On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes
This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order O(M *) where M * is the reference Mach number even if the initial data are well-prepared and contain only pressure fluct...
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| Veröffentlicht in: | Computers & fluids 2004-05, Vol.33 (4), p.655-675 |
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| container_title | Computers & fluids |
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| creator | Guillard, Hervé Murrone, Angelo |
| description | This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order
O(M
*)
where
M
* is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order
O(M
*
2)
. We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. We show that this strategy allows to recover a correct scaling of the pressure fluctuations. Numerical experiments confirm these theoretical results. |
| doi_str_mv | 10.1016/j.compfluid.2003.07.001 |
| format | Article |
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O(M
*)
where
M
* is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order
O(M
*
2)
. We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. We show that this strategy allows to recover a correct scaling of the pressure fluctuations. Numerical experiments confirm these theoretical results.</description><identifier>ISSN: 0045-7930</identifier><identifier>EISSN: 1879-0747</identifier><identifier>DOI: 10.1016/j.compfluid.2003.07.001</identifier><identifier>CODEN: CPFLBI</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Compressible flows; shock and detonation phenomena ; Computational methods in fluid dynamics ; Computational Physics ; Engineering Sciences ; Exact sciences and technology ; Fluid dynamics ; Fluid mechanics ; Fluids mechanics ; Fundamental areas of phenomenology (including applications) ; General subsonic flows ; Mathematical Physics ; Mathematics ; Mechanics ; Numerical Analysis ; Physics</subject><ispartof>Computers & fluids, 2004-05, Vol.33 (4), p.655-675</ispartof><rights>2003 Elsevier Ltd</rights><rights>2004 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c457t-68fce21a752c7a6de0b27608e546f64c330f8978b4b61ab75b939208903629b83</citedby><cites>FETCH-LOGICAL-c457t-68fce21a752c7a6de0b27608e546f64c330f8978b4b61ab75b939208903629b83</cites><orcidid>0000-0003-3099-4408</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0045793003000781$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15503249$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://inria.hal.science/hal-00871719$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Guillard, Hervé</creatorcontrib><creatorcontrib>Murrone, Angelo</creatorcontrib><title>On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes</title><title>Computers & fluids</title><description>This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order
O(M
*)
where
M
* is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order
O(M
*
2)
. We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. We show that this strategy allows to recover a correct scaling of the pressure fluctuations. Numerical experiments confirm these theoretical results.</description><subject>Compressible flows; shock and detonation phenomena</subject><subject>Computational methods in fluid dynamics</subject><subject>Computational Physics</subject><subject>Engineering Sciences</subject><subject>Exact sciences and technology</subject><subject>Fluid dynamics</subject><subject>Fluid mechanics</subject><subject>Fluids mechanics</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>General subsonic flows</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Mechanics</subject><subject>Numerical Analysis</subject><subject>Physics</subject><issn>0045-7930</issn><issn>1879-0747</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNqFkE1r3DAQQEVpoNukv6G6tNCDnZE_9NHbEppkYUMuLfQmZHmMtdiWK9kb8u9r4yQ99iRGvJkHj5DPDFIGjF-fUuv7selmV6cZQJ6CSAHYO7JjUqgERCHekx1AUSZC5fCBfIzxBMucZ8WO_H4c6NQirbA1Z-cD9Q2dxyc31DTaFnuM1G1E55_og7EtHea-wkA717vpOz0cUnrn63nwZzo9j_i6dkUuGtNF_PTyXpJftz9-3twnx8e7w83-mNiiFFPCZWMxY0aUmRWG1whVJjhILAve8MLmOTRSCVkVFWemEmWlcpWBVJDzTFUyvyTftrut6fQYXG_Cs_bG6fv9Ua9_AFIwwdSZLezXjR2D_zNjnHTvosWuMwP6OepMZpyXXC2g2EAbfIwBm7fLDPRaXZ_0W3W9VtcgFtOq-PKiMNGarglmsC7-Wy9LWLqvhv3G4dLm7DDoaB0OFmsX0E669u6_rr8SOJor</recordid><startdate>20040501</startdate><enddate>20040501</enddate><creator>Guillard, Hervé</creator><creator>Murrone, Angelo</creator><general>Elsevier Ltd</general><general>Elsevier Science</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-3099-4408</orcidid></search><sort><creationdate>20040501</creationdate><title>On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes</title><author>Guillard, Hervé ; Murrone, Angelo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c457t-68fce21a752c7a6de0b27608e546f64c330f8978b4b61ab75b939208903629b83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Compressible flows; shock and detonation phenomena</topic><topic>Computational methods in fluid dynamics</topic><topic>Computational Physics</topic><topic>Engineering Sciences</topic><topic>Exact sciences and technology</topic><topic>Fluid dynamics</topic><topic>Fluid mechanics</topic><topic>Fluids mechanics</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>General subsonic flows</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Mechanics</topic><topic>Numerical Analysis</topic><topic>Physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guillard, Hervé</creatorcontrib><creatorcontrib>Murrone, Angelo</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Computers & fluids</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guillard, Hervé</au><au>Murrone, Angelo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes</atitle><jtitle>Computers & fluids</jtitle><date>2004-05-01</date><risdate>2004</risdate><volume>33</volume><issue>4</issue><spage>655</spage><epage>675</epage><pages>655-675</pages><issn>0045-7930</issn><eissn>1879-0747</eissn><coden>CPFLBI</coden><abstract>This paper presents an analysis of Godunov scheme in the low Mach number regime. We study the Riemann problem and show that the interface pressure contains acoustic waves of order
O(M
*)
where
M
* is the reference Mach number even if the initial data are well-prepared and contain only pressure fluctuations of order
O(M
*
2)
. We then propose to modify the fluxes computed by Godunov type schemes by solving a preconditioned Riemann problem instead of the original one. We show that this strategy allows to recover a correct scaling of the pressure fluctuations. Numerical experiments confirm these theoretical results.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.compfluid.2003.07.001</doi><tpages>21</tpages><orcidid>https://orcid.org/0000-0003-3099-4408</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Computers & fluids, 2004-05, Vol.33 (4), p.655-675 |
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| source | Elsevier ScienceDirect Journals |
| subjects | Compressible flows shock and detonation phenomena Computational methods in fluid dynamics Computational Physics Engineering Sciences Exact sciences and technology Fluid dynamics Fluid mechanics Fluids mechanics Fundamental areas of phenomenology (including applications) General subsonic flows Mathematical Physics Mathematics Mechanics Numerical Analysis Physics |
| title | On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes |
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