needed for marching the conservative variables in time. As a result, the simplified SGKS with the LU-SGS method can be implemented easily. Numerical experiments, including the 3D lid-driven cavity flow and flow over a backward-facing step, showed that the incompressible isothermal flows can be well simulated by the developed scheme and its computational efficiency is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS). In addition, it was found that the present scheme with the LU-SGS method is more efficient than that with the explicit Euler method, and the speedup ratio is about 2 to 5. |
| doi_str_mv | 10.1016/j.compfluid.2017.11.001 |
| format | Article |
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In this work, an implicit simplified sphere function-based gas kinetic scheme (SGKS) is presented for simulation of 3D incompressible isothermal flows. At first, the numerical fluxes of governing equations are reconstructed by the local solution of Boltzmann equation with sphere function distribution. Due to incompressible limit, the sphere at cell interface can be approximately considered to be symmetric as shown in the work. Besides that, the energy equation is usually not needed for simulation of incompressible isothermal flows. With all these simplifications, the formulations of the simplified SGKS can be expressed concisely and explicitly. Secondly, the commonly-used implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method is adopted to further improve the computational efficiency and numerical stability of present scheme. In LU-SGS method, only a forward and a backward sweep are needed for marching the conservative variables in time. As a result, the simplified SGKS with the LU-SGS method can be implemented easily. Numerical experiments, including the 3D lid-driven cavity flow and flow over a backward-facing step, showed that the incompressible isothermal flows can be well simulated by the developed scheme and its computational efficiency is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS). In addition, it was found that the present scheme with the LU-SGS method is more efficient than that with the explicit Euler method, and the speedup ratio is about 2 to 5.</description><identifier>ISSN: 0045-7930</identifier><identifier>EISSN: 1879-0747</identifier><identifier>DOI: 10.1016/j.compfluid.2017.11.001</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>3D incompressible isothermal flows ; Boltzmann transport equation ; Cavity flow ; Computational efficiency ; Computational fluid dynamics ; Computational mathematics ; Computer simulation ; Computing time ; Explicit Euler method ; Fluid flow ; Fluxes ; Formulations ; Gas flow ; Implicit LU-SGS method ; Incompressible flow ; Lattice theory ; Numerical analysis ; Numerical stability ; Simplified SGKS ; Studies ; Three dimensional flow</subject><ispartof>Computers & fluids, 2018-01, Vol.160, p.204-218</ispartof><rights>2017 Elsevier Ltd</rights><rights>Copyright Elsevier BV Jan 4, 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c343t-ed62b1fef8a4fb704fbb404165d39d8b5fbe9c2cb5b791738459f86373f39d083</citedby><cites>FETCH-LOGICAL-c343t-ed62b1fef8a4fb704fbb404165d39d8b5fbe9c2cb5b791738459f86373f39d083</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S004579301730395X$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids></links><search><creatorcontrib>Yang, L.M.</creatorcontrib><creatorcontrib>Shu, C.</creatorcontrib><creatorcontrib>Yang, W.M.</creatorcontrib><creatorcontrib>Wang, Y.</creatorcontrib><creatorcontrib>Lee, C.B.</creatorcontrib><title>An implicit simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible isothermal flows</title><title>Computers & fluids</title><description>•An implicit simplified SGKS is presented for simulation of 3D incompressible isothermal flows.•The formulations for numerical fluxes at the cell interface can be given explicitly and concisely.•The implicit LU-SGS method is introduced to further improve the computational efficiency and numerical stability.•The computational efficiency of present scheme is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS).
In this work, an implicit simplified sphere function-based gas kinetic scheme (SGKS) is presented for simulation of 3D incompressible isothermal flows. At first, the numerical fluxes of governing equations are reconstructed by the local solution of Boltzmann equation with sphere function distribution. Due to incompressible limit, the sphere at cell interface can be approximately considered to be symmetric as shown in the work. Besides that, the energy equation is usually not needed for simulation of incompressible isothermal flows. With all these simplifications, the formulations of the simplified SGKS can be expressed concisely and explicitly. Secondly, the commonly-used implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method is adopted to further improve the computational efficiency and numerical stability of present scheme. In LU-SGS method, only a forward and a backward sweep are needed for marching the conservative variables in time. As a result, the simplified SGKS with the LU-SGS method can be implemented easily. Numerical experiments, including the 3D lid-driven cavity flow and flow over a backward-facing step, showed that the incompressible isothermal flows can be well simulated by the developed scheme and its computational efficiency is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS). In addition, it was found that the present scheme with the LU-SGS method is more efficient than that with the explicit Euler method, and the speedup ratio is about 2 to 5.