A Novel Fully Decoupled Scheme for the MHD System with Variable Density

In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) me...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 25; no. 1; pp. 215 - 236
Main Authors Wang, Zhaowei, Wang, Danxia, Jia, Hongen
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.01.2025
Walter de Gruyter GmbH
Subjects
65Mxx
65N12
65N22
65Nxx
Decoupling
Density
Error Analysis
Fully Decoupled
Gauge-Uzawa Method
Mathematical analysis
Mathematics
Unconditionally Stable
Variable Density
Online AccessGet full text
ISSN1609-4840
1609-9389
DOI10.1515/cmam-2024-0004

Cover

Abstract In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) method. And we prove its unconditional energy stability. Then we give the first-order finite element scheme and its implementation. Furthermore, we perform a rigorous error analysis of the proposed numerical scheme. Finally, we perform some numerical experiments to demonstrate the effectiveness of the decoupling scheme.
AbstractList In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) method. And we prove its unconditional energy stability. Then we give the first-order finite element scheme and its implementation. Furthermore, we perform a rigorous error analysis of the proposed numerical scheme. Finally, we perform some numerical experiments to demonstrate the effectiveness of the decoupling scheme.
In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) method. And we prove its unconditional energy stability. Then we give the first-order finite element scheme and its implementation. Furthermore, we perform a rigorous error analysis of the proposed numerical scheme. Finally, we perform some numerical experiments to demonstrate the effectiveness of the decoupling scheme.
Author Wang, Zhaowei
Wang, Danxia
Jia, Hongen
Author_xml – sequence: 1
  givenname: Zhaowei
  orcidid: 0009-0006-6793-8492
  surname: Wang
  fullname: Wang, Zhaowei
  email: 2544013412@qq.com
  organization: School of Mathematics, 47846 Taiyuan University of Technology , Taiyuan 030024, Shanxi, P. R. China
– sequence: 2
  givenname: Danxia
  surname: Wang
  fullname: Wang, Danxia
  email: 2621259544@qq.com
  organization: School of Mathematics, 47846 Taiyuan University of Technology , Taiyuan 030024, Shanxi, P. R. China
– sequence: 3
  givenname: Hongen
  surname: Jia
  fullname: Jia, Hongen
  email: jiahongen@tyut.edu.cn
  organization: School of Mathematics, 47846 Taiyuan University of Technology , Taiyuan 030024, Shanxi, P. R. China
BookMark eNp1kMtLAzEQh4NUsNZePQc8b81ksy_wUlrbClUPVa9LNpnYlX3UbNay_71bWhBET_M7zDeP75IMqrpCQq6BTSCA4FaVsvQ448JjjIkzMoSQJV7ix8nglEUs2AUZN02eMRZz4CKCIVlO6VP9hQVdtEXR0Tmqut0VqOlGbbFEampL3Rbp42pON13jsKT73G3pm7S5zArsiarJXXdFzo0sGhyf6oi8Lu5fZitv_bx8mE3XnvI5c14YIfIQTAZMKg1xphOjE6lBgIkjycGwwBhtAq4zCAVjWukE4x5WkWBC-SNyc5y7s_Vni41LP-rWVv3K1IcwifrnQfRdk2OXsnXTWDTpzualtF0KLD34Sg--0oOv9OCrB8QvQOVOuryunJV58T92d8T2snBoNb7btuvDz1F_gzwADoH_DRRnhBo
CitedBy_id crossref_primary_10_35633_inmateh_74_28
crossref_primary_10_1007_s40314_024_02891_4
crossref_primary_10_1007_s12190_024_02242_w
Cites_doi 10.2514/6.1996-2355
