Dynamic responses of a floating rigid hull subject to a pulsating bubble

A high-pressure pulsating bubble near the free surface casts intense nonlinear impacts on adjacent floating structure, and the rigid-body motion caused by the pulsating bubble jeopardize the stability of floating structure and even lead to a catastrophic sinkage. To address these critical fluid–stru...

Full description

Saved in:
Bibliographic Details
Published inPhysics of fluids (1994) Vol. 37; no. 6
Main Authors Liu, Yun-Long, Qin, Hao, Yang, Di, Tian, Zhao-Li
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.06.2025
Subjects
Online AccessGet full text
ISSN1070-6631
1089-7666
DOI10.1063/5.0267593

Cover

Loading…
Abstract A high-pressure pulsating bubble near the free surface casts intense nonlinear impacts on adjacent floating structure, and the rigid-body motion caused by the pulsating bubble jeopardize the stability of floating structure and even lead to a catastrophic sinkage. To address these critical fluid–structure interaction challenges, this study develops a novel numerical framework combining a modified penalty immersed boundary method with the Eulerian finite element method to simulate the interaction between a rigid hull and a pulsating bubble. The numerical model is validated by experiments between a steel hull and a small-weight underwater explosion. The experiment and simulations reveal two critical hydrodynamic phenomena: the formation of transient “side cavity” while bubble shrinking and the subsequent oblique jet toward broadside, both exhibiting strong correlations with the dynamic responses of hull. Parametric investigations on non-dimensional standoff parameters are conducted to elucidate the dynamic patterns of this cavity and the rigid motions of a Wigley hull. Our analysis demonstrates that while the motion of the rigid hull is correlated with the collapsing patterns of the side cavity, the hull's dynamic responses are predominantly driven by the accelerated flow field and the time-varying buoyancy environment induced by the heaving free surface surrounding the pulsating bubble. Yet, this jet is still worth further investigations, for that it might cause fatal damage to the local structures and endanger the vessels.
AbstractList A high-pressure pulsating bubble near the free surface casts intense nonlinear impacts on adjacent floating structure, and the rigid-body motion caused by the pulsating bubble jeopardize the stability of floating structure and even lead to a catastrophic sinkage. To address these critical fluid–structure interaction challenges, this study develops a novel numerical framework combining a modified penalty immersed boundary method with the Eulerian finite element method to simulate the interaction between a rigid hull and a pulsating bubble. The numerical model is validated by experiments between a steel hull and a small-weight underwater explosion. The experiment and simulations reveal two critical hydrodynamic phenomena: the formation of transient “side cavity” while bubble shrinking and the subsequent oblique jet toward broadside, both exhibiting strong correlations with the dynamic responses of hull. Parametric investigations on non-dimensional standoff parameters are conducted to elucidate the dynamic patterns of this cavity and the rigid motions of a Wigley hull. Our analysis demonstrates that while the motion of the rigid hull is correlated with the collapsing patterns of the side cavity, the hull's dynamic responses are predominantly driven by the accelerated flow field and the time-varying buoyancy environment induced by the heaving free surface surrounding the pulsating bubble. Yet, this jet is still worth further investigations, for that it might cause fatal damage to the local structures and endanger the vessels.
Author Yang, Di
Liu, Yun-Long
Qin, Hao
Tian, Zhao-Li
Author_xml – sequence: 1
  givenname: Yun-Long
  orcidid: 0000-0001-9958-2757
  surname: Liu
  fullname: Liu, Yun-Long
– sequence: 2
  givenname: Hao
  orcidid: 0009-0006-8660-253X
  surname: Qin
  fullname: Qin, Hao
– sequence: 3
  givenname: Di
  surname: Yang
  fullname: Yang, Di
– sequence: 4
  givenname: Zhao-Li
  orcidid: 0000-0001-6589-6934
  surname: Tian
  fullname: Tian, Zhao-Li
BookMark eNp90D1PwzAQBmALFYm2MPAPLDGBlOLPczKiUihSJRaYLSexS6rUDnYy9N-TKp2Z7oZHd3rfBZr54C1C95SsKAH-LFeEgZIFv0JzSvIiUwAwO--KZACc3qBFSgdCCC8YzNH29eTNsalwtKkLPtmEg8MGuzaYvvF7HJt9U-OfoW1xGsqDrXrchxF0Q5smUQ5l2dpbdO1Mm-zdZS7R99vma73Ndp_vH-uXXVYxKfrMCMaAA6M257ICxZUoHa0Nk7kDR5iyRV7IWlonVKkEt8AV5KKmpDCkAMeX6GG628XwO9jU60MYoh9fas6oULka44_qcVJVDClF63QXm6OJJ02JPhelpb4UNdqnyaaq6cdIwf-D_wAhiWe6
CODEN PHFLE6
Cites_doi 10.1007/s00466-002-0371-6
10.1007/s11804-025-00633-4
10.1016/0045-7825(92)90042-I
10.1119/1.1582187
10.1016/j.oceaneng.2023.114898
10.1007/s10483-014-1804-6
10.1016/j.compfluid.2013.04.002
10.1115/1.4009975
10.1063/5.0145415
10.1016/j.tws.2023.111547
10.1016/j.oceaneng.2021.109650
10.1016/j.apor.2018.06.004
10.1016/j.apor.2018.02.024
10.1016/0021-9991(72)90065-4
10.1016/j.jcp.2021.110198
10.1016/j.oceaneng.2023.114120
10.1017/jfm.2023.120
10.1016/j.jcp.2024.112888
10.1016/j.jfluidstructs.2004.08.003
10.1121/1.1458590
10.1146/annurev-fluid-010719-060228
10.1016/j.oceaneng.2021.109537
10.1016/j.jcp.2009.07.023
10.1016/j.jcp.2020.109937
10.1016/j.oceaneng.2023.115403
10.1063/1.2734674
10.1016/j.jcp.2018.09.035
10.1063/5.0224177
10.1017/S0962492902000077
10.1016/0021-9991(81)90145-5
10.1007/s11433-023-2204-x
10.1006/jcph.2001.6813
10.32604/cmes.2021.015259
10.1017/jfm.2024.1209
10.1016/j.jcp.2019.05.001
10.1017/jfm.2015.323
10.1155/2014/705256
10.1063/5.0230647
10.1017/S0022112086000460
10.1016/j.compfluid.2018.04.028
10.1063/1.4944565
10.1016/j.oceaneng.2016.03.040
10.1016/j.jcp.2022.111435
10.31614/cmes.2019.04419
10.1063/1.862940
10.1006/jcph.2001.6778
10.1017/jfm.2023.292
10.1017/jfm.2024.473
10.1016/j.jfluidstructs.2011.05.004
10.1016/j.marstruc.2014.07.003
10.1016/j.oceaneng.2018.08.001
10.1063/1.1722221
10.1002/nme.2310
10.1016/j.jcp.2022.111215
10.1006/jcph.1993.1051
10.1007/s11804-024-00422-5
10.1016/j.apor.2024.104339
10.1016/0021-9991(77)90095-X
10.1016/j.taml.2020.01.003
10.1016/j.ijmecsci.2023.108401
10.1016/j.compfluid.2012.10.012
10.1016/0021-9991(92)90316-Q
10.1017/jfm.2024.954
10.1016/j.jcp.2022.111042
10.1146/annurev.fl.09.010177.001045
ContentType Journal Article
Copyright Author(s)
