An adaptive viscosity regularization approach for the numerical solution of conservation laws: Application to finite element methods

We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of conservation laws and an additional Helmholtz equation for the...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational physics Vol. 494; no. C; p. 112507
Main Authors Nguyen, Ngoc Cuong, Vila-Pérez, Jordi, Peraire, Jaime
Format Journal Article
LanguageEnglish
Published United States Elsevier Inc 01.12.2023
Elsevier
Subjects
Online AccessGet full text
ISSN0021-9991
1090-2716
1090-2716
DOI10.1016/j.jcp.2023.112507

Cover

Abstract We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of conservation laws and an additional Helmholtz equation for the artificial viscosity. We propose a homotopy continuation of the regularization parameters to minimize the amount of artificial viscosity subject to positivity-preserving and smoothness constraints on the numerical solution. The regularization methodology is combined with a mesh adaptation strategy that identifies the shock location and generates shock-aligned meshes, which allows to further reduce the amount of artificial dissipation and capture shocks with increased accuracy. We use the hybridizable discontinuous Galerkin method to numerically solve the regularized system of conservation laws and the continuous Galerkin method to solve the Helmholtz equation for the artificial viscosity. We show that the approach can produce approximate solutions that converge to the exact solution of the Burgers' equation. Finally, we demonstrate the performance of the method on inviscid transonic, supersonic, hypersonic flows in two dimensions. The approach is found to be accurate, robust and efficient, and yields very sharp yet smooth solutions in a few homotopy iterations. •An adaptive viscosity regularization method is developed for nonlinear conservation laws with shock waves.•It minimizes the amount of artificial viscosity and enforces smoothness constraints on the numerical solution.•It is applied to several inviscid transonic, supersonic, and hypersonic flows.•The method is found to yield accurate, sharp and smooth solutions within a few iterations.
AbstractList We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of conservation laws and an additional Helmholtz equation for the artificial viscosity. We propose a homotopy continuation of the regularization parameters to minimize the amount of artificial viscosity subject to positivity-preserving and smoothness constraints on the numerical solution. The regularization methodology is combined with a mesh adaptation strategy that identifies the shock location and generates shock-aligned meshes, which allows to further reduce the amount of artificial dissipation and capture shocks with increased accuracy. We use the hybridizable discontinuous Galerkin method to numerically solve the regularized system of conservation laws and the continuous Galerkin method to solve the Helmholtz equation for the artificial viscosity. We show that the approach can produce approximate solutions that converge to the exact solution of the Burgers' equation. Finally, we demonstrate the performance of the method on inviscid transonic, supersonic, hypersonic flows in two dimensions. The approach is found to be accurate, robust and efficient, and yields very sharp yet smooth solutions in a few homotopy iterations. •An adaptive viscosity regularization method is developed for nonlinear conservation laws with shock waves.•It minimizes the amount of artificial viscosity and enforces smoothness constraints on the numerical solution.•It is applied to several inviscid transonic, supersonic, and hypersonic flows.•The method is found to yield accurate, sharp and smooth solutions within a few iterations.
