A Second Order in Time, Decoupled, Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Darcy System
We propose a novel second order in time, fully decoupled and unconditionally stable numerical scheme for solving the Cahn–Hilliard–Darcy system which models two-phase flow in porous medium or in a Hele–Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn–Hilliard...
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| Veröffentlicht in: | Journal of scientific computing 2018-11, Vol.77 (2), p.1210-1233 |
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| container_title | Journal of scientific computing |
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| creator | Han, Daozhi Wang, Xiaoming |
| description | We propose a novel second order in time, fully decoupled and unconditionally stable numerical scheme for solving the Cahn–Hilliard–Darcy system which models two-phase flow in porous medium or in a Hele–Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn–Hilliard equation and pressure-correction for the Darcy equation. The computation of order parameter, pressure and velocity is completely decoupled in our scheme. We show that the scheme is uniquely solvable, unconditionally energy stable and mass-conservative. Ample numerical results are presented to gauge the efficiency and robustness of our scheme. |
| doi_str_mv | 10.1007/s10915-018-0748-0 |
| format | Article |
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The scheme is based on the ideas of second order convex-splitting for the Cahn–Hilliard equation and pressure-correction for the Darcy equation. The computation of order parameter, pressure and velocity is completely decoupled in our scheme. We show that the scheme is uniquely solvable, unconditionally energy stable and mass-conservative. Ample numerical results are presented to gauge the efficiency and robustness of our scheme.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-018-0748-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Computational Mathematics and Numerical Analysis ; Energy ; Lagrange multiplier ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Order parameters ; Permeability ; Porous media ; Reynolds number ; Robustness (mathematics) ; Theoretical ; Two phase flow ; Velocity</subject><ispartof>Journal of scientific computing, 2018-11, Vol.77 (2), p.1210-1233</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-3c60ce07a15e1ce4deda9d70a18aeaa7d03b027c5a06765275acbd738fe419933</citedby><cites>FETCH-LOGICAL-c316t-3c60ce07a15e1ce4deda9d70a18aeaa7d03b027c5a06765275acbd738fe419933</cites><orcidid>0000-0002-2859-7609</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10915-018-0748-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918314271?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Han, Daozhi</creatorcontrib><creatorcontrib>Wang, Xiaoming</creatorcontrib><title>A Second Order in Time, Decoupled, Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Darcy System</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>We propose a novel second order in time, fully decoupled and unconditionally stable numerical scheme for solving the Cahn–Hilliard–Darcy system which models two-phase flow in porous medium or in a Hele–Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn–Hilliard equation and pressure-correction for the Darcy equation. The computation of order parameter, pressure and velocity is completely decoupled in our scheme. We show that the scheme is uniquely solvable, unconditionally energy stable and mass-conservative. Ample numerical results are presented to gauge the efficiency and robustness of our scheme.</description><subject>Algorithms</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Energy</subject><subject>Lagrange multiplier</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Order parameters</subject><subject>Permeability</subject><subject>Porous media</subject><subject>Reynolds number</subject><subject>Robustness (mathematics)</subject><subject>Theoretical</subject><subject>Two phase flow</subject><subject>Velocity</subject><issn>0885-7474</issn><issn>1573-7691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kM1OAjEQxxujiYg-gLcmXlmd2a_uHgmomBA5AOemtIMs2Q9odw_cfAff0CexZE08eZmZTH6_SebP2D3CIwKIJ4eQYxIAZgGI2JcLNsBERIFIc7xkA8iyJBCxiK_ZjXN7AMizPByw45gvSTe14QtryPKi5quiohGf-m13KMmM-Lo-A0VbNLUqyxNftmpTEn_vKrKFViVf6h1VxLeN5e2O-ETt6u_Pr1lRloWyxo9TZbX3Tq6l6pZdbVXp6O63D9n65Xk1mQXzxevbZDwPdIRpG0Q6BU0gFCaEmmJDRuVGgMJMkVLCQLSBUOhEQSrSJBSJ0hsjomxLMeZ5FA3ZQ3_3YJtjR66V-6az_gMnwxyzCONQoKewp7RtnLO0lQdbVMqeJII8Jyv7ZKVPVp6TleCdsHecZ-sPsn-X_5d-ALNifbA</recordid><startdate>20181101</startdate><enddate>20181101</enddate><creator>Han, Daozhi</creator><creator>Wang, Xiaoming</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><orcidid>https://orcid.org/0000-0002-2859-7609</orcidid></search><sort><creationdate>20181101</creationdate><title>A Second Order in Time, Decoupled, Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Darcy System</title><author>Han, Daozhi ; Wang, Xiaoming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-3c60ce07a15e1ce4deda9d70a18aeaa7d03b027c5a06765275acbd738fe419933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algorithms</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Energy</topic><topic>Lagrange multiplier</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Order parameters</topic><topic>Permeability</topic><topic>Porous media</topic><topic>Reynolds number</topic><topic>Robustness (mathematics)</topic><topic>Theoretical</topic><topic>Two phase flow</topic><topic>Velocity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Han, Daozhi</creatorcontrib><creatorcontrib>Wang, Xiaoming</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>Journal of scientific computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Han, Daozhi</au><au>Wang, Xiaoming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Second Order in Time, Decoupled, Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Darcy System</atitle><jtitle>Journal of scientific computing</jtitle><stitle>J Sci Comput</stitle><date>2018-11-01</date><risdate>2018</risdate><volume>77</volume><issue>2</issue><spage>1210</spage><epage>1233</epage><pages>1210-1233</pages><issn>0885-7474</issn><eissn>1573-7691</eissn><abstract>We propose a novel second order in time, fully decoupled and unconditionally stable numerical scheme for solving the Cahn–Hilliard–Darcy system which models two-phase flow in porous medium or in a Hele–Shaw cell. The scheme is based on the ideas of second order convex-splitting for the Cahn–Hilliard equation and pressure-correction for the Darcy equation. The computation of order parameter, pressure and velocity is completely decoupled in our scheme. We show that the scheme is uniquely solvable, unconditionally energy stable and mass-conservative. Ample numerical results are presented to gauge the efficiency and robustness of our scheme.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-018-0748-0</doi><tpages>24</tpages><orcidid>https://orcid.org/0000-0002-2859-7609</orcidid></addata></record> |
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| ispartof | Journal of scientific computing, 2018-11, Vol.77 (2), p.1210-1233 |
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| language | eng |
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| source | SpringerNature Journals; ProQuest Central UK/Ireland; ProQuest Central |
| subjects | Algorithms Computational Mathematics and Numerical Analysis Energy Lagrange multiplier Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Order parameters Permeability Porous media Reynolds number Robustness (mathematics) Theoretical Two phase flow Velocity |
| title | A Second Order in Time, Decoupled, Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Darcy System |
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