CFD high-order accurate scheme Jacobian-Free Newton Krylov method
•We applied JFNK method to CFD high-order accurate scheme.•We formed a nonlinear type of preconditioner.•A high efficiency precondition matrix for high-order accurate scheme was formed.•Test cases shown that wall time was saved half with JFNK method. High-order accurate scheme for Computational Flui...
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| Veröffentlicht in: | Computers & fluids 2015-03, Vol.110, p.43-47 |
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| container_title | Computers & fluids |
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| creator | Liu, Wei Zhang, Lilun Zhong, Ying Wang, Yongxian Che, Yonggang Xu, Chuanfu Cheng, Xinghua |
| description | •We applied JFNK method to CFD high-order accurate scheme.•We formed a nonlinear type of preconditioner.•A high efficiency precondition matrix for high-order accurate scheme was formed.•Test cases shown that wall time was saved half with JFNK method.
High-order accurate scheme for Computational Fluid Dynamics (CFD) finite difference method can provide more exact flow field solution than second order accurate scheme, but it is hard to get Jacobian matrix for lower–upper symmetric Gauss–Seidel (LU-SGS) method because of its complicated computing stencil, which lead to the poor convergence speed of LU-SGS. A Jacobian-Free Newton–Krylov (JFNK) method of high-order accurate scheme was developed, and a nonlinear type of preconditioner was applied based on traditional 7 diagonals matrix, which was solved with LU-SGS method. In cylinder steady flow case, JFNK method was better than original LU-SGS method, nearly one half wall time was saved. |
| doi_str_mv | 10.1016/j.compfluid.2014.11.019 |
| format | Article |
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High-order accurate scheme for Computational Fluid Dynamics (CFD) finite difference method can provide more exact flow field solution than second order accurate scheme, but it is hard to get Jacobian matrix for lower–upper symmetric Gauss–Seidel (LU-SGS) method because of its complicated computing stencil, which lead to the poor convergence speed of LU-SGS. A Jacobian-Free Newton–Krylov (JFNK) method of high-order accurate scheme was developed, and a nonlinear type of preconditioner was applied based on traditional 7 diagonals matrix, which was solved with LU-SGS method. In cylinder steady flow case, JFNK method was better than original LU-SGS method, nearly one half wall time was saved.</description><identifier>ISSN: 0045-7930</identifier><identifier>EISSN: 1879-0747</identifier><identifier>DOI: 10.1016/j.compfluid.2014.11.019</identifier><language>eng</language><publisher>Elsevier Ltd</publisher><subject>CFD ; Computational fluid dynamics ; Convergence ; Cylinders ; Finite difference method ; High-order accurate scheme ; Jacobian matrix ; JFNK ; Mathematical analysis ; Mathematical models ; Nonlinear preconditioner ; Walls</subject><ispartof>Computers & fluids, 2015-03, Vol.110, p.43-47</ispartof><rights>2014 Elsevier Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c521t-4d84d5af056baec1ae7dbfbc5deca20885c6361a7b8f36bbcd46dd456fb0058c3</citedby><cites>FETCH-LOGICAL-c521t-4d84d5af056baec1ae7dbfbc5deca20885c6361a7b8f36bbcd46dd456fb0058c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.compfluid.2014.11.019$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Liu, Wei</creatorcontrib><creatorcontrib>Zhang, Lilun</creatorcontrib><creatorcontrib>Zhong, Ying</creatorcontrib><creatorcontrib>Wang, Yongxian</creatorcontrib><creatorcontrib>Che, Yonggang</creatorcontrib><creatorcontrib>Xu, Chuanfu</creatorcontrib><creatorcontrib>Cheng, Xinghua</creatorcontrib><title>CFD high-order accurate scheme Jacobian-Free Newton Krylov method</title><title>Computers & fluids</title><description>•We applied JFNK method to CFD high-order accurate scheme.•We formed a nonlinear type of preconditioner.•A high efficiency precondition matrix for high-order accurate scheme was formed.•Test cases shown that wall time was saved half with JFNK method.