ArticleNumber 112507
Author Nguyen, Ngoc Cuong
Vila-Pérez, Jordi
Peraire, Jaime
Author_xml – sequence: 1
  givenname: Ngoc Cuong
  orcidid: 0000-0001-9167-5780
  surname: Nguyen
  fullname: Nguyen, Ngoc Cuong
  email: cuongng@mit.edu, cuongng@icloud.com
– sequence: 2
  givenname: Jordi
  surname: Vila-Pérez
  fullname: Vila-Pérez, Jordi
– sequence: 3
  givenname: Jaime
  surname: Peraire
  fullname: Peraire, Jaime
BackLink https://www.osti.gov/biblio/2202503$$D View this record in Osti.gov
BookMark eNqNkEtrGzEUhUVJoU7aH9CdyH5cPTyvZmVC0gYC3bRrobm6U8vI0iDJDs46Pzyyp6ssQlcCcb7Dud8lufDBIyFfOVtyxptv2-UWpqVgQi45FzVrP5AFZz2rRMubC7JgTPCq73v-iVymtGWMdfWqW5CXtafa6CnbA9KDTRCSzUca8e_e6WifdbahJKYpBg0bOoZI8wap3-8wWtCOpuD250wYKQSfMB5mxumn9J2up8mV3PknBzpabzNSdLhDn-kO8yaY9Jl8HLVL-OXfe0X-3N_9vv1ZPf768XC7fqxANm2uACSX2MlaciF0iwMOshcr3regTddobvjQrFgNo2xAGmP6tpw9dI0cgI3NKK-ImHv3ftLHJ-2cmqLd6XhUnKmTR7VVxaM6eVSzxwJdz1BI2aoEZT9syqUeIStRkjWTJcTnEMSQUsTxv4rbN0zpPpvKUVv3Lnkzk1hkHSzG0yz0gMbG0yoT7Dv0K9ulrpw
CitedBy_id crossref_primary_10_1063_5_0249655
crossref_primary_10_1016_j_jcp_2024_113713
crossref_primary_10_1016_j_paerosci_2024_100999
crossref_primary_10_1080_10618562_2024_2326559
crossref_primary_10_1016_j_jcp_2024_113005
Cites_doi 10.1016/j.jcp.2009.06.040
10.1016/j.apnum.2003.11.002
10.1016/j.compfluid.2013.12.013
10.1016/j.camwa.2020.09.012
10.1002/fld.4223
10.1016/j.jcp.2013.03.026
10.1007/s10915-016-0287-5
10.1016/j.jcp.2015.04.026
10.1007/s10915-018-0811-x
10.1080/10618569508940734
10.1016/j.jcp.2018.03.029
10.1016/j.jcp.2006.12.017
10.1006/jcph.1998.5892
10.1016/0045-7825(86)90110-6
10.1137/S1064827503425298
10.1006/jcph.2001.6718
10.1051/mmnp/20116303
10.1007/s11831-020-09508-z
10.2514/1.J060459
10.1016/j.jcp.2009.10.028
10.1006/jcph.2002.7206
10.1016/j.jcp.2003.10.012
10.1016/j.jcp.2007.05.011
10.1002/nme.2579
10.1063/1.2728937
10.1090/mcom/3199
10.1016/j.jcp.2016.06.052
10.1016/j.jcp.2009.04.009
10.1002/fld.4697
10.1002/fld.4939
10.1016/j.jcp.2006.07.020
10.1016/j.compfluid.2014.01.024
10.1063/1.1699639
10.1007/s00220-015-2376-y
10.1137/0730016
10.1016/j.jcp.2012.02.033
10.1137/0726003
10.1016/j.compfluid.2016.04.004
10.1016/j.jcp.2009.11.005
10.1016/j.jcp.2016.11.042
10.1016/j.jcp.2017.02.015
10.1016/j.compfluid.2014.03.023
10.1016/j.jcp.2020.109385
10.1002/fld.3762
10.1016/j.jcp.2021.110906
10.1016/j.jcp.2008.06.034
10.1016/j.jcp.2018.09.016
10.1016/j.jcp.2009.11.010
10.4007/annals.2005.161.223
10.1016/j.compfluid.2014.01.022
10.1016/j.jcp.2004.09.011
10.1016/j.jcp.2007.12.024
10.1016/j.jcp.2013.04.012
10.2514/1.J061783
ContentType Journal Article
Copyright 2023 Elsevier Inc.
Copyright_xml – notice: 2023 Elsevier Inc.
DBID AAYXX
CITATION
OTOTI
ADTOC
UNPAY
DOI 10.1016/j.jcp.2023.112507
DatabaseName CrossRef
OSTI.GOV
Unpaywall for CDI: Periodical Content
Unpaywall
DatabaseTitle CrossRef
DatabaseTitleList
Database_xml – sequence: 1
  dbid: UNPAY
  name: Unpaywall
  url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/
  sourceTypes: Open Access Repository
DeliveryMethod fulltext_linktorsrc
Discipline Applied Sciences
EISSN 1090-2716
ExternalDocumentID oai:osti.gov:2202503
2202503
10_1016_j_jcp_2023_112507
S0021999123006022
GroupedDBID --K
--M
-~X
.~1
0R~
1B1
1RT
1~.
