A Characteristic Mapping method for the two-dimensional incompressible Euler equations
•The method achieves third-order global convergence as derived in section 3.3.1 and demonstrated numerically in section 3.3.2.•The method provides an accurate conservation of all vorticity moments (Corollary 1, section 3.3.1), and e.g. 4.1 and 4.2 (Tables 2 and 4).•The method has long-time stability...
Gespeichert in:
Veröffentlicht in: | Journal of computational physics 2021-01, Vol.424, p.109781, Article 109781 |
---|---|
Hauptverfasser: | , , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | |
container_start_page | 109781 |
container_title | Journal of computational physics |
container_volume | 424 |
creator | Yin, Xi-Yuan Mercier, Olivier Yadav, Badal Schneider, Kai Nave, Jean-Christophe |
description | •The method achieves third-order global convergence as derived in section 3.3.1 and demonstrated numerically in section 3.3.2.•The method provides an accurate conservation of all vorticity moments (Corollary 1, section 3.3.1), and e.g. 4.1 and 4.2 (Tables 2 and 4).•The method has long-time stability. Section 4.1 and 4.2 carry out the same tests featured in [15]. Additionally, similar tests are run to longer times with no issues.•The Characteristic Mapping method provides arbitrary subgrid resolution of the solution. We provide a 8192X zoom into the solution in Figs. 7, 8, 9 and 10.
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. This new approach evolves the flow map using a combination of the Characteristic Mapping (CM) method [1] the gradient-augmented level-set (GALS) method [2]. The flow map possesses a semigroup structure which allows for the decomposition of a long-time deformation into short-time submaps. This leads to a numerical scheme that achieves exponential resolution in linear time. Error estimates are provided and conservation properties are analysed. The computational efficiency and the high precision of the method are illustrated in the vortex merger, four-modes and random flow problems. Comparisons with the Cauchy-Lagrangian method [3] are also presented. |
doi_str_mv | 10.1016/j.jcp.2020.109781 |
format | Article |
fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_02616194v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0021999120305556</els_id><sourcerecordid>2469188174</sourcerecordid><originalsourceid>FETCH-LOGICAL-c359t-8364d235efe0d225f845e9ed9c3e649c053042434a8f17cbf383bd2473b9b583</originalsourceid><addsrcrecordid>eNp9kDtPwzAUhS0EEuXxA9gsMTGk-JXEFlNVAUUqYqlYLce5oY7SOLVdEP-eVEGMTPd1zpHuh9ANJXNKaHHfzls7zBlhx1mVkp6g2diQjJW0OEUzQhjNlFL0HF3E2BJCZC7kDL0v8HJrgrEJgovJWfxqhsH1H3gHaetr3PiA0xZw-vJZ7XbQR-d702HXW78bAsToqg7w46GDgGF_MGm8xyt01pguwvVvvUSbp8fNcpWt355flot1ZnmuUiZ5IWrGc2iA1IzljRQ5KKiV5VAIZUnOiWCCCyMbWtqq4ZJXNRMlr1SVS36J7qbYren0ENzOhG_tjdOrxVofd4QVtKBKfNJReztph-D3B4hJt_4QxleiZqJQVEpailFFJ5UNPsYAzV8sJfpIWrd6JK2PpPVEevQ8TB4YP_10EHS0DnoLtQtgk669-8f9A-EuhUI</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2469188174</pqid></control><display><type>article</type><title>A Characteristic Mapping method for the two-dimensional incompressible Euler equations</title><source>Access via ScienceDirect (Elsevier)</source><creator>Yin, Xi-Yuan ; Mercier, Olivier ; Yadav, Badal ; Schneider, Kai ; Nave, Jean-Christophe</creator><creatorcontrib>Yin, Xi-Yuan ; Mercier, Olivier ; Yadav, Badal ; Schneider, Kai ; Nave, Jean-Christophe</creatorcontrib><description>•The method achieves third-order global convergence as derived in section 3.3.1 and demonstrated numerically in section 3.3.2.•The method provides an accurate conservation of all vorticity moments (Corollary 1, section 3.3.1), and e.g. 4.1 and 4.2 (Tables 2 and 4).•The method has long-time stability. Section 4.1 and 4.2 carry out the same tests featured in [15]. Additionally, similar tests are run to longer times with no issues.•The Characteristic Mapping method provides arbitrary subgrid resolution of the solution. We provide a 8192X zoom into the solution in Figs. 7, 8, 9 and 10.