10.1093/imanum/dru015
10.1137/1.9781611970050
10.1016/j.camwa.2022.01.025
10.1016/j.cma.2010.05.007
10.1016/j.apnum.2018.01.005
10.1016/j.apnum.2019.06.001
10.1016/j.jcp.2008.12.036
10.1007/BF00247696
10.4310/CMS.2003.v1.n2.a6
10.1007/978-3-7091-8083-9
10.1142/S0218202522500117
10.1109/TAC.2005.861704
10.1016/j.jcp.2014.08.044
10.1016/j.jcp.2006.06.013
10.1002/num.23067
10.3934/dcdsb.2005.5.817
10.1016/j.camwa.2022.10.013
10.1016/j.apnum.2021.04.006
10.1093/acprof:oso/9780198566656.001.0001
10.1016/j.vacuum.2009.10.017
10.1137/0729004
10.1016/j.cam.2019.06.037
10.1016/j.cam.2016.09.005
10.1016/j.jfa.2014.06.002
10.1142/S0218202506001649
10.1137/040609756
10.1016/j.jcp.2017.10.021
10.1090/S0025-5718-1968-0242392-2
10.1016/j.cma.2019.07.022
10.1137/21M1430376
10.1016/j.mattod.2021.10.027
10.1215/00127094-2022-0051
10.1137/090768758
ContentType Journal Article
Copyright 2024 Walter de Gruyter GmbH, Berlin/Boston
Copyright_xml – notice: 2024 Walter de Gruyter GmbH, Berlin/Boston
DBID AAYXX
CITATION
JQ2
DOI 10.1515/cmam-2024-0004
DatabaseName CrossRef
ProQuest Computer Science Collection
DatabaseTitle CrossRef
ProQuest Computer Science Collection
DatabaseTitleList ProQuest Computer Science Collection

CrossRef
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1609-9389
EndPage 236
ExternalDocumentID 10_1515_cmam_2024_0004
10_1515_cmam_2024_0004251215
GrantInformation_xml – fundername: Shanxi Scholarship Council of China
  grantid: 2021-029
– fundername: Applied Basic Research Project of Shanxi Province, China
  grantid: 202203021211129
– fundername: International Science and Technology Cooperation Program of Shanxi Province
  grantid: 202104041101019
GroupedDBID 0R~
2WC
4.4
8FE
8FG
AAAEU
AAAVF
AACIX
AADQG
AAFPC
AAGVJ
AAILP
AAJBH
AAKDD
AALGR
AAOUV
AAPJK
AAQCX
AARVR
AASOL
AASQH
AAXCG
ABAOT
ABAQN
ABFKT
ABIQR
ABJNI
ABMBZ
ABPLS
ABSOE
ABUVI
ABWLS
ABXMZ
ABYKJ
ACDEB
ACEFL
ACGFS
ACHNZ
ACIPV
ACIWK
ACONX
ACPMA
ACUND
ACZBO
ADEQT
ADGQD
ADGYE
ADJVZ
ADNPR
ADOZN
AECWL
AEDGQ
AEGVQ
AEICA
AEJQW
AEMOE
AENEX
AEQDQ
AEQLX
AERZL
AEXIE
AFBAA
AFBDD
AFBQV
AFCXV
AFKRA
AFQUK
AFYRI
AGBEV
AGQYU
AHCWZ
AHVWV
AHXUK
AIERV
AIWOI
AJATJ
AKXKS
ALMA_UNASSIGNED_HOLDINGS
ALUKF
ALWYM
AMVHM
ARAPS
ASYPN
BAKPI
BBCWN
BCIFA
BENPR
BGLVJ
CFGNV
DASCH
DSRVY
EBS
HCIFZ
HZ~
IY9
J9A
K.~
K6V
KDIRW
L6V
O9-
P2P
P62
QD8
SA.
SLJYH
TR2
UK5
WTRAM
AAYXX
CITATION
JQ2
ID FETCH-LOGICAL-c320t-67ee261fb10acd18bd9fd9ad141f87a21f05ffdf52db16400dcd9e8c32c7404c3
ISSN 1609-4840
IngestDate Wed Aug 13 08:56:59 EDT 2025
Wed Oct 01 03:48:25 EDT 2025
Thu Apr 24 22:58:36 EDT 2025
Sat Sep 06 16:57:33 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c320t-67ee261fb10acd18bd9fd9ad141f87a21f05ffdf52db16400dcd9e8c32c7404c3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0009-0006-6793-8492
PQID 3169700414
PQPubID 2038872
PageCount 22
ParticipantIDs proquest_journals_3169700414
crossref_primary_10_1515_cmam_2024_0004
crossref_citationtrail_10_1515_cmam_2024_0004
walterdegruyter_journals_10_1515_cmam_2024_0004251215
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2025-01-01
20250101
PublicationDateYYYYMMDD 2025-01-01