High-order accurate scheme for Computational Fluid Dynamics (CFD) finite difference method can provide more exact flow field solution than second order accurate scheme, but it is hard to get Jacobian matrix for lower–upper symmetric Gauss–Seidel (LU-SGS) method because of its complicated computing stencil, which lead to the poor convergence speed of LU-SGS. A Jacobian-Free Newton–Krylov (JFNK) method of high-order accurate scheme was developed, and a nonlinear type of preconditioner was applied based on traditional 7 diagonals matrix, which was solved with LU-SGS method. In cylinder steady flow case, JFNK method was better than original LU-SGS method, nearly one half wall time was saved.</description><subject>CFD</subject><subject>Computational fluid dynamics</subject><subject>Convergence</subject><subject>Cylinders</subject><subject>Finite difference method</subject><subject>High-order accurate scheme</subject><subject>Jacobian matrix</subject><subject>JFNK</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Nonlinear preconditioner</subject><subject>Walls</subject><issn>0045-7930</issn><issn>1879-0747</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNqNkMtOwzAQRS0EEuXxDWTJJsGTOHG6rArlVcEG1pYznhBXSVzstKh_T6oitrAaXencK81h7Ap4AhyKm1WCrlvX7caaJOUgEoCEw_SITaCU05hLIY_ZhHORx3Ka8VN2FsKKjzlLxYTN5ovbqLEfTey8IR9pxI3XA0UBG-ooetLoKqv7eOGJohf6GlwfPftd67ZRR0PjzAU7qXUb6PLnnrP3xd3b_CFevt4_zmfLGPMUhliYUphc1zwvKk0ImqSp6gpzQ6hTXpY5FlkBWlZlnRVVhUYUxoi8qCvO8xKzc3Z92F1797mhMKjOBqS21T25TVAg-VSmaSbkv1AoiwzKEZUHFL0LwVOt1t522u8UcLX3q1bq16_a-1UAavQ7NmeHJo1Pby15FdBSj2SsJxyUcfbPjW84dohF</recordid><startdate>20150301</startdate><enddate>20150301</enddate><creator>Liu, Wei</creator><creator>Zhang, Lilun</creator><creator>Zhong, Ying</creator><creator>Wang, Yongxian</creator><creator>Che, Yonggang</creator><creator>Xu, Chuanfu</creator><creator>Cheng, Xinghua</creator><general>Elsevier Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7UA</scope><scope>C1K</scope><scope>F1W</scope><scope>H96</scope><scope>L.G</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>20150301</creationdate><title>CFD high-order accurate scheme Jacobian-Free Newton Krylov method</title><author>Liu, Wei ; Zhang, Lilun ; Zhong, Ying ; Wang, Yongxian ; Che, Yonggang ; Xu, Chuanfu ; Cheng, Xinghua</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c521t-4d84d5af056baec1ae7dbfbc5deca20885c6361a7b8f36bbcd46dd456fb0058c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>CFD</topic><topic>Computational fluid dynamics</topic><topic>Convergence</topic><topic>Cylinders</topic><topic>Finite difference method</topic><topic>High-order accurate scheme</topic><topic>Jacobian matrix</topic><topic>JFNK</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Nonlinear preconditioner</topic><topic>Walls</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Wei</creatorcontrib><creatorcontrib>Zhang, Lilun</creatorcontrib><creatorcontrib>Zhong, Ying</creatorcontrib><creatorcontrib>Wang, Yongxian</creatorcontrib><creatorcontrib>Che, Yonggang</creatorcontrib><creatorcontrib>Xu, Chuanfu</creatorcontrib><creatorcontrib>Cheng, Xinghua</creatorcontrib><collection>CrossRef</collection><collection>Water Resources Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</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>Liu, Wei</au><au>Zhang, Lilun</au><au>Zhong, Ying</au><au>Wang, Yongxian</au><au>Che, Yonggang</au><au>Xu, Chuanfu</au><au>Cheng, Xinghua</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>CFD high-order accurate scheme Jacobian-Free Newton Krylov method</atitle><jtitle>Computers & fluids</jtitle><date>2015-03-01</date><risdate>2015</risdate><volume>110</volume><spage>43</spage><epage>47</epage><pages>43-47</pages><issn>0045-7930</issn><eissn>1879-0747</eissn><abstract>•We applied JFNK method to CFD high-order accurate scheme.•We formed a nonlinear type of preconditioner.•A high efficiency precondition matrix for high-order accurate scheme was formed.•Test cases shown that wall time was saved half with JFNK method.
High-order accurate scheme for Computational Fluid Dynamics (CFD) finite difference method can provide more exact flow field solution than second order accurate scheme, but it is hard to get Jacobian matrix for lower–upper symmetric Gauss–Seidel (LU-SGS) method because of its complicated computing stencil, which lead to the poor convergence speed of LU-SGS. A Jacobian-Free Newton–Krylov (JFNK) method of high-order accurate scheme was developed, and a nonlinear type of preconditioner was applied based on traditional 7 diagonals matrix, which was solved with LU-SGS method. In cylinder steady flow case, JFNK method was better than original LU-SGS method, nearly one half wall time was saved.</abstract><pub>Elsevier Ltd</pub><doi>10.1016/j.compfluid.2014.11.019</doi><tpages>5</tpages></addata></record> |
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| subjects | CFD Computational fluid dynamics Convergence Cylinders Finite difference method High-order accurate scheme Jacobian matrix JFNK Mathematical analysis Mathematical models Nonlinear preconditioner Walls |
| title | CFD high-order accurate scheme Jacobian-Free Newton Krylov method |
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