1~5
4.4
457
4G.
5GY
5VS
6OB
7-5
71M
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAXUO
AAYFN
ABBOA
ABFRF
ABJNI
ABMAC
ABNEU
ABYKQ
ACBEA
ACDAQ
ACFVG
ACGFO
ACGFS
ACNCT
ACRLP
ACZNC
ADBBV
ADEZE
AEBSH
AEFWE
AEKER
AENEX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHZHX
AIALX
AIEXJ
AIKHN
AITUG
AIVDX
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
AXJTR
BKOJK
BLXMC
CS3
DM4
DU5
EBS
EFBJH
EFLBG
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FIRID
FNPLU
FYGXN
G-Q
GBLVA
GBOLZ
HLZ
HVGLF
IHE
J1W
K-O
KOM
LG5
LX9
LZ4
M37
M41
MO0
N9A
O-L
O9-
OAUVE
OGIMB
OZT
P-8
P-9
P2P
PC.
Q38
RNS
ROL
RPZ
SDF
SDG
SDP
SES
SEW
SPC
SPCBC
SPD
SSQ
SSV
SSZ
T5K
TN5
UPT
YQT
ZMT
ZU3
~02
~G-
29K
6TJ
8WZ
A6W
AAQXK
AATTM
AAXKI
AAYWO
AAYXX
ABFNM
ABWVN
ABXDB
ACLOT
ACNNM
ACRPL
ACVFH
ADCNI
ADFGL
ADIYS
ADJOM
ADMUD
ADNMO
AEIPS
AEUPX
AFFNX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
ASPBG
AVWKF
AZFZN
BBWZM
CAG
CITATION
COF
D-I
EFKBS
EJD
FGOYB
G-2
HME
HMV
HZ~
NDZJH
R2-
SBC
SHN
SPG
T9H
UQL
WUQ
ZY4
~HD
OTOTI
RIG
ADTOC
UNPAY
ID FETCH-LOGICAL-c367t-cc313e8353122a7ebeb3924197cad86a1d1b6405cf36c3ddd97002b863bc0f6f3
IEDL.DBID .~1
ISSN 0021-9991
1090-2716
IngestDate Sun Oct 26 03:58:41 EDT 2025
Mon Oct 21 03:31:28 EDT 2024
Wed Oct 01 02:37:06 EDT 2025
Thu Apr 24 23:10:38 EDT 2025
Fri Feb 23 02:36:04 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue C
Keywords Conservation laws
Adaptive viscosity
Shock waves
Discontinuous Galerkin methods
Finite element methods
Shock capturing
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c367t-cc313e8353122a7ebeb3924197cad86a1d1b6405cf36c3ddd97002b863bc0f6f3
Notes NA0003965
USDOE
ORCID 0000-0001-9167-5780
0000000191675780
OpenAccessLink https://proxy.k.utb.cz/login?url=https://www.osti.gov/biblio/2202503
ParticipantIDs unpaywall_primary_10_1016_j_jcp_2023_112507
osti_scitechconnect_2202503
crossref_primary_10_1016_j_jcp_2023_112507
crossref_citationtrail_10_1016_j_jcp_2023_112507
elsevier_sciencedirect_doi_10_1016_j_jcp_2023_112507
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2023-12-01
2023-12-00
PublicationDateYYYYMMDD 2023-12-01
PublicationDate_xml – month: 12
  year: 2023
  text: 2023-12-01
  day: 01
PublicationDecade 2020
PublicationPlace United States
PublicationPlace_xml – name: United States
PublicationTitle Journal of computational physics
PublicationYear 2023
Publisher Elsevier Inc
Elsevier
Publisher_xml – name: Elsevier Inc
– name: Elsevier
References Moro, Nguyen, Peraire (br0150) 2016; 82
Nguyen, Terrana, Peraire (br0630) 2023
Maday, Kaber, Tadmor (br0360) 1993; 30
Persson (br0110) 2013
Corrigan, Kercher, Kessler (br0480) 2019; 89
Kercher, Corrigan (br0500) 2021; 95
Premasuthan, Liang, Jameson (br0130) 2014; 98
Nguyen, Peraire (br0520) 2012; 231
Fernandez, Nguyen, Peraire (br0140) 2018
Mani, Larsson, Moin (br0080) 2009; 228
