Explicit time integration scheme with large time steps for first order transient problems using finite increment calculus
We present an explicit integration scheme for solving the transient heat conduction equation that allows larger time steps than the standard forward Euler scheme. The derivation starts from a higher order form of the governing differential equations of the problem obtained using a Finite Increment C...
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| Veröffentlicht in: | Computer methods in applied mechanics and engineering 2022-12, Vol.402, p.115332, Article 115332 |
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| container_title | Computer methods in applied mechanics and engineering |
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| creator | Oñate, Eugenio de Pouplana, Ignasi Zárate, Francisco |
| description | We present an explicit integration scheme for solving the transient heat conduction equation that allows larger time steps than the standard forward Euler scheme. The derivation starts from a higher order form of the governing differential equations of the problem obtained using a Finite Increment Calculus (FIC) procedure. The efficiency of the new explicit integration scheme in terms of substantial gains in the time step size versus the forward Euler scheme is verified in the solution of transient heat conduction problems in one and two dimensions. The method is readily extendible to other problems in mechanics governed by the first order transient differential equation. |
| doi_str_mv | 10.1016/j.cma.2022.115332 |
| format | Article |
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The method is readily extendible to other problems in mechanics governed by the first order transient differential equation.</description><identifier>ISSN: 0045-7825</identifier><identifier>EISSN: 1879-2138</identifier><identifier>DOI: 10.1016/j.cma.2022.115332</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Conduction heating ; Conductive heat transfer ; Differential calculus ; Differential equations ; Explicit scheme ; Finite increment calculus ; First order equation ; Heat conduction ; Large time steps ; Time integration ; Transient heat conduction</subject><ispartof>Computer methods in applied mechanics and engineering, 2022-12, Vol.402, p.115332, Article 115332</ispartof><rights>2022</rights><rights>Copyright Elsevier BV Dec 1, 2022</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c255t-15375913328fcc8bb44b89b008ddb10ce40009eb2b76e68af3595022df2b32803</citedby><cites>FETCH-LOGICAL-c255t-15375913328fcc8bb44b89b008ddb10ce40009eb2b76e68af3595022df2b32803</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S004578252200425X$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65534</link.rule.ids></links><search><creatorcontrib>Oñate, Eugenio</creatorcontrib><creatorcontrib>de Pouplana, Ignasi</creatorcontrib><creatorcontrib>Zárate, Francisco</creatorcontrib><title>Explicit time integration scheme with large time steps for first order transient problems using finite increment calculus</title><title>Computer methods in applied mechanics and engineering</title><description>We present an explicit integration scheme for solving the transient heat conduction equation that allows larger time steps than the standard forward Euler scheme. 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The method is readily extendible to other problems in mechanics governed by the first order transient differential equation.</description><subject>Conduction heating</subject><subject>Conductive heat transfer</subject><subject>Differential calculus</subject><subject>Differential equations</subject><subject>Explicit scheme</subject><subject>Finite increment calculus</subject><subject>First order equation</subject><subject>Heat conduction</subject><subject>Large time steps</subject><subject>Time integration</subject><subject>Transient heat conduction</subject><issn>0045-7825</issn><issn>1879-2138</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kEtPwzAQhC0EEqXwA7hZ4pxiO0njiBOqykOqxAXOlu1sWkd5YTtA_z1bhTO-WLJndmc-Qm45W3HG1_fNynZ6JZgQK87zNBVnZMFlUSaCp_KcLBjL8qSQIr8kVyE0DI_kYkGO25-xddZFGl0H1PUR9l5HN_Q02APg07eLB9pqv4dZEiKMgdaDp7XzIdLBV-Bp9LoPDvpIRz-YFrpAp-D6PYp6F0-Drcdp-G91a6d2CtfkotZtgJu_e0k-nrbvm5dk9_b8unncJVbkeUywTJGXHBvJ2lppTJYZWRqMX1WGMwsZVinBCFOsYS11neZljhiqWhj0sHRJ7ua5GOxzghBVM0y-x5VKFEUmsqzgElV8Vlk_hOChVqN3nfZHxZk6EVaNQsLqRFjNhNHzMHsA43858CpYRGChch5sVNXg_nH_Akd9hSQ</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Oñate, Eugenio</creator><creator>de Pouplana, Ignasi</creator><creator>Zárate, Francisco</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20221201</creationdate><title>Explicit time integration scheme with large time steps for first order transient problems using finite increment calculus</title><author>Oñate, Eugenio ; de Pouplana, Ignasi ; Zárate, Francisco</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c255t-15375913328fcc8bb44b89b008ddb10ce40009eb2b76e68af3595022df2b32803</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Conduction heating</topic><topic>Conductive heat transfer</topic><topic>Differential calculus</topic><topic>Differential equations</topic><topic>Explicit scheme</topic><topic>Finite increment calculus</topic><topic>First order equation</topic><topic>Heat conduction</topic><topic>Large time steps</topic><topic>Time integration</topic><topic>Transient heat conduction</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Oñate, Eugenio</creatorcontrib><creatorcontrib>de Pouplana, Ignasi</creatorcontrib><creatorcontrib>Zárate, Francisco</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research 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>Computer methods in applied mechanics and engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Oñate, Eugenio</au><au>de Pouplana, Ignasi</au><au>Zárate, Francisco</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Explicit time integration scheme with large time steps for first order transient problems using finite increment calculus</atitle><jtitle>Computer methods in applied mechanics and engineering</jtitle><date>2022-12-01</date><risdate>2022</risdate><volume>402</volume><spage>115332</spage><pages>115332-</pages><artnum>115332</artnum><issn>0045-7825</issn><eissn>1879-2138</eissn><abstract>We present an explicit integration scheme for solving the transient heat conduction equation that allows larger time steps than the standard forward Euler scheme. 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| ispartof | Computer methods in applied mechanics and engineering, 2022-12, Vol.402, p.115332, Article 115332 |
| issn | 0045-7825 1879-2138 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Conduction heating Conductive heat transfer Differential calculus Differential equations Explicit scheme Finite increment calculus First order equation Heat conduction Large time steps Time integration Transient heat conduction |
| title | Explicit time integration scheme with large time steps for first order transient problems using finite increment calculus |
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