Performance of Geometric Multigrid Method for Two-Dimensional Burgers' Equations with Non-Orthogonal, Structured Curvilinear Grids

This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry. For this, the differential equations were discretized by Finite Volume Method (FVM) with second-order approximation scheme an...

Full description

Saved in:
Bibliographic Details
Published in:Computer modeling in engineering & sciences Vol. 125; no. 3; pp. 1061 - 1081
Main Authors: Zanatta, Daiane Cristina, Araki, Luciano Kiyoshi, Pinto, Marcio Augusto Villela, Moro, Diego Fernando
Format: Journal Article
Language:English
Published: Tech Science Press 15.12.2020
Subjects:
Burgers' Equation
Computational Fluid Dynamics
Geometric Multigrid
Nite Volume Method
Non-Orthogonal Curvilinear Grids
ISSN:1526-1492
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry. For this, the differential equations were discretized by Finite Volume Method (FVM) with second-order approximation scheme and deferred correction. Moreover, the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids. Furthermore, the in uence of some parameters of geometric multigrid method, as well as lexicographical Gauss-Seidel (Lex-GS), η-line Gauss-Seidel (η-line-GS), Modified Strongly Implicit (MSI) and modified incomplete LU decomposition (MILU) solvers on the Central Processing Unit (CPU) time was investigated. Therefore, several parameters of multigrid method and solvers were tested for the problem, with the use of nonorthogonal structured curvilinear grids and multigrid method, resulting in an algorithm with the combination that achieved the best results and CPU time. The geometric multigrid method with Full Approximation Scheme (FAS), V-cycle and standard coarsening ratio for this problem were utilized. This article shows how to calculate the coordinates transformation metrics in the coarser grids. Results show that the MSI and MILU solvers are the most efficient. Moreover, the MSI solver is faster than MILU for both grids generators; and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.
AbstractList This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry. For this, the differential equations were discretized by Finite Volume Method (FVM) with second-order approximation scheme and deferred correction. Moreover, the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids. Furthermore, the in uence of some parameters of geometric multigrid method, as well as lexicographical Gauss-Seidel (Lex-GS), η-line Gauss-Seidel (η-line-GS), Modified Strongly Implicit (MSI) and modified incomplete LU decomposition (MILU) solvers on the Central Processing Unit (CPU) time was investigated. Therefore, several parameters of multigrid method and solvers were tested for the problem, with the use of nonorthogonal structured curvilinear grids and multigrid method, resulting in an algorithm with the combination that achieved the best results and CPU time. The geometric multigrid method with Full Approximation Scheme (FAS), V-cycle and standard coarsening ratio for this problem were utilized. This article shows how to calculate the coordinates transformation metrics in the coarser grids. Results show that the MSI and MILU solvers are the most efficient. Moreover, the MSI solver is faster than MILU for both grids generators; and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.