Jameson (br0340) 1995; 5
Moro, Nguyen, Peraire (br0540) 2011
Kawai, Lele (br0040) 2008; 227
Nguyen, Peraire (br0160) 2011
Zahr, Persson (br0450) 2018; 365
Hartmann (br0280) 2013; 72
Zhu, Zhong, Shu, Qiu (br0260) 2013; 248
Woopen, Balan, May, Schütz (br0560) 2014; 98
Hartmann, Houston (br0390) 2002; 183
Premasuthan, Liang, Jameson (br0120) 2013; 98
Zhu, Qiu, Shu, Dumbser (br0250) 2008; 227
Ching, Lv, Gnoffo, Barnhardt, Ihme (br0380) 2019; 376
Zahr, Shi, Persson (br0460) 2020; 410
Peraire, Nguyen, Cockburn (br0550) 2010
Chen, Perepelitsa (br0610) 2015; 338
Luo, Baum, Löhner (br0230) 2007; 225
Tadmor (br0370) 1989; 26
Bhagatwala, Lele (br0420) 2009; 228
Fernandez, Christophe, Terrana, Nguyen, Peraire (br0530) 2018; 77
Abbassi, Mashayek, Jacobs (br0300) 2014; 98
Kercher, Corrigan, Kessler (br0490) 2021; 93
Cockburn, Shu (br0200) 1998; 141
Hughes, Mallet, Akira (br0350) 1986; 54
Premasuthan, Liang, Jameson (br0440) 2010
Fernandez, Nguyen, Peraire (br0580) 2017; 336
Lv, See, Ihme (br0290) 2016; 322
Persson, Peraire (br0100) 2006
Burbeau, Sagaut, Bruneau (br0170) 2001; 169
Chaudhuri, Jacobs, Don, Abbassi, Mashayek (br0310) 2017; 332
Kawai, Shankar, Lele (br0050) 2010; 229
Qiu, Shu (br0240) 2005; 26
Vila-Pérez, Giacomini, Sevilla, Huerta (br0410) 2021; 28
Olson, Lele (br0090) 2013; 246
Fiorina, Lele (br0030) 2007; 222
Hicken, Buckley, Osusky, Zingg (br0510) 2011
Williams (br0590) 2018; 87
Von Neumann, Richtmyer (br0330) 1950; 21
Krivodonova (br0190) 2007; 226
Cook, Cabot (br0010) 2004; 195
Cook, Cabot (br0020) 2005; 203
Barter, Darmofal (br0270) 2010; 229
Johnsen, Larsson, Bhagatwala, Cabot, Moin, Olson, Rawat, Shankar, Sjögreen, Yee, Zhong, Lele (br0320) 2010; 229
Shi, Persson, Zahr (br0470) 2022; 454
Cook (br0430) 2007; 19
Klöckner, Warburton, Hesthaven (br0060) 2011; 6
Geuzaine, Remacle (br0640) 2009; 79
Krivodonova, Xin, Remacle, Chevaugeon, Flaherty (br0070) 2004; 48
Lv, Ihme (br0210) 2015; 295
Sonntag, Munz (br0220) 2017; 70
Bai, Fidkowski (br0400) 2022; 60
Cockburn, Shu (br0180) 1989; 52
Bianchini, Bressan (br0600) 2005; 161
Nguyen, Terrana, Peraire (br0620) 2022; 60
Fidkowski (br0570) 2016; 139
Sonntag (10.1016/j.jcp.2023.112507_br0220) 2017; 70
Maday (10.1016/j.jcp.2023.112507_br0360) 1993; 30
Hicken (10.1016/j.jcp.2023.112507_br0510) 2011
Hartmann (10.1016/j.jcp.2023.112507_br0280) 2013; 72
Lv (10.1016/j.jcp.2023.112507_br0290) 2016; 322
Krivodonova (10.1016/j.jcp.2023.112507_br0190) 2007; 226
Nguyen (10.1016/j.jcp.2023.112507_br0520) 2012; 231
Nguyen (10.1016/j.jcp.2023.112507_br0630) 2023
Zhu (10.1016/j.jcp.2023.112507_br0250) 2008; 227
Chen (10.1016/j.jcp.2023.112507_br0610) 2015; 338
Premasuthan (10.1016/j.jcp.2023.112507_br0130) 2014; 98
Cockburn (10.1016/j.jcp.2023.112507_br0200) 1998; 141
Krivodonova (10.1016/j.jcp.2023.112507_br0070) 2004; 48
