A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems
This paper presents a new consistent and stabilized finite-element formulation for fourth-order incompressible flow problems. The formulation is based on the C0-interior penalty method, the Galerkin least-square (GLS) scheme, which assures that the formulation is weakly coercive for spaces that fail...
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| Veröffentlicht in: | Journal of computational physics 2012-06, Vol.231 (16), p.5469-5488 |
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| container_title | Journal of computational physics |
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| creator | Cruz, A.G.B. Dutra do Carmo, E.G. Duda, F.P. |
| description | This paper presents a new consistent and stabilized finite-element formulation for fourth-order incompressible flow problems. The formulation is based on the C0-interior penalty method, the Galerkin least-square (GLS) scheme, which assures that the formulation is weakly coercive for spaces that fail to satisfy the inf-sup condition, and considers discontinuous pressure interpolations. A stability analysis through a lemma establishes that the proposed formulation satisfies the inf-sup condition, thus confirming the robustness of the method. This lemma indicates that, at the element level, there exists an optimal or quasi-optimal GLS stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, the geometry of the finite element, and the fluid viscosity term. Numerical experiments are carried out to illustrate the ability of the formulation to deal with arbitrary interpolations for velocity and pressure, and to stabilize large pressure gradients. |
| doi_str_mv | 10.1016/j.jcp.2012.05.002 |
| format | Article |
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The formulation is based on the C0-interior penalty method, the Galerkin least-square (GLS) scheme, which assures that the formulation is weakly coercive for spaces that fail to satisfy the inf-sup condition, and considers discontinuous pressure interpolations. A stability analysis through a lemma establishes that the proposed formulation satisfies the inf-sup condition, thus confirming the robustness of the method. This lemma indicates that, at the element level, there exists an optimal or quasi-optimal GLS stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, the geometry of the finite element, and the fluid viscosity term. Numerical experiments are carried out to illustrate the ability of the formulation to deal with arbitrary interpolations for velocity and pressure, and to stabilize large pressure gradients.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2012.05.002</identifier><identifier>CODEN: JCTPAH</identifier><language>eng</language><publisher>Kidlington: Elsevier Inc</publisher><subject>Computational fluid dynamics ; Computational techniques ; Discontinuous Galerkin methods ; Exact sciences and technology ; Finite element method ; Fluid flow ; Fourth-order problems ; Galerkin methods ; GLS stability ; Incompressible flow ; Interpolation ; Mathematical analysis ; Mathematical methods in physics ; Mathematical models ; Physics ; Second gradient</subject><ispartof>Journal of computational physics, 2012-06, Vol.231 (16), p.5469-5488</ispartof><rights>2012 Elsevier Inc.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c403t-7814168fe0e46d2a05c1df9e6e93a3b95c5681b671611320961f591c6e0125093</citedby><cites>FETCH-LOGICAL-c403t-7814168fe0e46d2a05c1df9e6e93a3b95c5681b671611320961f591c6e0125093</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0021999112002264$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26030911$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Cruz, A.G.B.</creatorcontrib><creatorcontrib>Dutra do Carmo, E.G.</creatorcontrib><creatorcontrib>Duda, F.P.</creatorcontrib><title>A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems</title><title>Journal of computational physics</title><description>This paper presents a new consistent and stabilized finite-element formulation for fourth-order incompressible flow problems. The formulation is based on the C0-interior penalty method, the Galerkin least-square (GLS) scheme, which assures that the formulation is weakly coercive for spaces that fail to satisfy the inf-sup condition, and considers discontinuous pressure interpolations. A stability analysis through a lemma establishes that the proposed formulation satisfies the inf-sup condition, thus confirming the robustness of the method. This lemma indicates that, at the element level, there exists an optimal or quasi-optimal GLS stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, the geometry of the finite element, and the fluid viscosity term. Numerical experiments are carried out to illustrate the ability of the formulation to deal with arbitrary interpolations for velocity and pressure, and to stabilize large pressure gradients.