2025 Author(s). Published under an exclusive license by AIP Publishing.
Copyright_xml – notice: Author(s)
– notice: 2025 Author(s). Published under an exclusive license by AIP Publishing.
DBID AAYXX
CITATION
8FD
H8D
L7M
DOI 10.1063/5.0267593
DatabaseName CrossRef
Technology Research Database
Aerospace Database
Advanced Technologies Database with Aerospace
DatabaseTitle CrossRef
Technology Research Database
Aerospace Database
Advanced Technologies Database with Aerospace
DatabaseTitleList
Technology Research Database
CrossRef
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
Physics
EISSN 1089-7666
ExternalDocumentID 10_1063_5_0267593
GrantInformation_xml – fundername: Industrial Technology Development Program
  grantid: JCKY2021604B027
– fundername: National Natural Science Foundation of China
  grantid: 52101349
  funderid: 10.13039/501100001809
GroupedDBID -~X
0ZJ
1UP
2-P
29O
2WC
4.4
5VS
6TJ
AAAAW
AABDS
AAGWI
AAPUP
AAYIH
ABJGX
ABJNI
ACBRY
ACGFS
ACLYJ
ACNCT
ACZLF
ADCTM
ADMLS
AEJMO
AENEX
AFATG
AFFNX
AFHCQ
AGKCL
AGLKD
AGMXG
AGTJO
AHSDT
AIDUJ
AJJCW
AJQPL
ALEPV
ALMA_UNASSIGNED_HOLDINGS
ATXIE
AWQPM
BDMKI
BPZLN
CS3
DU5
EBS
EJD
F5P
FDOHQ
FFFMQ
HAM
H~9
M6X
M71
M73
NEUPN
NPSNA
O-B
P2P
RDFOP
RIP
RNS
ROL
RQS
SC5
TN5
UQL
WH7
XJT
~02
AAYXX
CITATION
8FD
H8D
L7M
ID FETCH-LOGICAL-c254t-a42263621e835c67374bf1da258f6f027e9895d5ef47b743e637684d109a096f3
ISSN 1070-6631
IngestDate Mon Jun 30 07:32:49 EDT 2025
Thu Jul 03 08:16:12 EDT 2025
Tue Jun 03 03:55:31 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 6
Language English
License Published under an exclusive license by AIP Publishing.
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c254t-a42263621e835c67374bf1da258f6f027e9895d5ef47b743e637684d109a096f3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0001-9958-2757
0009-0006-8660-253X
0000-0001-6589-6934
PQID 3214787675
PQPubID 2050667
PageCount 17
ParticipantIDs crossref_primary_10_1063_5_0267593
proquest_journals_3214787675
scitation_primary_10_1063_5_0267593
PublicationCentury 2000
PublicationDate 20250600
2025-06-01
20250601
PublicationDateYYYYMMDD 2025-06-01
PublicationDate_xml – month: 06
  year: 2025
  text: 20250600
PublicationDecade 2020
PublicationPlace Melville
PublicationPlace_xml – name: Melville
PublicationTitle Physics of fluids (1994)
PublicationYear 2025
Publisher American Institute of Physics
Publisher_xml – name: American Institute of Physics
References Lee, Tarver (c57) 1980
Wang (c7) 2018
Li (c3) 2023
Hirt, Nichols (c52) 1981
Gruninger (c64) 2024
Zhang (c17) 2015
Frantzis, Grigoriadis (c48) 2019
Kim, Peskin (c46) 2007
He (c43) 2021
Yang (c62) 2009
Keller, Kolodner (c12) 1956
Prosperetti, Lezzi (c11) 1986
Miller (c18) 2013
Li, Lai (c68) 2001
Tian (c29) 2019
Peskin, Printz (c67) 1993
Zhang (c15) 2024
Plesset (c8) 1949
Kim, Peskin (c47) 2016
Liu (c24) 2003
Peskin (c65) 2002
Benson (c59) 2008
He, Zhang, Liu (c21) 2020
Qiu, Liu, Khoo (c55) 2008
Li (c19) 2018
Zhang (c36) 2025
Plesset, Prosperetti (c9) 1977
Li, Liu, Tang (c16) 2024
Ming, Sun, Zhang (c26) 2014
Lee, Griffith (c63) 2022
Zhang (c25) 2013
Hu (c2) 2021
Ming (c27) 2016
Sun (c28) 2021
Benson (c38) 1992
Zhang (c33) 2023
Zhang (c13) 2023
Wang (c30) 2014
Tian (c42) 2021
Benson (c58) 1992
Liu (c41) 2024
Zhang (c20) 2025
Wu (c23) 2024
Kim, Kim, Choi (c45) 2001
May, Monaghan (c4) 2003
Van Leer (c60) 1977
Choung (c51) 2021
Li (c69) 2025
Duan, Li, Yang (c22) 2022
Gong, Zhang, Du (c32) 2023
Li (c50) 2023
Zhang, Zong (c6) 2011
Li (c34) 2024
Hua, Peskin (c61) 2022
Geers, Hunter (c10) 2002
Zhang (c37) 2024
Li (c1) 2019
Zong (c5) 2005
Peskin (c44) 1972
Liu (c40) 2023
Griffith, Patankar (c49) 2020
Tian (c53) 2018
Zhang (c14) 2023
Liu (c39) 2018
Xiao (c35)
Gong (c31) 2023
(2025060206242922100_c59) 2008; 75
(2025060206242922100_c47) 2016; 28
(2025060206242922100_c40) 2023; 958
(2025060206242922100_c42) 2021; 236
(2025060206242922100_c60) 1977; 23
(2025060206242922100_c62) 2009; 228
(2025060206242922100_c68) 2001; 171
(2025060206242922100_c26) 2014; 35
(2025060206242922100_c45) 2001; 171
