An Efficient Second-Order Algorithm Upon MAC Scheme for Nonlinear Incompressible Darcy–Brinkman–Forchheimer Model
In this paper, the Marker and Cell scheme based on a two-grid algorithm is proposed for the two-dimensional incompressible Darcy–Brinkman–Forchheimer equations in porous media. The motivation of the two-grid Marker and Cell algorithm is figuring out a nonlinear equation on a coarse grid with mesh si...
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| Veröffentlicht in: | Journal of mathematical fluid mechanics 2024-05, Vol.26 (2), Article 28 |
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| creator | Wang, Pengshan Liu, Wei Fan, Gexian Song, Yingxue |
| description | In this paper, the Marker and Cell scheme based on a two-grid algorithm is proposed for the two-dimensional incompressible Darcy–Brinkman–Forchheimer equations in porous media. The motivation of the two-grid Marker and Cell algorithm is figuring out a nonlinear equation on a coarse grid with mesh size
H
and a linear equation on a fine grid with mesh size
h
. A small positive parameter
ε
is introduced. By using it, the non-differentiable nonlinear term can be transformed into the term which is twice continuously differentiable. The error estimates of the velocity and pressure in the
L
2
norms are obtained, which show
O
(
ε
+
H
4
+
h
2
)
. Second-order accuracy for some terms of velocity in the
H
1
norms is also obtained. Several numerical experiments are provided to confirm the availability of this efficient second-order algorithm. Behavior of the fluid flow with different Brinkman number is considered. |
| doi_str_mv | 10.1007/s00021-024-00851-w |
| format | Article |
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H
and a linear equation on a fine grid with mesh size
h
. A small positive parameter
ε
is introduced. By using it, the non-differentiable nonlinear term can be transformed into the term which is twice continuously differentiable. The error estimates of the velocity and pressure in the
L
2
norms are obtained, which show
O
(
ε
+
H
4
+
h
2
)
. Second-order accuracy for some terms of velocity in the
H
1
norms is also obtained. Several numerical experiments are provided to confirm the availability of this efficient second-order algorithm. Behavior of the fluid flow with different Brinkman number is considered.</description><identifier>ISSN: 1422-6928</identifier><identifier>EISSN: 1422-6952</identifier><identifier>DOI: 10.1007/s00021-024-00851-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algorithms ; Brinkman model ; Classical and Continuum Physics ; Finite element method ; Fluid flow ; Fluid- and Aerodynamics ; Incompressible flow ; Linear equations ; Mathematical Methods in Physics ; Nonlinear equations ; Norms ; Original Research ; Physics ; Physics and Astronomy ; Porous media</subject><ispartof>Journal of mathematical fluid mechanics, 2024-05, Vol.26 (2), Article 28</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-1277d82f6513896a2a798815ff0f0f7cb0dd87c022973ef11f766c15d889e6bb3</cites><orcidid>0000-0002-1970-4951</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/s00021-024-00851-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00021-024-00851-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Wang, Pengshan</creatorcontrib><creatorcontrib>Liu, Wei</creatorcontrib><creatorcontrib>Fan, Gexian</creatorcontrib><creatorcontrib>Song, Yingxue</creatorcontrib><title>An Efficient Second-Order Algorithm Upon MAC Scheme for Nonlinear Incompressible Darcy–Brinkman–Forchheimer Model</title><title>Journal of mathematical fluid mechanics</title><addtitle>J. Math. Fluid Mech</addtitle><description>In this paper, the Marker and Cell scheme based on a two-grid algorithm is proposed for the two-dimensional incompressible Darcy–Brinkman–Forchheimer equations in porous media. The motivation of the two-grid Marker and Cell algorithm is figuring out a nonlinear equation on a coarse grid with mesh size
H
and a linear equation on a fine grid with mesh size
h
. A small positive parameter
ε
is introduced. By using it, the non-differentiable nonlinear term can be transformed into the term which is twice continuously differentiable. The error estimates of the velocity and pressure in the
L
2
norms are obtained, which show
O
(
ε
+
H
4
+
h
2
)
. Second-order accuracy for some terms of velocity in the
H
1