PublicationDate_xml – month: 01
  year: 2025
  text: 2025-01-01
  day: 01
PublicationDecade 2020
PublicationPlace Minsk
PublicationPlace_xml – name: Minsk
PublicationTitle Journal of computational methods in applied mathematics
PublicationYear 2025
Publisher De Gruyter
Walter de Gruyter GmbH
Publisher_xml – name: De Gruyter
– name: Walter de Gruyter GmbH
References 2025010318340249899_j_cmam-2024-0004_ref_011
2025010318340249899_j_cmam-2024-0004_ref_033
2025010318340249899_j_cmam-2024-0004_ref_010
2025010318340249899_j_cmam-2024-0004_ref_032
2025010318340249899_j_cmam-2024-0004_ref_031
2025010318340249899_j_cmam-2024-0004_ref_030
2025010318340249899_j_cmam-2024-0004_ref_015
2025010318340249899_j_cmam-2024-0004_ref_014
2025010318340249899_j_cmam-2024-0004_ref_036
2025010318340249899_j_cmam-2024-0004_ref_013
2025010318340249899_j_cmam-2024-0004_ref_035
2025010318340249899_j_cmam-2024-0004_ref_012
2025010318340249899_j_cmam-2024-0004_ref_034
2025010318340249899_j_cmam-2024-0004_ref_019
2025010318340249899_j_cmam-2024-0004_ref_018
2025010318340249899_j_cmam-2024-0004_ref_017
2025010318340249899_j_cmam-2024-0004_ref_016
2025010318340249899_j_cmam-2024-0004_ref_022
2025010318340249899_j_cmam-2024-0004_ref_021
2025010318340249899_j_cmam-2024-0004_ref_020
2025010318340249899_j_cmam-2024-0004_ref_009
2025010318340249899_j_cmam-2024-0004_ref_004
2025010318340249899_j_cmam-2024-0004_ref_026
2025010318340249899_j_cmam-2024-0004_ref_003
2025010318340249899_j_cmam-2024-0004_ref_025
2025010318340249899_j_cmam-2024-0004_ref_002
2025010318340249899_j_cmam-2024-0004_ref_024
2025010318340249899_j_cmam-2024-0004_ref_001
2025010318340249899_j_cmam-2024-0004_ref_023
2025010318340249899_j_cmam-2024-0004_ref_008
2025010318340249899_j_cmam-2024-0004_ref_007
2025010318340249899_j_cmam-2024-0004_ref_029
2025010318340249899_j_cmam-2024-0004_ref_006
2025010318340249899_j_cmam-2024-0004_ref_028
2025010318340249899_j_cmam-2024-0004_ref_005
2025010318340249899_j_cmam-2024-0004_ref_027
References_xml – ident: 2025010318340249899_j_cmam-2024-0004_ref_002
  doi: 10.2514/6.1996-2355
– ident: 2025010318340249899_j_cmam-2024-0004_ref_015
  doi: 10.1093/imanum/dru015
– ident: 2025010318340249899_j_cmam-2024-0004_ref_033
  doi: 10.1137/1.9781611970050
– ident: 2025010318340249899_j_cmam-2024-0004_ref_030
  doi: 10.1016/j.camwa.2022.01.025
– ident: 2025010318340249899_j_cmam-2024-0004_ref_011
  doi: 10.1016/j.cma.2010.05.007
– ident: 2025010318340249899_j_cmam-2024-0004_ref_021
  doi: 10.1016/j.apnum.2018.01.005
– ident: 2025010318340249899_j_cmam-2024-0004_ref_020
  doi: 10.1016/j.apnum.2019.06.001
– ident: 2025010318340249899_j_cmam-2024-0004_ref_012
  doi: 10.1016/j.jcp.2008.12.036
– ident: 2025010318340249899_j_cmam-2024-0004_ref_032
  doi: 10.1007/BF00247696
– ident: 2025010318340249899_j_cmam-2024-0004_ref_008
  doi: 10.4310/CMS.2003.v1.n2.a6
– ident: 2025010318340249899_j_cmam-2024-0004_ref_003
– ident: 2025010318340249899_j_cmam-2024-0004_ref_024
  doi: 10.1007/978-3-7091-8083-9
– ident: 2025010318340249899_j_cmam-2024-0004_ref_017
  doi: 10.1142/S0218202522500117
– ident: 2025010318340249899_j_cmam-2024-0004_ref_004