(2025060206242922100_c41) 2024; 988
(2025060206242922100_c55) 2008; 3
(2025060206242922100_c34) 2024; 196
(2025060206242922100_c4) 2003; 71
(2025060206242922100_c32) 2023; 285
(2025060206242922100_c28) 2021; 426
(2025060206242922100_c64) 2024; 506
(2025060206242922100_c33) 2023; 283
(2025060206242922100_c27) 2016; 117
(2025060206242922100_c30) 2014; 39
(2025060206242922100_c52) 1981; 39
(2025060206242922100_c35); 2014
(2025060206242922100_c57) 1980; 23
(2025060206242922100_c10) 2002; 111
(2025060206242922100_c25) 2013; 71
(2025060206242922100_c46) 2007; 19
(2025060206242922100_c23) 2024; 36
(2025060206242922100_c3) 2023; 962
(2025060206242922100_c14) 2023; 66
(2025060206242922100_c51) 2021; 433
(2025060206242922100_c12) 1956; 27
(2025060206242922100_c53) 2018; 170
(2025060206242922100_c24) 2003; 30
(2025060206242922100_c66) 1994
(2025060206242922100_c29) 2019; 118
(2025060206242922100_c36) 2025; 24
(2025060206242922100_c16) 2024; 36
(2025060206242922100_c6) 2011; 27
(2025060206242922100_c56) 1968
(2025060206242922100_c38) 1992; 99
(2025060206242922100_c18) 2013; 87
(2025060206242922100_c43) 2021; 127
(2025060206242922100_c67) 1993; 105
(2025060206242922100_c54) 1982
(2025060206242922100_c1) 2019; 392
(2025060206242922100_c49) 2020; 52
(2025060206242922100_c13) 2023; 35
(2025060206242922100_c48) 2019; 376
(2025060206242922100_c50) 2023; 253
(2025060206242922100_c65) 2002; 11
(2025060206242922100_c37) 2024; 23
(2025060206242922100_c69) 2025; 154
(2025060206242922100_c9) 1977; 9
(2025060206242922100_c11) 1986; 168
(2025060206242922100_c31) 2023; 276
(2025060206242922100_c8) 1949; 16
(2025060206242922100_c39) 2018; 166
(2025060206242922100_c7) 2018; 78
(2025060206242922100_c20) 2025; 1003
(2025060206242922100_c63) 2022; 457
(2025060206242922100_c2) 2021; 238
(2025060206242922100_c19) 2018; 74
(2025060206242922100_c21) 2020; 10
(2025060206242922100_c44) 1972; 10
(2025060206242922100_c17) 2015; 776
(2025060206242922100_c61) 2022; 467
(2025060206242922100_c15) 2024; 999
(2025060206242922100_c22) 2022; 461
(2025060206242922100_c5) 2005; 20
(2025060206242922100_c58) 1992; 100
References_xml – start-page: 1326
  year: 2011
  ident: c6
  article-title: The effect of rigid-body motions on the whipping response of a ship hull subjected to an underwater bubble
  publication-title: J. Fluids Struct.
– start-page: 114898
  year: 2023
  ident: c33
  article-title: Multi-peak phenomenon of large-scale hull structural damage under near-field underwater explosion
  publication-title: Ocean Eng.
– start-page: 90
  year: 2014
  ident: c30
  article-title: Experimental and numerical investigation of ship structure subjected to close-in underwater shock wave and following gas bubble pulse
  publication-title: Mar. Struct.
– start-page: 132
  year: 2001
  ident: c45
  article-title: An immersed-boundary finite-volume method for simulations of flow in complex geometries
  publication-title: J. Comput. Phys.
– start-page: 285
  year: 2025
  ident: c36
  article-title: Review of research on underwater explosions related to ship damage and stability
  publication-title: J. Mar. Sci. Appl.
– start-page: A4
  year: 2025
  ident: c20
  article-title: Free-surface jetting driven by a cavitating vortex ring
  publication-title: J. Fluid Mech.
– start-page: 112888
  year: 2024
  ident: c64
  article-title: Benchmarking the immersed boundary method for viscoelastic flows
  publication-title: J. Comput. Phys.
– start-page: 201
  year: 1981
  ident: c52
  article-title: Volume of fluid (VOF) method for the dynamics of free boundaries
  publication-title: J. Comput. Phys.
– start-page: 252
  year: 1972
  ident: c44
  article-title: Flow patterns around heart valves: A numerical method
  publication-title: J. Comput. Phys.
– start-page: 479
  year: 2002
  ident: c65
  article-title: The immersed boundary method
  publication-title: Acta Numer.
– start-page: 235
  year: 1992
  ident: c38
  article-title: Computational methods in Lagrangian and Eulerian hydrocodes
  publication-title: Comput. Methods Appl. Mech. Eng.