Persson (10.1016/j.jcp.2023.112507_br0110) 2013
Fernandez (10.1016/j.jcp.2023.112507_br0140) 2018
Barter (10.1016/j.jcp.2023.112507_br0270) 2010; 229
Hughes (10.1016/j.jcp.2023.112507_br0350) 1986; 54
Qiu (10.1016/j.jcp.2023.112507_br0240) 2005; 26
Peraire (10.1016/j.jcp.2023.112507_br0550) 2010
Johnsen (10.1016/j.jcp.2023.112507_br0320) 2010; 229
Woopen (10.1016/j.jcp.2023.112507_br0560) 2014; 98
Kawai (10.1016/j.jcp.2023.112507_br0040) 2008; 227
Zhu (10.1016/j.jcp.2023.112507_br0260) 2013; 248
Tadmor (10.1016/j.jcp.2023.112507_br0370) 1989; 26
Abbassi (10.1016/j.jcp.2023.112507_br0300) 2014; 98
Ching (10.1016/j.jcp.2023.112507_br0380) 2019; 376
Fiorina (10.1016/j.jcp.2023.112507_br0030) 2007; 222
Chaudhuri (10.1016/j.jcp.2023.112507_br0310) 2017; 332
Premasuthan (10.1016/j.jcp.2023.112507_br0440) 2010
Olson (10.1016/j.jcp.2023.112507_br0090) 2013; 246
Persson (10.1016/j.jcp.2023.112507_br0100) 2006
Luo (10.1016/j.jcp.2023.112507_br0230) 2007; 225
Bai (10.1016/j.jcp.2023.112507_br0400) 2022; 60
Kercher (10.1016/j.jcp.2023.112507_br0490) 2021; 93
Von Neumann (10.1016/j.jcp.2023.112507_br0330) 1950; 21
Cook (10.1016/j.jcp.2023.112507_br0430) 2007; 19
Shi (10.1016/j.jcp.2023.112507_br0470) 2022; 454
Kawai (10.1016/j.jcp.2023.112507_br0050) 2010; 229
Kercher (10.1016/j.jcp.2023.112507_br0500) 2021; 95
Cook (10.1016/j.jcp.2023.112507_br0010) 2004; 195
Moro (10.1016/j.jcp.2023.112507_br0150) 2016; 82
Klöckner (10.1016/j.jcp.2023.112507_br0060) 2011; 6
Fernandez (10.1016/j.jcp.2023.112507_br0580) 2017; 336
Nguyen (10.1016/j.jcp.2023.112507_br0160) 2011
Zahr (10.1016/j.jcp.2023.112507_br0450) 2018; 365
Lv (10.1016/j.jcp.2023.112507_br0210) 2015; 295
Fernandez (10.1016/j.jcp.2023.112507_br0530) 2018; 77
Burbeau (10.1016/j.jcp.2023.112507_br0170) 2001; 169
Zahr (10.1016/j.jcp.2023.112507_br0460) 2020; 410
Cook (10.1016/j.jcp.2023.112507_br0020) 2005; 203
Fidkowski (10.1016/j.jcp.2023.112507_br0570) 2016; 139
Vila-Pérez (10.1016/j.jcp.2023.112507_br0410) 2021; 28
Moro (10.1016/j.jcp.2023.112507_br0540) 2011
Nguyen (10.1016/j.jcp.2023.112507_br0620) 2022; 60
Hartmann (10.1016/j.jcp.2023.112507_br0390) 2002; 183
Bhagatwala (10.1016/j.jcp.2023.112507_br0420) 2009; 228
Cockburn (10.1016/j.jcp.2023.112507_br0180) 1989; 52
Geuzaine (10.1016/j.jcp.2023.112507_br0640) 2009; 79
Corrigan (10.1016/j.jcp.2023.112507_br0480) 2019; 89
Premasuthan (10.1016/j.jcp.2023.112507_br0120) 2013; 98
Mani (10.1016/j.jcp.2023.112507_br0080) 2009; 228
Bianchini (10.1016/j.jcp.2023.112507_br0600) 2005; 161
Jameson (10.1016/j.jcp.2023.112507_br0340) 1995; 5
Williams (10.1016/j.jcp.2023.112507_br0590) 2018; 87
References_xml – volume: 231
  start-page: 5955
  year: 2012
  end-page: 5988
  ident: br0520
  article-title: Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics
  publication-title: J. Comput. Phys.