  doi: 10.1109/TAC.2005.861704
– ident: 2025010318340249899_j_cmam-2024-0004_ref_036
  doi: 10.1016/j.jcp.2014.08.044
– ident: 2025010318340249899_j_cmam-2024-0004_ref_026
  doi: 10.1016/j.jcp.2006.06.013
– ident: 2025010318340249899_j_cmam-2024-0004_ref_005
  doi: 10.1002/num.23067
– ident: 2025010318340249899_j_cmam-2024-0004_ref_028
  doi: 10.3934/dcdsb.2005.5.817
– ident: 2025010318340249899_j_cmam-2024-0004_ref_016
  doi: 10.1016/j.camwa.2022.10.013
– ident: 2025010318340249899_j_cmam-2024-0004_ref_019
  doi: 10.1016/j.apnum.2021.04.006
– ident: 2025010318340249899_j_cmam-2024-0004_ref_010
  doi: 10.1093/acprof:oso/9780198566656.001.0001
– ident: 2025010318340249899_j_cmam-2024-0004_ref_031
  doi: 10.1016/j.vacuum.2009.10.017
– ident: 2025010318340249899_j_cmam-2024-0004_ref_027
  doi: 10.1137/0729004
– ident: 2025010318340249899_j_cmam-2024-0004_ref_006
  doi: 10.1016/j.cam.2019.06.037
– ident: 2025010318340249899_j_cmam-2024-0004_ref_001
  doi: 10.1016/j.cam.2016.09.005
– ident: 2025010318340249899_j_cmam-2024-0004_ref_014
  doi: 10.1016/j.jfa.2014.06.002
– ident: 2025010318340249899_j_cmam-2024-0004_ref_023
  doi: 10.1142/S0218202506001649
– ident: 2025010318340249899_j_cmam-2024-0004_ref_022
  doi: 10.1137/040609756
– ident: 2025010318340249899_j_cmam-2024-0004_ref_029
  doi: 10.1016/j.jcp.2017.10.021
– ident: 2025010318340249899_j_cmam-2024-0004_ref_007
  doi: 10.1090/S0025-5718-1968-0242392-2
– ident: 2025010318340249899_j_cmam-2024-0004_ref_034
  doi: 10.1016/j.cma.2019.07.022
– ident: 2025010318340249899_j_cmam-2024-0004_ref_018
  doi: 10.1137/21M1430376
– ident: 2025010318340249899_j_cmam-2024-0004_ref_035
  doi: 10.1016/j.mattod.2021.10.027
– ident: 2025010318340249899_j_cmam-2024-0004_ref_025
– ident: 2025010318340249899_j_cmam-2024-0004_ref_009
  doi: 10.1215/00127094-2022-0051
– ident: 2025010318340249899_j_cmam-2024-0004_ref_013
  doi: 10.1137/090768758
SSID ssib008212471
ssj0033936
ssib006285865
Score 2.3459036
Snippet In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable...
SourceID proquest
crossref
walterdegruyter
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 215
SubjectTerms 65Mxx
65N12
65N22
65Nxx
Decoupling
Density
Error Analysis
Fully Decoupled
Gauge-Uzawa Method
Mathematical analysis
Mathematics
Unconditionally Stable
Variable Density
Title A Novel Fully Decoupled Scheme for the MHD System with Variable Density
URI https://www.degruyter.com/doi/10.1515/cmam-2024-0004
https://www.proquest.com/docview/3169700414
Volume 25
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVPQU
  databaseName: ProQuest Technology Collection
  customDbUrl:
  eissn: 1609-9389
  dateEnd: 20250403
  omitProxy: true
  ssIdentifier: ssj0033936
  issn: 1609-4840
  databaseCode: 8FG
  dateStart: 20160101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/technologycollection1
  providerName: ProQuest
– providerCode: PRVAZK
  databaseName: de Gruyter: Complete Journal Package 2023 [unlimited simultaneous users]
  customDbUrl:
  eissn: 1609-9389
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0033936
  issn: 1609-4840