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. This new approach evolves the flow map using a combination of the Characteristic Mapping (CM) method [1] the gradient-augmented level-set (GALS) method [2]. The flow map possesses a semigroup structure which allows for the decomposition of a long-time deformation into short-time submaps. This leads to a numerical scheme that achieves exponential resolution in linear time. Error estimates are provided and conservation properties are analysed. The computational efficiency and the high precision of the method are illustrated in the vortex merger, four-modes and random flow problems. Comparisons with the Cauchy-Lagrangian method [3] are also presented.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2020.109781</identifier><language>eng</language><publisher>Cambridge: Elsevier Inc</publisher><subject>Characteristic Mapping method ; Computational fluid dynamics ; Computational physics ; Euler equations ; Euler-Lagrange equation ; Eulers equations ; Flow mapping ; Fluid dynamics ; Gradient-Augmented Level-set method ; Mathematical analysis ; Mathematics ; Numerical Analysis</subject><ispartof>Journal of computational physics, 2021-01, Vol.424, p.109781, Article 109781</ispartof><rights>2020 Elsevier Inc.</rights><rights>Copyright Elsevier Science Ltd. Jan 1, 2021</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-8364d235efe0d225f845e9ed9c3e649c053042434a8f17cbf383bd2473b9b583</citedby><cites>FETCH-LOGICAL-c359t-8364d235efe0d225f845e9ed9c3e649c053042434a8f17cbf383bd2473b9b583</cites><orcidid>0000-0003-0542-020X ; 0000-0003-1243-6621</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jcp.2020.109781$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,780,784,885,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttps://hal.science/hal-02616194$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Yin, Xi-Yuan</creatorcontrib><creatorcontrib>Mercier, Olivier</creatorcontrib><creatorcontrib>Yadav, Badal</creatorcontrib><creatorcontrib>Schneider, Kai</creatorcontrib><creatorcontrib>Nave, Jean-Christophe</creatorcontrib><title>A Characteristic Mapping method for the two-dimensional incompressible Euler equations</title><title>Journal of computational physics</title><description>•The method achieves third-order global convergence as derived in section 3.3.1 and demonstrated numerically in section 3.3.2.•The method provides an accurate conservation of all vorticity moments (Corollary 1, section 3.3.1), and e.g. 4.1 and 4.2 (Tables 2 and 4).•The method has long-time stability. Section 4.1 and 4.2 carry out the same tests featured in [15]. Additionally, similar tests are run to longer times with no issues.•The Characteristic Mapping method provides arbitrary subgrid resolution of the solution. We provide a 8192X zoom into the solution in Figs. 7, 8, 9 and 10.
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. This new approach evolves the flow map using a combination of the Characteristic Mapping (CM) method [1] the gradient-augmented level-set (GALS) method [2]. The flow map possesses a semigroup structure which allows for the decomposition of a long-time deformation into short-time submaps. This leads to a numerical scheme that achieves exponential resolution in linear time. Error estimates are provided and conservation properties are analysed. The computational efficiency and the high precision of the method are illustrated in the vortex merger, four-modes and random flow problems. Comparisons with the Cauchy-Lagrangian method [3] are also presented.</description><subject>Characteristic Mapping method</subject><subject>Computational fluid dynamics</subject><subject>Computational physics</subject><subject>Euler equations</subject><subject>Euler-Lagrange equation</subject><subject>Eulers equations</subject><subject>Flow mapping</subject><subject>Fluid dynamics</subject><subject>Gradient-Augmented Level-set method</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Numerical Analysis</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kDtPwzAUhS0EEuXxA9gsMTGk-JXEFlNVAUUqYqlYLce5oY7SOLVdEP-eVEGMTPd1zpHuh9ANJXNKaHHfzls7zBlhx1mVkp6g2diQjJW0OEUzQhjNlFL0HF3E2BJCZC7kDL0v8HJrgrEJgovJWfxqhsH1H3gHaetr3PiA0xZw-vJZ7XbQR-d702HXW78bAsToqg7w46GDgGF_MGm8xyt01pguwvVvvUSbp8fNcpWt355flot1ZnmuUiZ5IWrGc2iA1IzljRQ5KKiV5VAIZUnOiWCCCyMbWtqq4ZJXNRMlr1SVS36J7qbYren0ENzOhG_tjdOrxVofd4QVtKBKfNJReztph-D3B4hJt_4QxleiZqJQVEpailFFJ5UNPsYAzV8sJfpIWrd6JK2PpPVEevQ8TB4YP_10EHS0DnoLtQtgk669-8f9A-EuhUI</recordid><startdate>20210101</startdate><enddate>20210101</enddate><creator>Yin, Xi-Yuan</creator><creator>Mercier, Olivier</creator><creator>Yadav, Badal</creator><creator>Schneider, Kai</creator><creator>Nave, Jean-Christophe</creator><general>Elsevier