Author Moro, Diego Fernando
Zanatta, Daiane Cristina
Pinto, Marcio Augusto Villela
Araki, Luciano Kiyoshi
Author_xml – sequence: 1
  givenname: Daiane Cristina
  surname: Zanatta
  fullname: Zanatta, Daiane Cristina
– sequence: 2
  givenname: Luciano Kiyoshi
  surname: Araki
  fullname: Araki, Luciano Kiyoshi
– sequence: 3
  givenname: Marcio Augusto Villela
  surname: Pinto
  fullname: Pinto, Marcio Augusto Villela
– sequence: 4
  givenname: Diego Fernando
  surname: Moro
  fullname: Moro, Diego Fernando
BookMark eNp1kD1PxDAMhjOAxOcPYMvGQo989NJ2Aw44kLgDCZgj0zol6C6BJAWJkV9OCqx4sWW9fmQ9O2TDeYeEHHA2kUKx8rhdY5wIJtiEcaFkuUG2-VSogpeN2CI7Mb4wJpWsm23ydYfB-LAG1yL1hs7RrzEF29LFsEq2D7ajC0zPvqM5Rh8-fHFu1-ii9Q5W9GwIPYZ4SC_eBkh5F-mHTc906V1xG_JZP8aO6H0KQ5uGgB2dDeHdrqxDCHSe8XGPbBpYRdz_67vk8fLiYXZV3NzOr2enN4UVtUxFCWiMkhXnpuaiEW3ZCQGAYOqSsW7KnlrgOK0kqrqCp1KBqVqsKuDQqUZ1cpec_HKt69El0C9-CPm7qFN81aMzPTrTbCwupr9DNqUhpHGoMmL5D8K2P5RR82hZv2eAkyOQs4YrzUvOdIcGslWdIOj-U8dKfgMn4ofL
ContentType Journal Article
DOI 10.32604/cmes.2020.012634
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EndPage 1081
ExternalDocumentID tsp/cmes/2020/00000125/00000003/art00007
GroupedDBID -~X
AAFWJ
ACIWK
AFKRA
ALMA_UNASSIGNED_HOLDINGS
BENPR
CCPQU
EBS
EJD
F5P
IPNFZ
J9A
OK1
PIMPY
RTS
ID FETCH-LOGICAL-i283t-4aeff63711f81292c4d22aaeaf8400d50bca1e573e687ab46af7ce77a1ad696d3
ISICitedReferencesCount 1
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000602627600007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1526-1492
IngestDate Fri Nov 08 06:06:18 EST 2024
Thu Jan 27 13:03:24 EST 2022
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 3
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-i283t-4aeff63711f81292c4d22aaeaf8400d50bca1e573e687ab46af7ce77a1ad696d3
Notes 1526-1492(20201210)125:3L.1061;1-
PageCount 21
ParticipantIDs ingenta_journals_tsp_cmes_2020_00000125_00000003_art00007
ingenta_journals_ic_tsp_15261492_v125n3_20210916_1410_default_tar_gz_s7
PublicationCentury 2000
PublicationDate 2020-12-15
PublicationDateYYYYMMDD 2020-12-15
PublicationDate_xml – month: 12
  year: 2020
  text: 2020-12-15
  day: 15
PublicationDecade 2020
PublicationTitle Computer modeling in engineering & sciences
PublicationYear 2020
Publisher Tech Science Press
Publisher_xml – name: Tech Science Press
SSID ssj0036389
Score 2.2532852
Snippet This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in...
SourceID ingenta
SourceType Enrichment Source
Publisher
StartPage 1061
SubjectTerms Burgers' Equation
Computational Fluid Dynamics
Geometric Multigrid
Nite Volume Method
Non-Orthogonal Curvilinear Grids
Title Performance of Geometric Multigrid Method for Two-Dimensional Burgers' Equations with Non-Orthogonal, Structured Curvilinear Grids
URI https://www.ingentaconnect.com/content/tsp/cmes/2020/00000125/00000003/art00007
Volume 125
WOSCitedRecordID wos000602627600007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVPQU
  databaseName: Advanced Technologies & Aerospace Database
  issn: 1526-1492
  databaseCode: P5Z
  dateStart: 20000101
  customDbUrl:
  isFulltext: true