– start-page: 106
  year: 2003
  ident: c24
  article-title: Smoothed particle hydrodynamics for numerical simulation of underwater explosion
  publication-title: Comput. Mech.
– start-page: 705256
  ident: c35
  article-title: Experimental research on the dynamic response of floating structures with coatings subjected to underwater explosion
  publication-title: Shock Vib.
– start-page: A28
  year: 2023
  ident: c3
  article-title: Vertically neutral collapse of a pulsating bubble at the corner of a free surface and a rigid wall
  publication-title: J. Fluid Mech.
– start-page: 302
  year: 2024
  ident: c37
  article-title: Characterization of underwater explosive loads of blasting and shaped charges
  publication-title: J. Mar. Sci. Appl.
– start-page: 713
  year: 2019
  ident: c1
  article-title: 3D full coupling model for strong interaction between a pulsating bubble and a movable sphere
  publication-title: J. Comput. Phys.
– start-page: 111547
  year: 2024
  ident: c34
  article-title: Experimental study of the coupled damage characteristics of a large-scale hull girder subjected to an underwater near-field explosion
  publication-title: Thin-Walled Struct.
– start-page: 1152
  year: 1956
  ident: c12
  article-title: Damping of underwater explosion bubble oscillations
  publication-title: J. Appl. Phys.
– start-page: 124711
  year: 2023
  ident: c14
  article-title: Theoretical study on bubble dynamics under hybrid-boundary and multi-bubble conditions using the unified equation
  publication-title: Sci. China Phys. Mech. Astron.
– start-page: 842
  year: 2003
  ident: c4
  article-title: Can a single bubble sink a ship?
  publication-title: Am. J. Phys.
– start-page: 2362
  year: 1980
  ident: c57
  article-title: Phenomenological model of shock initiation in heterogeneous explosives
  publication-title: Phys. Fluids
– start-page: 033323
  year: 2023
  ident: c13
  article-title: A unified theory for bubble dynamics
  publication-title: Phys. Fluids
– start-page: 276
  year: 1977
  ident: c60
  article-title: Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
  publication-title: J. Comput. Phys.
– start-page: 1549
  year: 2008
  ident: c59
  article-title: Momentum advection on unstructured staggered quadrilateral meshes
  publication-title: Int. J. Numer. Methods Eng.
– start-page: 359
  year: 2016
  ident: c27
  article-title: Damage characteristics of ship structures subjected to shockwaves of underwater contact explosions
  publication-title: Ocean Eng.
– start-page: 108401
  year: 2023
  ident: c50
  article-title: A sharp interface immersed boundary method for thin-walled geometries in viscous compressible flows
  publication-title: Int. J. Mech. Sci.
– start-page: 115403
  year: 2023
  ident: c32
  article-title: Damage mechanisms of a typical simplified hull girder with thinner plates subjected to near-field underwater explosions
  publication-title: Ocean Eng.
– start-page: 104339
  year: 2025
  ident: c69
  article-title: Predicting the collapse direction of large-scale pulsating bubbles based on Kelvin impulse theory
  publication-title: Appl. Ocean Res.
– start-page: 28
  year: 2019
  ident: c48
  article-title: An efficient method for two-fluid incompressible flows appropriate for the immersed boundary method
  publication-title: J. Comput. Phys.
– start-page: 111042
  year: 2022
  ident: c63
  article-title: On the Lagrangian-Eulerian coupling in the immersed finite element/difference method
  publication-title: J. Comput. Phys.
– start-page: 1584
  year: 2002
  ident: c10
  article-title: An integrated wave-effects model for an underwater explosion bubble
  publication-title: J. Acoust. Soc. Am.
– start-page: 093309
  year: 2024
  ident: c16
  article-title: Multi-cycle dynamics of underwater explosion bubbles: An experimental investigation
  publication-title: Phys. Fluids
– start-page: 277
  year: 1949
  ident: c8
  article-title: The dynamics of cavitation bubbles
  publication-title: J. Appl. Mech.
– start-page: 359
  year: 2005
  ident: c5
  article-title: A hydroplastic analysis of a free–free beam floating on water subjected to an underwater bubble
  publication-title: J. Fluids Struct.
– start-page: 923
  year: 2021
  ident: c43
  article-title: The nonlinear coupling of oscillating bubble and floating body with circular hole
  publication-title: Comput. Model. Eng. Sci.
– start-page: 111215
  year: 2022
  ident: c22
  article-title: An energy diminishing arbitrary Lagrangian–Eulerian finite element method for two-phase Navier–Stokes flow
  publication-title: J. Comput. Phys.
– start-page: 169
  year: 2013
  ident: c25
  article-title: Numerical simulation of column charge underwater explosion based on SPH and BEM combination
  publication-title: Comput. Fluids
– start-page: 397
  year: 2019
  ident: c29
  article-title: Dynamic response of floating body subjected to underwater explosion bubble and generated waves with 2D numerical model
  publication-title: Comput. Model. Eng. Sci.
– start-page: 111435
  year: 2022
  ident: c61
  article-title: An analysis of the numerical stability of the immersed boundary method
  publication-title: J. Comput. Phys.
– start-page: 49
  year: 2018
  ident: c19
  article-title: Numerical investigation of an underwater explosion bubble based on FVM and VOF
  publication-title: Appl. Ocean Res.
– start-page: A42
  year: 2023
  ident: c40
  article-title: Investigation of hydrodynamics of water impact and tail slamming of high-speed water entry with a novel immersed boundary method
  publication-title: J. Fluid Mech.
– start-page: 033603
  year: 2016
  ident: c47
  article-title: A penalty immersed boundary method for a rigid body in fluid
  publication-title: Phys. Fluids
– start-page: 16
  year: 2020
  ident: c21
  article-title: Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method
  publication-title: Theor. Appl. Mech. Lett.
– start-page: 41
  year: 2018
  ident: c53
  article-title: Analysis of breaking and re-closure of a bubble near a free surface based on the Eulerian finite element method
  publication-title: Comput. Fluids
– start-page: 453
  year: 2014
  ident: c26
  article-title: Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method
  publication-title: Appl. Math. Mech.