– volume: 161
  start-page: 223
  year: 2005
  end-page: 342
  ident: br0600
  article-title: Vanishing viscosity solutions of nonlinear hyperbolic systems
  publication-title: Ann. Math.
– year: 2011
  ident: br0540
  article-title: Navier-Stokes solution using hybridizable discontinuous Galerkin methods
  publication-title: 20th AIAA Computational Fluid Dynamics Conference 2011
– year: 2018
  ident: br0140
  article-title: A physics-based shock capturing method for unsteady laminar and turbulent flows
  publication-title: 56th AIAA Aerospace Sciences Meeting
– volume: 222
  start-page: 246
  year: 2007
  end-page: 264
  ident: br0030
  article-title: An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
  publication-title: J. Comput. Phys.
– volume: 21
  start-page: 232
  year: 1950
  end-page: 237
  ident: br0330
  article-title: A method for the numerical calculation of hydrodynamic shocks
  publication-title: J. Appl. Phys.
– volume: 98
  start-page: 152
  year: 2014
  end-page: 163
  ident: br0300
  article-title: Shock capturing with entropy-based artificial viscosity for staggered grid discontinuous spectral element method
  publication-title: Comput. Fluids
– volume: 77
  start-page: 1566
  year: 2018
  end-page: 1604
  ident: br0530
  article-title: Hybridized discontinuous Galerkin methods for wave propagation
  publication-title: J. Sci. Comput.
– volume: 229
  start-page: 1810
  year: 2010
  end-page: 1827
  ident: br0270
  article-title: Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation
  publication-title: J. Comput. Phys.
– volume: 98
  start-page: 3
  year: 2014
  end-page: 16
  ident: br0560
  article-title: A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow
  publication-title: Comput. Fluids
– year: 2011
  ident: br0160
  article-title: An adaptive shock-capturing HDG method for compressible flows
  publication-title: 20th AIAA Computational Fluid Dynamics Conference 2011
– volume: 54
  start-page: 341
  year: 1986
  end-page: 355
  ident: br0350
  article-title: A new finite element formulation for computational fluid dynamics: II. Beyond SUPG
  publication-title: Comput. Methods Appl. Mech. Eng.
– volume: 365
  start-page: 105
  year: 2018
  end-page: 134
  ident: br0450
  article-title: An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions
  publication-title: J. Comput. Phys.
– volume: 98
  start-page: 122
  year: 2014
  end-page: 133
  ident: br0130
  article-title: Computation of flows with shocks using the spectral difference method with artificial viscosity, II: modified formulation with local mesh refinement
  publication-title: Comput. Fluids
– volume: 169
  start-page: 111
  year: 2001
  end-page: 150
  ident: br0170
  article-title: A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
  publication-title: J. Comput. Phys.
– year: 2023
  ident: br0630
  article-title: Implicit large eddy simulation of hypersonic boundary-layer transition for a flared cone
  publication-title: AIAA SCITECH 2023 Forum, AIAA SciTech Forum
– volume: 26
  start-page: 30
  year: 1989
  end-page: 44
  ident: br0370
  article-title: Convergence of spectral methods for nonlinear conservation laws
  publication-title: SIAM J. Numer. Anal.
– volume: 248
  start-page: 200
  year: 2013
  end-page: 220
  ident: br0260
  article-title: Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
  publication-title: J. Comput. Phys.
– volume: 228
  start-page: 4965
  year: 2009
  end-page: 4969
  ident: br0420
  article-title: A modified artificial viscosity approach for compressible turbulence simulations
  publication-title: J. Comput. Phys.