  dateEnd: 99991231
  titleUrlDefault: https://search.proquest.com/hightechjournals
  omitProxy: false
  ssIdentifier: ssj0036389
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Computer Science Database
  issn: 1526-1492
  databaseCode: K7-
  dateStart: 20000101
  customDbUrl:
  isFulltext: true
  dateEnd: 99991231
  titleUrlDefault: http://search.proquest.com/compscijour
  omitProxy: false
  ssIdentifier: ssj0036389
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  issn: 1526-1492
  databaseCode: M7S
  dateStart: 20000101
  customDbUrl:
  isFulltext: true
  dateEnd: 99991231
  titleUrlDefault: http://search.proquest.com
  omitProxy: false
  ssIdentifier: ssj0036389
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  issn: 1526-1492
  databaseCode: BENPR
  dateStart: 20000101
  customDbUrl:
  isFulltext: true
  dateEnd: 99991231
  titleUrlDefault: https://www.proquest.com/central
  omitProxy: false
  ssIdentifier: ssj0036389
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Publicly Available Content Database
  issn: 1526-1492
  databaseCode: PIMPY
  dateStart: 20000101
  customDbUrl:
  isFulltext: true
  dateEnd: 99991231
  titleUrlDefault: http://search.proquest.com/publiccontent
  omitProxy: false
  ssIdentifier: ssj0036389
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Nb9MwFLe2wYEL39PGl3xA4hACzUfj5DjWUaRtZYcyTVws13FKpC0ZTVIGR_5y3rOdNC0XEOISRZHtpn6_PP_8_D4IeQmrtg-6N3DlEEuYpfjNAU93JWjDWeyFItR1yM5P2GQSX1wkZ1vbu20szPKSFUV8c5Nc_1dRwzMQNobO_oW4u0HhAdyD0OEKYofrHwn-rBcKAExwrMorrJolHR1rO1_kqXOqy0ZrD8Ppt9IdYYZ_k53DeafDpLVrxdHXxvrJaWPtpCzcjwvoOMeGxkMMc8826MF-2IDKQcYqFs4YfqLqk962coQpu2ODaNQqEaKGn12KO4r_WRSiNtR2JADDCiuQgT4qxAqjwtTcPmnQNFM6x_n3svqSd9o-L3SNKIxHknnpHDTzBqiuc47hj5fdMKelCfUZ5WpeOtauXvatIb72LDHxoBq_eB7RacW-E4vW7X7kwoZwXfmbsGuL8qCnynGv3KMF3sCUltlccoD-DkLAhLxSmP3dH7yBJT-yBtr1TN51dW0bYhgONLW-ndBh2N6CksXVeVHrM-ZtcstnwwRdFY-Z2zKMAFmmzgNs_5A5rddv8nbzPVZRej3eNL1P7toNDz0wQH1AtlTxkNxrIUHtLD4iP3u4pWVGO9zSDrfU4JZCM7qBW2px-4p2qKWIWrqO2td0hVnawyzVmH1MPr0_mh5-cG2BEDcHVly7oVBZFgXM8zLgqYkvw9T3hVAii2FpSoeDmRSeGrJARTETszASGZOKMeGJNEqiNNglO0VZqD1CZ37GgkwlAi0kAvRUJEUkA-HLJEiiLN4nYzuN3H7rFc8lB5FyFANKgS9BjkXAfTSjwK6Lows1T1UmYJp4LRZ8_oNXbJ8kv42Ew6DgsC-m6zWY4C0ieIuHJ__Q9ym5s_pgnpEdmG71nNyWyzqvFi80wH4BnyjPwg
linkProvider ProQuest
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Performance+of+Geometric+Multigrid+Method+for+Two-Dimensional+Burgers%27+Equations+with+Non-Orthogonal%2C+Structured+Curvilinear+Grids&rft.jtitle=Computer+modeling+in+engineering+%26+sciences&rft.au=Zanatta%2C+Daiane+Cristina&rft.au=Araki%2C+Luciano+Kiyoshi&rft.au=Pinto%2C+Marcio+Augusto+Villela&rft.au=Moro%2C+Diego+Fernando&rft.date=2020-12-15&rft.pub=Tech+Science+Press&rft.issn=1526-1492&rft.volume=125&rft.issue=3&rft.spage=1061&rft.epage=1081&rft_id=info:doi/10.32604%2Fcmes.2020.012634&rft.externalDocID=tsp%2Fcmes%2F2020%2F00000125%2F00000003%2Fart00007
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1526-1492&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1526-1492&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1526-1492&client=summon