norms is also obtained. Several numerical experiments are provided to confirm the availability of this efficient second-order algorithm. Behavior of the fluid flow with different Brinkman number is considered.</description><subject>Algorithms</subject><subject>Brinkman model</subject><subject>Classical and Continuum Physics</subject><subject>Finite element method</subject><subject>Fluid flow</subject><subject>Fluid- and Aerodynamics</subject><subject>Incompressible flow</subject><subject>Linear equations</subject><subject>Mathematical Methods in Physics</subject><subject>Nonlinear equations</subject><subject>Norms</subject><subject>Original Research</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Porous media</subject><issn>1422-6928</issn><issn>1422-6952</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAYhCMEEqXwAkyWmAO_nSZ2xlAoVGrpUDpbiWM3Lokd7FRVN96BN-RJCBTBhv7hbri7X_qC4BLDNQagNx4ACA6BjEIAFuNwdxQM8IiQMEljcvzrCTsNzrzfAGAap2QQbDOD7pXSQkvToaUU1pThwpXSoaxeW6e7qkGr1ho0z8ZoKSrZSKSsQ0_W1NrI3KGpEbZpnfReF7VEd7kT-4-391unzUuTm95OrBNVJXXTr85tKevz4ETltZcXPzoMVpP75_FjOFs8TMfZLBSEQhdiQmnJiEpiHLE0yUlOU8ZwrBT0R0UBZcmoAEJSGkmFsaJJInBcMpbKpCiiYXB12G2dfd1K3_GN3TrTv-QR4BGQOI2TPkUOKeGs904q3jrd5G7PMfAvvPyAl_d4-TdevutL0aHk-7BZS_c3_U_rE2dTf9s</recordid><startdate>20240501</startdate><enddate>20240501</enddate><creator>Wang, Pengshan</creator><creator>Liu, Wei</creator><creator>Fan, Gexian</creator><creator>Song, Yingxue</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-1970-4951</orcidid></search><sort><creationdate>20240501</creationdate><title>An Efficient Second-Order Algorithm Upon MAC Scheme for Nonlinear Incompressible Darcy–Brinkman–Forchheimer Model</title><author>Wang, Pengshan ; Liu, Wei ; Fan, Gexian ; Song, Yingxue</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-1277d82f6513896a2a798815ff0f0f7cb0dd87c022973ef11f766c15d889e6bb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Brinkman model</topic><topic>Classical and Continuum Physics</topic><topic>Finite element method</topic><topic>Fluid flow</topic><topic>Fluid- and Aerodynamics</topic><topic>Incompressible flow</topic><topic>Linear equations</topic><topic>Mathematical Methods in Physics</topic><topic>Nonlinear equations</topic><topic>Norms</topic><topic>Original Research</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Porous media</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Pengshan</creatorcontrib><creatorcontrib>Liu, Wei</creatorcontrib><creatorcontrib>Fan, Gexian</creatorcontrib><creatorcontrib>Song, Yingxue</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of mathematical fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Pengshan</au><au>Liu, Wei</au><au>Fan, Gexian</au><au>Song, Yingxue</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Efficient Second-Order Algorithm Upon MAC Scheme for Nonlinear Incompressible Darcy–Brinkman–Forchheimer Model</atitle><jtitle>Journal of mathematical fluid mechanics</jtitle><stitle>J. Math. Fluid Mech</stitle><date>2024-05-01</date><risdate>2024</risdate><volume>26</volume><issue>2</issue><artnum>28</artnum><issn>1422-6928</issn><eissn>1422-6952</eissn><abstract>In this paper, the Marker and Cell scheme based on a two-grid algorithm is proposed for the two-dimensional incompressible Darcy–Brinkman–Forchheimer equations in porous media. The motivation of the two-grid Marker and Cell algorithm is figuring out a nonlinear equation on a coarse grid with mesh size
H
and a linear equation on a fine grid with mesh size
h
. A small positive parameter
ε
is introduced. By using it, the non-differentiable nonlinear term can be transformed into the term which is twice continuously differentiable. The error estimates of the velocity and pressure in the
L
2
norms are obtained, which show
O
(
ε
+
H
4
+
h
2
)
. Second-order accuracy for some terms of velocity in the
H
1
norms is also obtained. Several numerical experiments are provided to confirm the availability of this efficient second-order algorithm. Behavior of the fluid flow with different Brinkman number is considered.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00021-024-00851-w</doi><orcidid>https://orcid.org/0000-0002-1970-4951</orcidid></addata></record> |
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| subjects | Algorithms Brinkman model Classical and Continuum Physics Finite element method Fluid flow Fluid- and Aerodynamics Incompressible flow Linear equations Mathematical Methods in Physics Nonlinear equations Norms Original Research Physics Physics and Astronomy Porous media |
| title | An Efficient Second-Order Algorithm Upon MAC Scheme for Nonlinear Incompressible Darcy–Brinkman–Forchheimer Model |
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