– start-page: 114120
  year: 2023
  ident: c31
  article-title: Research on the progressive sagging damage and plastic hinge line mechanism of basic simplified hull girder subjected to near-field underwater explosion bubble
  publication-title: Ocean Eng.
– start-page: 421
  year: 2020
  ident: c49
  article-title: Immersed methods for fluid–structure interaction
  publication-title: Annu. Rev. Fluid Mech.
– start-page: 145
  year: 1977
  ident: c9
  article-title: Bubble dynamics and cavitation
  publication-title: Annu. Rev. Fluid Mech.
– start-page: A53
  year: 2024
  ident: c41
  article-title: Investigation of free surface effect on the cavity expansion and contraction in high-speed water entry
  publication-title: J. Fluid Mech.
– start-page: 822
  year: 2001
  ident: c68
  article-title: The immersed interface method for the Navier–Stokes equations with singular forces
  publication-title: J. Comput. Phys.
– start-page: 053103
  year: 2007
  ident: c46
  article-title: Penalty immersed boundary method for an elastic boundary with mass
  publication-title: Phys. Fluids
– start-page: 50
  year: 2018
  ident: c7
  article-title: Simulations of the dynamics and interaction between a floating structure and a near-field explosion bubble
  publication-title: Appl. Ocean Res.
– start-page: 143
  year: 1992
  ident: c58
  article-title: Momentum advection on a staggered mesh
  publication-title: J. Comput. Phys.
– start-page: 132
  year: 2013
  ident: c18
  article-title: A pressure-based, compressible, two-phase flow finite volume method for underwater explosions
  publication-title: Comput. Fluids
– start-page: 109537
  year: 2021
  ident: c42
  article-title: Transient fluid–solid interaction with the improved penalty immersed boundary method
  publication-title: Ocean Eng.
– start-page: A58
  year: 2024
  ident: c15
  article-title: A theoretical model for compressible bubble dynamics considering phase transition and migration
  publication-title: J. Fluid Mech.
– start-page: 110198
  year: 2021
  ident: c51
  article-title: Nonlinear weighting process in ghost-cell immersed boundary methods for compressible flow
  publication-title: J. Comput. Phys.
– start-page: 182
  year: 2018
  ident: c39
  article-title: Investigation of free-field underwater explosion with Eulerian finite element method
  publication-title: Ocean Eng.
– start-page: 33
  year: 1993
  ident: c67
  article-title: Improved volume conservation in the computation of flows with immersed elastic boundaries
  publication-title: J. Comput. Phys.
– start-page: 109937
  year: 2021
  ident: c28
  article-title: An accurate SPH volume adaptive scheme for modeling strongly-compressible multiphase flows. Part 1: Numerical scheme and validations with basic 1D and 2D benchmarks
  publication-title: J. Comput. Phys.
– start-page: 479
  year: 2008
  ident: c55
  article-title: Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with the ghost fluid method
  publication-title: Commun. Comput. Phys.
– start-page: 7821
  year: 2009
  ident: c62
  article-title: A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations
  publication-title: J. Comput. Phys.
– start-page: 109650
  year: 2021
  ident: c2
  article-title: The role of fluid–structure interaction in pulsating bubble dynamics near a movable structure
  publication-title: Ocean Eng.
– start-page: 457
  year: 1986
  ident: c11
  article-title: Bubble dynamics in a compressible liquid. Part 1. First-order theory
  publication-title: J. Fluid Mech.
– start-page: 137
  year: 2015
  ident: c17
  article-title: Experimental study on bubble dynamics subject to buoyancy
  publication-title: J. Fluid Mech.
– start-page: 106125
  year: 2024
  ident: c23
  article-title: Study on the jetting characteristics of an underwater explosion bubble collapsing near a floating body
  publication-title: Phys. Fluids
– volume: 30
  start-page: 106
  issue: 2
  year: 2003
  ident: 2025060206242922100_c24
  article-title: Smoothed particle hydrodynamics for numerical simulation of underwater explosion
  publication-title: Comput. Mech.
  doi: 10.1007/s00466-002-0371-6
– volume: 24
  start-page: 285
  year: 2025
  ident: 2025060206242922100_c36
  article-title: Review of research on underwater explosions related to ship damage and stability
  publication-title: J. Mar. Sci. Appl.
  doi: 10.1007/s11804-025-00633-4
– volume: 99
  start-page: 235
  issue: 2
  year: 1992
  ident: 2025060206242922100_c38
  article-title: Computational methods in Lagrangian and Eulerian hydrocodes
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/0045-7825(92)90042-I
– volume: 71
  start-page: 842
  issue: 9
  year: 2003
  ident: 2025060206242922100_c4
  article-title: Can a single bubble sink a ship?
  publication-title: Am. J. Phys.
  doi: 10.1119/1.1582187
– volume: 283
  start-page: 114898
  year: 2023
  ident: 2025060206242922100_c33
  article-title: Multi-peak phenomenon of large-scale hull structural damage under near-field underwater explosion
  publication-title: Ocean Eng.
  doi: 10.1016/j.oceaneng.2023.114898
– volume: 35
  start-page: 453
  issue: 4
  year: 2014
  ident: 2025060206242922100_c26
  article-title: Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method
  publication-title: Appl. Math. Mech.
  doi: 10.1007/s10483-014-1804-6
– volume: 87
  start-page: 132
  year: 2013
  ident: 2025060206242922100_c18
  article-title: A pressure-based, compressible, two-phase flow finite volume method for underwater explosions
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2013.04.002
– volume: 16
  start-page: 277
  issue: 3
  year: 1949
  ident: 2025060206242922100_c8
  article-title: The dynamics of cavitation bubbles
  publication-title: J. Appl. Mech.