</description><subject>Computational fluid dynamics</subject><subject>Computational techniques</subject><subject>Discontinuous Galerkin methods</subject><subject>Exact sciences and technology</subject><subject>Finite element method</subject><subject>Fluid flow</subject><subject>Fourth-order problems</subject><subject>Galerkin methods</subject><subject>GLS stability</subject><subject>Incompressible flow</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Mathematical methods in physics</subject><subject>Mathematical models</subject><subject>Physics</subject><subject>Second gradient</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9kMFuHCEMhlGVSt1s-wC9canUy0zsmYEd1FMUNWmkSL0kZ8SCR2E7A1tgE7VPH1YbNbcekDH-bfN_jH1GaBFQXuzand23HWDXgmgBundshaCg6TYoz9iqvmCjlMIP7DznHQCMYhhXLF1yG0P2uVAo3ATHczFbP_u_5I6V4sMhHvKF8_kt4zdmpvTLB75QeYyOTzHVc0jlsYnJUeI-2LjsE-XstzPxaY7PfJ9ivS_5I3s_mTnTp9e4Zg_X3--vfjR3P29ury7vGjtAX5rNiAPKcSKgQbrOgLDoJkWSVG_6rRJWyBG3svpD7DtQEieh0EqqEASofs2-nubWxb8PlIteqgmaZxOomtAI_dgNQslNleJJalPMOdGk98kvJv2pIn3kq3e68tVHvhqErjRrz5fX8SZbM0_JBOvzv8ZOQg-q_mzNvp10VL0-eUo6W0_BkvOJbNEu-v9seQH-DJGE</recordid><startdate>20120620</startdate><enddate>20120620</enddate><creator>Cruz, A.G.B.</creator><creator>Dutra do Carmo, E.G.</creator><creator>Duda, F.P.</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20120620</creationdate><title>A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems</title><author>Cruz, A.G.B. ; Dutra do Carmo, E.G. ; Duda, F.P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c403t-7814168fe0e46d2a05c1df9e6e93a3b95c5681b671611320961f591c6e0125093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Computational fluid dynamics</topic><topic>Computational techniques</topic><topic>Discontinuous Galerkin methods</topic><topic>Exact sciences and technology</topic><topic>Finite element method</topic><topic>Fluid flow</topic><topic>Fourth-order problems</topic><topic>Galerkin methods</topic><topic>GLS stability</topic><topic>Incompressible flow</topic><topic>Interpolation</topic><topic>Mathematical analysis</topic><topic>Mathematical methods in physics</topic><topic>Mathematical models</topic><topic>Physics</topic><topic>Second gradient</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cruz, A.G.B.</creatorcontrib><creatorcontrib>Dutra do Carmo, E.G.</creatorcontrib><creatorcontrib>Duda, F.P.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cruz, A.G.B.</au><au>Dutra do Carmo, E.G.</au><au>Duda, F.P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems</atitle><jtitle>Journal of computational physics</jtitle><date>2012-06-20</date><risdate>2012</risdate><volume>231</volume><issue>16</issue><spage>5469</spage><epage>5488</epage><pages>5469-5488</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><coden>JCTPAH</coden><abstract>This paper presents a new consistent and stabilized finite-element formulation for fourth-order incompressible flow problems. The formulation is based on the C0-interior penalty method, the Galerkin least-square (GLS) scheme, which assures that the formulation is weakly coercive for spaces that fail to satisfy the inf-sup condition, and considers discontinuous pressure interpolations. A stability analysis through a lemma establishes that the proposed formulation satisfies the inf-sup condition, thus confirming the robustness of the method. This lemma indicates that, at the element level, there exists an optimal or quasi-optimal GLS stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, the geometry of the finite element, and the fluid viscosity term. Numerical experiments are carried out to illustrate the ability of the formulation to deal with arbitrary interpolations for velocity and pressure, and to stabilize large pressure gradients.</abstract><cop>Kidlington</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jcp.2012.05.002</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Computational fluid dynamics Computational techniques Discontinuous Galerkin methods Exact sciences and technology Finite element method Fluid flow Fourth-order problems Galerkin methods GLS stability Incompressible flow Interpolation Mathematical analysis Mathematical methods in physics Mathematical models Physics Second gradient |
| title | A consistent and stabilized continuous/discontinuous Galerkin method for fourth-order incompressible flow problems |
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