  databaseCode: AGBEV
  dateStart: 20010120
  isFulltext: true
  titleUrlDefault: https://www.degruyterbrill.com
  providerName: Walter de Gruyter
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3Lb9MwGLeqcYHDxFMMBvIBiQPKSBw7cY4VZasmdacNJi5R_IJJbTONdA_-CP5mPtuJk5aBYJcocu2k8ffz97C_B0JvSM6NYHEVpZpmEU1yEwmZ04jxvCJEZiRJbbzz7CibntDDU3Y6Gv0ceC2tGrEnf9waV3IXqkIb0NVGyf4HZcNDoQHugb5wBQrD9Z9oPH53VF_qufPguAHWIevV-dxqkECJhQ4ehLPppM1M7rddP4F97CKmJtZ7vVk72B0oqNIVfOg2C32paec9W7Wa6yKkfA2K-ed2-_nLt6q-0mebzYCx67MgCA69o-60tvFdw-0Hwja2HyaA5YvVTedK7JloZivXcZ-GaU_3bUXqywV1nNeHPK8hrGOjbCCRiU-R8huzZy4vhlxUC0AFoS5Avhdr3VH-hrQLPojW-oEnlHZ8acfbc3hq1T2bs-AeybPMVsTg-wc9fyKc8cGpMAe5T_PgUpSmhStJGb6_TRIKb3m__i_XlaDestm-cj4SSn_1czpQdY4fou0WAnjsAfcIjfTyMXow66n9BB2MsYMedtDDAXrYQw8D9DB0xwA97KGHLfRwBz3cQu8pOtn_ePxhGrU1OSKZkriJslxrMLqNSOJKqoQLVRhVVCqhibHLOzExM0YZRpQASzyOlVSF5jAYOEBMZfoMbS3rpX6OcG4U9KZccJ1QorhIBatiJUhmCsJjuoOibpJK2Sast3VT5uXtpNtBb0P_c5-q5Y89d7s5L9vl_L1Mk6ywtR4S-Jlt0KHv9TfUvLjjuJfofr-ydtFWc7HSr0DVbcRrh79fyGOkBg
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Lc9MwENZAegAOLeUxQB_owAwnN5Is2fIxfaa0yYW205vHesEMeXRaG6b8enZjx0lbeoGzV7KlXVn7SbvfEvJJpDoYxYoo9jKJJE9DZGwqI6XTQgibCB5jvvNgmPTP5ZdLdbmUC4Nhlc5_u65uy5ohteumtsKDspZrAHbgrh0XY1CwkLOs6O73cjx6SlYArCSyQ1Z6R7sHFwurElrppbs8DX9rmbaBIHGczQoJ8gTrrUEXDbXjw9fc3boW_ujqr9nNdvvZSxvU4Rqx86HVcSk_dqrS7Njf91gf_2_sL8lq47_SXm1w6-SJn7wiLwYt-evNa3LUo8PpTz-iCG9v6T4A3Opq5B39CgYy9hTcZAridNDfpzVhOsXTYHoBsB0TuaDFBCNF3pDzw4OzvX7U1GuIbCxYGSWp9wDIguGssI5r47LgssJxyQOqngemQnBBCWcApTHmrMu8hsZgHUza-C3pTKYT_47QNDiQltpoz6Vw2sRGFcwZkYRMaCbfk2iuitw2ZOZYU2OUI6iBWcpxlnKcJbxeB_nPrfxVTePxqOTmXLN5s5xv8pgnGdYB4PBY3dP2QurvHaIDydWHf2z3kTzrnw1O89Pj4ckGeS6w-vDsAGiTdMrrym-BS1Sa7cbm_wA5-ALw
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT9wwELYoSBUcKJQiXi0-IPUU1nbsxDkuXZblsatKPNRbFL84sC-xCYj--o432SylcKHnjJN4ZpKZzx5_g9ABi6VTgmRBaHkUcBq7QOmYB0LGGWM6YjT05527vahzzc9-iVk14aQqqzT29r54ykuG1IYZ6cIvlNVcAxCBG3qQDcDAjE9PRTfGxn1ASxDrJeCvpebJ0fHN3KmYFPLZVp6EnzWP6zqQMEymfQRp5NutAdypmB3_fcrfkWuejq4-Tje267d-Fp_an5CazawsS7k7LHJ1qH-_IH38r6mvodUqe8XN0t3W0YIdfkYr3Zr6dbKBTpq4N3qwfezB7RNuAbwtxn1r8CW4x8BiSJIxiONup4VLunTs14LxDYB2f4wLRgx9ncgXdN0-vvrRCapuDYEOGcmDKLYW4JhTlGTaUKlM4kySGcqp84anjgjnjBPMKMBohBhtEithMPgG4TrcRIvD0dBuIRw7A9JcKmkpZ0aqUImMGMUilzBJ-DYKZpZIdUVl7jtq9FMPaUBJqVdS6pXkN9dB_nstPy5JPN6U3JsZNq0-5kka0ijxXQAoXBYvjD2Xev2GPn2kYued4_bRx5-tdnpx2jvfRcvMtx6erv7socX8vrBfIR_K1bfK4_8AXmIBqQ
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=A+Novel+Fully+Decoupled+Scheme+for+the+MHD+System+with+Variable+Density&rft.jtitle=Journal+of+computational+methods+in+applied+mathematics&rft.au=Wang%2C+Zhaowei&rft.au=Wang%2C+Danxia&rft.au=Jia%2C+Hongen&rft.date=2025-01-01&rft.pub=De+Gruyter&rft.issn=1609-4840&rft.eissn=1609-9389&rft.volume=25&rft.issue=1&rft.spage=215&rft.epage=236&rft_id=info:doi/10.1515%2Fcmam-2024-0004&rft.externalDBID=n%2Fa&rft.externalDocID=10_1515_cmam_2024_0004251215
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1609-4840&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1609-4840&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1609-4840&client=summon