  doi: 10.1115/1.4009975
– volume: 35
  start-page: 033323
  issue: 3
  year: 2023
  ident: 2025060206242922100_c13
  article-title: A unified theory for bubble dynamics
  publication-title: Phys. Fluids
  doi: 10.1063/5.0145415
– volume: 196
  start-page: 111547
  year: 2024
  ident: 2025060206242922100_c34
  article-title: Experimental study of the coupled damage characteristics of a large-scale hull girder subjected to an underwater near-field explosion
  publication-title: Thin-Walled Struct.
  doi: 10.1016/j.tws.2023.111547
– volume: 238
  start-page: 109650
  year: 2021
  ident: 2025060206242922100_c2
  article-title: The role of fluid–structure interaction in pulsating bubble dynamics near a movable structure
  publication-title: Ocean Eng.
  doi: 10.1016/j.oceaneng.2021.109650
– volume: 78
  start-page: 50
  year: 2018
  ident: 2025060206242922100_c7
  article-title: Simulations of the dynamics and interaction between a floating structure and a near-field explosion bubble
  publication-title: Appl. Ocean Res.
  doi: 10.1016/j.apor.2018.06.004
– volume: 74
  start-page: 49
  year: 2018
  ident: 2025060206242922100_c19
  article-title: Numerical investigation of an underwater explosion bubble based on FVM and VOF
  publication-title: Appl. Ocean Res.
  doi: 10.1016/j.apor.2018.02.024
– volume: 10
  start-page: 252
  issue: 2
  year: 1972
  ident: 2025060206242922100_c44
  article-title: Flow patterns around heart valves: A numerical method
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(72)90065-4
– volume: 433
  start-page: 110198
  year: 2021
  ident: 2025060206242922100_c51
  article-title: Nonlinear weighting process in ghost-cell immersed boundary methods for compressible flow
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2021.110198
– volume: 276
  start-page: 114120
  year: 2023
  ident: 2025060206242922100_c31
  article-title: Research on the progressive sagging damage and plastic hinge line mechanism of basic simplified hull girder subjected to near-field underwater explosion bubble
  publication-title: Ocean Eng.
  doi: 10.1016/j.oceaneng.2023.114120
– volume: 958
  start-page: A42
  year: 2023
  ident: 2025060206242922100_c40
  article-title: Investigation of hydrodynamics of water impact and tail slamming of high-speed water entry with a novel immersed boundary method
  publication-title: J. Fluid Mech.
  doi: 10.1017/jfm.2023.120
– volume: 506
  start-page: 112888
  year: 2024
  ident: 2025060206242922100_c64
  article-title: Benchmarking the immersed boundary method for viscoelastic flows
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2024.112888
– volume: 20
  start-page: 359
  issue: 3
  year: 2005
  ident: 2025060206242922100_c5
  article-title: A hydroplastic analysis of a free–free beam floating on water subjected to an underwater bubble
  publication-title: J. Fluids Struct.
  doi: 10.1016/j.jfluidstructs.2004.08.003
– volume: 111
  start-page: 1584
  issue: 4
  year: 2002
  ident: 2025060206242922100_c10
  article-title: An integrated wave-effects model for an underwater explosion bubble
  publication-title: J. Acoust. Soc. Am.
  doi: 10.1121/1.1458590
– volume: 52
  start-page: 421
  year: 2020
  ident: 2025060206242922100_c49
  article-title: Immersed methods for fluid–structure interaction
  publication-title: Annu. Rev. Fluid Mech.
  doi: 10.1146/annurev-fluid-010719-060228
– volume: 3
  start-page: 479
  issue: 2
  year: 2008
  ident: 2025060206242922100_c55
  article-title: Simulations of compressible two-medium flow by Runge-Kutta discontinuous Galerkin methods with the ghost fluid method
  publication-title: Commun. Comput. Phys.
– volume: 236
  start-page: 109537
  year: 2021
  ident: 2025060206242922100_c42
  article-title: Transient fluid–solid interaction with the improved penalty immersed boundary method
  publication-title: Ocean Eng.
  doi: 10.1016/j.oceaneng.2021.109537
– volume: 228
  start-page: 7821
  issue: 20
  year: 2009
  ident: 2025060206242922100_c62
  article-title: A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2009.07.023
– volume: 426
  start-page: 109937
  year: 2021
  ident: 2025060206242922100_c28
  article-title: An accurate SPH volume adaptive scheme for modeling strongly-compressible multiphase flows. Part 1: Numerical scheme and validations with basic 1D and 2D benchmarks
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2020.109937
– volume: 285
  start-page: 115403
  year: 2023
  ident: 2025060206242922100_c32
  article-title: Damage mechanisms of a typical simplified hull girder with thinner plates subjected to near-field underwater explosions
  publication-title: Ocean Eng.
  doi: 10.1016/j.oceaneng.2023.115403
– volume: 19
  start-page: 053103
  issue: 5
  year: 2007
  ident: 2025060206242922100_c46
  article-title: Penalty immersed boundary method for an elastic boundary with mass
  publication-title: Phys. Fluids
  doi: 10.1063/1.2734674
– volume: 376
  start-page: 28
  year: 2019
  ident: 2025060206242922100_c48
  article-title: An efficient method for two-fluid incompressible flows appropriate for the immersed boundary method
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2018.09.035
– volume: 36
  start-page: 093309
  issue: 9
  year: 2024
  ident: 2025060206242922100_c16
  article-title: Multi-cycle dynamics of underwater explosion bubbles: An experimental investigation
  publication-title: Phys. Fluids
  doi: 10.1063/5.0224177
– volume: 11
  start-page: 479
  year: 2002
  ident: 2025060206242922100_c65
  article-title: The immersed boundary method
  publication-title: Acta Numer.
  doi: 10.1017/S0962492902000077
– volume: 39
  start-page: 201
  issue: 1
  year: 1981
  ident: 2025060206242922100_c52
  article-title: Volume of fluid (VOF) method for the dynamics of free boundaries
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(81)90145-5
– volume: 66
  start-page: 124711
  issue: 12
  year: 2023
  ident: 2025060206242922100_c14
  article-title: Theoretical study on bubble dynamics under hybrid-boundary and multi-bubble conditions using the unified equation
  publication-title: Sci. China Phys. Mech. Astron.