</description><subject>3D incompressible isothermal flows</subject><subject>Boltzmann transport equation</subject><subject>Cavity flow</subject><subject>Computational efficiency</subject><subject>Computational fluid dynamics</subject><subject>Computational mathematics</subject><subject>Computer simulation</subject><subject>Computing time</subject><subject>Explicit Euler method</subject><subject>Fluid flow</subject><subject>Fluxes</subject><subject>Formulations</subject><subject>Gas flow</subject><subject>Implicit LU-SGS method</subject><subject>Incompressible flow</subject><subject>Lattice theory</subject><subject>Numerical analysis</subject><subject>Numerical stability</subject><subject>Simplified SGKS</subject><subject>Studies</subject><subject>Three dimensional flow</subject><issn>0045-7930</issn><issn>1879-0747</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNqFUE1PxCAQJUYT19XfIInnVii0tMfN-pls4kXPpNDBpbalQqvx30td49ULw8y892bmIXRJSUoJLa7bVLt-NN1smzQjVKSUpoTQI7SipagSIrg4RitCeJ6IipFTdBZCS2LOMr5C02bAth87q-2Ew8_PWGhwGPfgAZt50JN1Q6LqEKuvdcBvdoDJahz0HvqIcH7hzV294LAzmN1gOyw7eQjBqg6wDW6Kcn3dYdO5z3COTkzdBbj4jWv0cnf7vH1Idk_3j9vNLtGMsymBpsgUNWDKmhslSHwUJ5wWecOqplS5UVDpTKtciYoKVvK8MmXBBDOxT0q2RlcH3dG79xnCJFs3-yGOlLQq84oUnPKIEgeU9i4ED0aO3va1_5KUyMVi2co_i-VisaRURosjc3NgQjziw4KXQVsYNDTWg55k4-y_Gt9nHIuZ</recordid><startdate>20180104</startdate><enddate>20180104</enddate><creator>Yang, L.M.</creator><creator>Shu, C.</creator><creator>Yang, W.M.</creator><creator>Wang, Y.</creator><creator>Lee, C.B.</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20180104</creationdate><title>An implicit simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible isothermal flows</title><author>Yang, L.M. ; Shu, C. ; Yang, W.M. ; Wang, Y. ; Lee, C.B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-ed62b1fef8a4fb704fbb404165d39d8b5fbe9c2cb5b791738459f86373f39d083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>3D incompressible isothermal flows</topic><topic>Boltzmann transport equation</topic><topic>Cavity flow</topic><topic>Computational efficiency</topic><topic>Computational fluid dynamics</topic><topic>Computational mathematics</topic><topic>Computer simulation</topic><topic>Computing time</topic><topic>Explicit Euler method</topic><topic>Fluid flow</topic><topic>Fluxes</topic><topic>Formulations</topic><topic>Gas flow</topic><topic>Implicit LU-SGS method</topic><topic>Incompressible flow</topic><topic>Lattice theory</topic><topic>Numerical analysis</topic><topic>Numerical stability</topic><topic>Simplified SGKS</topic><topic>Studies</topic><topic>Three dimensional flow</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yang, L.M.</creatorcontrib><creatorcontrib>Shu, C.</creatorcontrib><creatorcontrib>Yang, W.M.</creatorcontrib><creatorcontrib>Wang, Y.</creatorcontrib><creatorcontrib>Lee, C.B.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace 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>Computers & fluids</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yang, L.M.</au><au>Shu, C.</au><au>Yang, W.M.</au><au>Wang, Y.</au><au>Lee, C.B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An implicit simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible isothermal flows</atitle><jtitle>Computers & fluids</jtitle><date>2018-01-04</date><risdate>2018</risdate><volume>160</volume><spage>204</spage><epage>218</epage><pages>204-218</pages><issn>0045-7930</issn><eissn>1879-0747</eissn><abstract>•An implicit simplified SGKS is presented for simulation of 3D incompressible isothermal flows.•The formulations for numerical fluxes at the cell interface can be given explicitly and concisely.•The implicit LU-SGS method is introduced to further improve the computational efficiency and numerical stability.•The computational efficiency of present scheme is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS).
In this work, an implicit simplified sphere function-based gas kinetic scheme (SGKS) is presented for simulation of 3D incompressible isothermal flows. At first, the numerical fluxes of governing equations are reconstructed by the local solution of Boltzmann equation with sphere function distribution. Due to incompressible limit, the sphere at cell interface can be approximately considered to be symmetric as shown in the work. Besides that, the energy equation is usually not needed for simulation of incompressible isothermal flows. With all these simplifications, the formulations of the simplified SGKS can be expressed concisely and explicitly. Secondly, the commonly-used implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method is adopted to further improve the computational efficiency and numerical stability of present scheme. In LU-SGS method, only a forward and a backward sweep are needed for marching the conservative variables in time. As a result, the simplified SGKS with the LU-SGS method can be implemented easily. Numerical experiments, including the 3D lid-driven cavity flow and flow over a backward-facing step, showed that the incompressible isothermal flows can be well simulated by the developed scheme and its computational efficiency is significantly higher than that of the original SGKS and the lattice Boltzmann flux solver (LBFS). In addition, it was found that the present scheme with the LU-SGS method is more efficient than that with the explicit Euler method, and the speedup ratio is about 2 to 5.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.compfluid.2017.11.001</doi><tpages>15</tpages></addata></record> |
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| subjects | 3D incompressible isothermal flows Boltzmann transport equation Cavity flow Computational efficiency Computational fluid dynamics Computational mathematics Computer simulation Computing time Explicit Euler method Fluid flow Fluxes Formulations Gas flow Implicit LU-SGS method Incompressible flow Lattice theory Numerical analysis Numerical stability Simplified SGKS Studies Three dimensional flow |
| title | An implicit simplified sphere function-based gas kinetic scheme for simulation of 3D incompressible isothermal flows |
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