Inc</general><general>Elsevier Science Ltd</general><general>Elsevier</general><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><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-0542-020X</orcidid><orcidid>https://orcid.org/0000-0003-1243-6621</orcidid></search><sort><creationdate>20210101</creationdate><title>A Characteristic Mapping method for the two-dimensional incompressible Euler equations</title><author>Yin, Xi-Yuan ; Mercier, Olivier ; Yadav, Badal ; Schneider, Kai ; Nave, Jean-Christophe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-8364d235efe0d225f845e9ed9c3e649c053042434a8f17cbf383bd2473b9b583</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Characteristic Mapping method</topic><topic>Computational fluid dynamics</topic><topic>Computational physics</topic><topic>Euler equations</topic><topic>Euler-Lagrange equation</topic><topic>Eulers equations</topic><topic>Flow mapping</topic><topic>Fluid dynamics</topic><topic>Gradient-Augmented Level-set method</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Numerical Analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yin, Xi-Yuan</creatorcontrib><creatorcontrib>Mercier, Olivier</creatorcontrib><creatorcontrib>Yadav, Badal</creatorcontrib><creatorcontrib>Schneider, Kai</creatorcontrib><creatorcontrib>Nave, Jean-Christophe</creatorcontrib><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><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yin, Xi-Yuan</au><au>Mercier, Olivier</au><au>Yadav, Badal</au><au>Schneider, Kai</au><au>Nave, Jean-Christophe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Characteristic Mapping method for the two-dimensional incompressible Euler equations</atitle><jtitle>Journal of computational physics</jtitle><date>2021-01-01</date><risdate>2021</risdate><volume>424</volume><spage>109781</spage><pages>109781-</pages><artnum>109781</artnum><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>•The method achieves third-order global convergence as derived in section 3.3.1 and demonstrated numerically in section 3.3.2.•The method provides an accurate conservation of all vorticity moments (Corollary 1, section 3.3.1), and e.g. 4.1 and 4.2 (Tables 2 and 4).•The method has long-time stability. Section 4.1 and 4.2 carry out the same tests featured in [15]. Additionally, similar tests are run to longer times with no issues.•The Characteristic Mapping method provides arbitrary subgrid resolution of the solution. We provide a 8192X zoom into the solution in Figs. 7, 8, 9 and 10.
We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. This new approach evolves the flow map using a combination of the Characteristic Mapping (CM) method [1] the gradient-augmented level-set (GALS) method [2]. The flow map possesses a semigroup structure which allows for the decomposition of a long-time deformation into short-time submaps. This leads to a numerical scheme that achieves exponential resolution in linear time. Error estimates are provided and conservation properties are analysed. The computational efficiency and the high precision of the method are illustrated in the vortex merger, four-modes and random flow problems. Comparisons with the Cauchy-Lagrangian method [3] are also presented.</abstract><cop>Cambridge</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jcp.2020.109781</doi><orcidid>https://orcid.org/0000-0003-0542-020X</orcidid><orcidid>https://orcid.org/0000-0003-1243-6621</orcidid></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0021-9991 |
ispartof | Journal of computational physics, 2021-01, Vol.424, p.109781, Article 109781 |
issn | 0021-9991 1090-2716 |
language | eng |
recordid | cdi_hal_primary_oai_HAL_hal_02616194v1 |
source | Access via ScienceDirect (Elsevier) |
subjects | Characteristic Mapping method Computational fluid dynamics Computational physics Euler equations Euler-Lagrange equation Eulers equations Flow mapping Fluid dynamics Gradient-Augmented Level-set method Mathematical analysis Mathematics Numerical Analysis |
title | A Characteristic Mapping method for the two-dimensional incompressible Euler equations |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T22%3A27%3A09IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Characteristic%20Mapping%20method%20for%20the%20two-dimensional%20incompressible%20Euler%20equations&rft.jtitle=Journal%20of%20computational%20physics&rft.au=Yin,%20Xi-Yuan&rft.date=2021-01-01&rft.volume=424&rft.spage=109781&rft.pages=109781-&rft.artnum=109781&rft.issn=0021-9991&rft.eissn=1090-2716&rft_id=info:doi/10.1016/j.jcp.2020.109781&rft_dat=%3Cproquest_hal_p%3E2469188174%3C/proquest_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2469188174&rft_id=info:pmid/&rft_els_id=S0021999120305556&rfr_iscdi=true |