  doi: 10.1007/s11433-023-2204-x
– volume: 171
  start-page: 822
  issue: 2
  year: 2001
  ident: 2025060206242922100_c68
  article-title: The immersed interface method for the Navier–Stokes equations with singular forces
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.2001.6813
– volume: 127
  start-page: 923
  issue: 3
  year: 2021
  ident: 2025060206242922100_c43
  article-title: The nonlinear coupling of oscillating bubble and floating body with circular hole
  publication-title: Comput. Model. Eng. Sci.
  doi: 10.32604/cmes.2021.015259
– volume: 1003
  start-page: A4
  year: 2025
  ident: 2025060206242922100_c20
  article-title: Free-surface jetting driven by a cavitating vortex ring
  publication-title: J. Fluid Mech.
  doi: 10.1017/jfm.2024.1209
– volume: 392
  start-page: 713
  year: 2019
  ident: 2025060206242922100_c1
  article-title: 3D full coupling model for strong interaction between a pulsating bubble and a movable sphere
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2019.05.001
– volume-title: Adiabatic Expansion of High Explosive Detonation Products
  year: 1968
  ident: 2025060206242922100_c56
– volume: 776
  start-page: 137
  year: 2015
  ident: 2025060206242922100_c17
  article-title: Experimental study on bubble dynamics subject to buoyancy
  publication-title: J. Fluid Mech.
  doi: 10.1017/jfm.2015.323
– volume: 2014
  start-page: 705256
  issue: 1
  ident: 2025060206242922100_c35
  article-title: Experimental research on the dynamic response of floating structures with coatings subjected to underwater explosion
  publication-title: Shock Vib.
  doi: 10.1155/2014/705256
– volume: 36
  start-page: 106125
  issue: 10
  year: 2024
  ident: 2025060206242922100_c23
  article-title: Study on the jetting characteristics of an underwater explosion bubble collapsing near a floating body
  publication-title: Phys. Fluids
  doi: 10.1063/5.0230647
– volume: 168
  start-page: 457
  year: 1986
  ident: 2025060206242922100_c11
  article-title: Bubble dynamics in a compressible liquid. Part 1. First-order theory
  publication-title: J. Fluid Mech.
  doi: 10.1017/S0022112086000460
– volume: 170
  start-page: 41
  year: 2018
  ident: 2025060206242922100_c53
  article-title: Analysis of breaking and re-closure of a bubble near a free surface based on the Eulerian finite element method
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2018.04.028
– volume: 28
  start-page: 033603
  issue: 3
  year: 2016
  ident: 2025060206242922100_c47
  article-title: A penalty immersed boundary method for a rigid body in fluid
  publication-title: Phys. Fluids
  doi: 10.1063/1.4944565
– volume: 117
  start-page: 359
  year: 2016
  ident: 2025060206242922100_c27
  article-title: Damage characteristics of ship structures subjected to shockwaves of underwater contact explosions
  publication-title: Ocean Eng.
  doi: 10.1016/j.oceaneng.2016.03.040
– volume: 467
  start-page: 111435
  year: 2022
  ident: 2025060206242922100_c61
  article-title: An analysis of the numerical stability of the immersed boundary method
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2022.111435
– volume: 118
  start-page: 397
  issue: 2
  year: 2019
  ident: 2025060206242922100_c29
  article-title: Dynamic response of floating body subjected to underwater explosion bubble and generated waves with 2D numerical model
  publication-title: Comput. Model. Eng. Sci.
  doi: 10.31614/cmes.2019.04419
– volume-title: Guidance and Control of Ocean Vehicles
  year: 1994
  ident: 2025060206242922100_c66
– volume: 23
  start-page: 2362
  issue: 12
  year: 1980
  ident: 2025060206242922100_c57
  article-title: Phenomenological model of shock initiation in heterogeneous explosives
  publication-title: Phys. Fluids
  doi: 10.1063/1.862940
– volume: 171
  start-page: 132
  issue: 1
  year: 2001
  ident: 2025060206242922100_c45
  article-title: An immersed-boundary finite-volume method for simulations of flow in complex geometries
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.2001.6778
– volume: 962
  start-page: A28
  year: 2023
  ident: 2025060206242922100_c3
  article-title: Vertically neutral collapse of a pulsating bubble at the corner of a free surface and a rigid wall
  publication-title: J. Fluid Mech.
  doi: 10.1017/jfm.2023.292
– volume: 988
  start-page: A53
  year: 2024
  ident: 2025060206242922100_c41
  article-title: Investigation of free surface effect on the cavity expansion and contraction in high-speed water entry
  publication-title: J. Fluid Mech.
  doi: 10.1017/jfm.2024.473
– volume: 27
  start-page: 1326
  issue: 8
  year: 2011
  ident: 2025060206242922100_c6
  article-title: The effect of rigid-body motions on the whipping response of a ship hull subjected to an underwater bubble
  publication-title: J. Fluids Struct.
  doi: 10.1016/j.jfluidstructs.2011.05.004
– volume: 39
  start-page: 90
  year: 2014
  ident: 2025060206242922100_c30
  article-title: Experimental and numerical investigation of ship structure subjected to close-in underwater shock wave and following gas bubble pulse
  publication-title: Mar. Struct.
  doi: 10.1016/j.marstruc.2014.07.003
– volume: 166
  start-page: 182
  year: 2018
  ident: 2025060206242922100_c39
  article-title: Investigation of free-field underwater explosion with Eulerian finite element method
  publication-title: Ocean Eng.
  doi: 10.1016/j.oceaneng.2018.08.001
– volume: 27
  start-page: 1152
  issue: 10
  year: 1956
  ident: 2025060206242922100_c12
  article-title: Damping of underwater explosion bubble oscillations
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1722221
– volume: 75
  start-page: 1549
  issue: 13
  year: 2008
  ident: 2025060206242922100_c59
  article-title: Momentum advection on unstructured staggered quadrilateral meshes
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.2310
– volume: 461
  start-page: 111215
  year: 2022
  ident: 2025060206242922100_c22
  article-title: An energy diminishing arbitrary Lagrangian–Eulerian finite element method for two-phase Navier–Stokes flow
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2022.111215
– volume: 105
  start-page: 33
  issue: 1
  year: 1993
  ident: 2025060206242922100_c67
  article-title: Improved volume conservation in the computation of flows with immersed elastic boundaries
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.1993.1051
– volume: 23
  start-page: 302
  issue: 2
  year: 2024
  ident: 2025060206242922100_c37
  article-title: Characterization of underwater explosive loads of blasting and shaped charges
  publication-title: J. Mar. Sci. Appl.
  doi: 10.1007/s11804-024-00422-5
– volume: 154
  start-page: 104339
  year: 2025
  ident: 2025060206242922100_c69
  article-title: Predicting the collapse direction of large-scale pulsating bubbles based on Kelvin impulse theory
  publication-title: Appl. Ocean Res.
  doi: 10.1016/j.apor.2024.104339
– volume: 23
  start-page: 276
  issue: 3
  year: 1977
  ident: 2025060206242922100_c60
  article-title: Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(77)90095-X
– volume: 10
  start-page: 16
  issue: 1
  year: 2020
  ident: 2025060206242922100_c21
  article-title: Prolonged simulation of near-free surface underwater explosion based on Eulerian finite element method
  publication-title: Theor. Appl. Mech. Lett.
  doi: 10.1016/j.taml.2020.01.003
– volume: 253
  start-page: 108401
  year: 2023
  ident: 2025060206242922100_c50
  article-title: A sharp interface immersed boundary method for thin-walled geometries in viscous compressible flows
  publication-title: Int. J. Mech. Sci.
  doi: 10.1016/j.ijmecsci.2023.108401
– volume: 71
  start-page: 169
  year: 2013
  ident: 2025060206242922100_c25
  article-title: Numerical simulation of column charge underwater explosion based on SPH and BEM combination
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2012.10.012
– volume: 100
  start-page: 143
  issue: 1
  year: 1992
  ident: 2025060206242922100_c58
  article-title: Momentum advection on a staggered mesh
  publication-title: J. Comput. Phys.
  doi: 10.1016/0021-9991(92)90316-Q
– volume: 999
  start-page: A58
  year: 2024
  ident: 2025060206242922100_c15
  article-title: A theoretical model for compressible bubble dynamics considering phase transition and migration
  publication-title: J. Fluid Mech.
  doi: 10.1017/jfm.2024.954
– volume: 457
  start-page: 111042
  year: 2022
  ident: 2025060206242922100_c63
  article-title: On the Lagrangian-Eulerian coupling in the immersed finite element/difference method
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2022.111042
– volume: 9
  start-page: 145
  issue: 1
  year: 1977
  ident: 2025060206242922100_c9
  article-title: Bubble dynamics and cavitation
  publication-title: Annu. Rev. Fluid Mech.
  doi: 10.1146/annurev.fl.09.010177.001045
– volume-title: Numerical Methods for Fluid Dynamics
  year: 1982
  ident: 2025060206242922100_c54
SSID ssj0003926
Score 2.4632807
Snippet A high-pressure pulsating bubble near the free surface casts intense nonlinear impacts on adjacent floating structure, and the rigid-body motion caused by the...
SourceID proquest
crossref
scitation
SourceType Aggregation Database
Index Database
Publisher
SubjectTerms Finite element method
Floating structures
Fluid-structure interaction
Free surfaces
Mathematical analysis
Numerical models
Rigid-body dynamics
Underwater explosions
Title Dynamic responses of a floating rigid hull subject to a pulsating bubble
URI http://dx.doi.org/10.1063/5.0267593
https://www.proquest.com/docview/3214787675
Volume 37
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3fa9swEBZdythe-iNbadZuiLVvxlliybL9WLqGULr2xYG8GcmSWCEkpbFf9tfv9MN2DF3Z9mKMcA5z31l8p3x3h9Cl1IRKQeFDIiI1CYoKs0TqsJSkpJKYMDKFwj_u2XxBb5fxspvzaatLKjEuf71YV_I_qMIa4GqqZP8B2dYoLMA94AtXQBiuf4XxdzdOPnh2QlfXP5YHerXhVs1shl7J4CdkmcG2FubExVBNHjzVq617QtRCrHpqICsJLa0lvaofpWvllGW0OTPwRwRR3EmZdlT5fN3XH3hzO3sffP0hEBD3Q-XX0ixMmBuM0myYrkuLDwz24j4MxAecF4_NfKvYjUDs97q-fyhmi7u7Ir9Z5m_QfgQkP7LCy06gA8yNOcWoe62mLxQj31rDfTbRpQjvgD84KcMOW8iP0IGn-fjKYXaM9tR6iA495cd-Q90O0Vvvnw9o7sHELZh4ozHHDZjYgokNmNiDiasNPNCCiR2YH9FidpNfz0M_5iIsITuvQm6KmYFHTBWw4dLMDaJCTyWP4lQzPYkSlaVZLGOlaSKA8ClGzL-ncjrJOCSgmpygwXqzVqcIC50wKRkVJSF0QoCNSUVKlkURV6aEeYS-Nu4qnlw3k8KqEBgp4sL7dITOG0cWPti3hZ1nlZrOPyN00Tr3z0Y-vW7kDL3vAvUcDarnWn0GdleJLzYIfgMJbE23
linkProvider American Institute of Physics
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=Dynamic+responses+of+a+floating+rigid+hull+subject+to+a+pulsating+bubble&rft.jtitle=Physics+of+fluids+%281994%29&rft.date=2025-06-01&rft.pub=American+Institute+of+Physics&rft.issn=1070-6631&rft.eissn=1089-7666&rft.volume=37&rft.issue=6&rft_id=info:doi/10.1063%2F5.0267593&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1070-6631&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1070-6631&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1070-6631&client=summon