– volume: 338
  start-page: 771
  year: 2015
  end-page: 800
  ident: br0610
  article-title: Vanishing viscosity solutions of the compressible Euler equations with spherical symmetry and large initial data
  publication-title: Commun. Math. Phys.
– volume: 60
  start-page: 3060
  year: 2022
  end-page: 3077
  ident: br0620
  article-title: Large-eddy simulation of transonic buffet using matrix-free discontinuous Galerkin method
  publication-title: AIAA J.
– start-page: 3061
  year: 2013
  ident: br0110
  article-title: Shock capturing for high-order discontinuous Galerkin simulation of transient flow problems
  publication-title: 21st AIAA Computational Fluid Dynamics Conference
– volume: 72
  start-page: 883
  year: 2013
  end-page: 894
  ident: br0280
  article-title: Higher-order and adaptive discontinuous Galerkin methods with shock-capturing applied to transonic turbulent delta wing flow
  publication-title: Int. J. Numer. Methods Fluids
– volume: 98
  start-page: 111
  year: 2013
  end-page: 121
  ident: br0120
  article-title: Computation of flows with shocks using the spectral difference method with artificial viscosity: Part I
  publication-title: Comput. Fluids
– volume: 52
  start-page: 411
  year: 1989
  ident: br0180
  article-title: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework
  publication-title: Math. Comput.
– volume: 295
  start-page: 715
  year: 2015
  end-page: 739
  ident: br0210
  article-title: Entropy-bounded discontinuous Galerkin scheme for Euler equations
  publication-title: J. Comput. Phys.
– volume: 227
  start-page: 9498
  year: 2008
  end-page: 9526
  ident: br0040
  article-title: Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes
  publication-title: J. Comput. Phys.
– volume: 226
  start-page: 879
  year: 2007
  end-page: 896
  ident: br0190
  article-title: Limiters for high-order discontinuous Galerkin methods
  publication-title: J. Comput. Phys.
– volume: 28
  start-page: 753
  year: 2021
  end-page: 784
  ident: br0410
  article-title: Hybridisable discontinuous Galerkin formulation of compressible flows
  publication-title: Arch. Comput. Methods Eng.
– volume: 95
  start-page: 143
  year: 2021
  end-page: 171
  ident: br0500
  article-title: A least-squares formulation of the moving discontinuous Galerkin finite element method with interface condition enforcement
  publication-title: Comput. Math. Appl.
– volume: 454
  year: 2022
  ident: br0470
  article-title: Implicit shock tracking for unsteady flows by the method of lines
  publication-title: J. Comput. Phys.
– volume: 195
  start-page: 594
  year: 2004
  end-page: 601
  ident: br0010
  article-title: A high-wavenumber viscosity for high-resolution numerical methods
  publication-title: J. Comput. Phys.
– volume: 183
  start-page: 508
  year: 2002
  end-page: 532
  ident: br0390
  article-title: Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
  publication-title: J. Comput. Phys.
– year: 2011
  ident: br0510
  article-title: Dissipation-based continuation: a globalization for inexact-Newton solvers
  publication-title: 20th AIAA Computational Fluid Dynamics Conference 2011
– volume: 87
  start-page: 95
  year: 2018
  end-page: 121
  ident: br0590
  article-title: An entropy stable, hybridizable discontinuous Galerkin method for the compressible Navier-Stokes equations
  publication-title: Math. Comput.
– volume: 336
  start-page: 308
  year: 2017
  end-page: 329
  ident: br0580
  article-title: The hybridized discontinuous Galerkin method for implicit large-eddy simulation of transitional turbulent flows
  publication-title: J. Comput. Phys.
– volume: 19
  year: 2007
  ident: br0430
  article-title: Artificial fluid properties for large-eddy simulation of compressible turbulent mixing
  publication-title: Phys. Fluids
– volume: 89
  start-page: 362
  year: 2019
  end-page: 406
  ident: br0480
  article-title: A moving discontinuous Galerkin finite element method for flows with interfaces
  publication-title: Int. J. Numer. Methods Fluids
– volume: 139
  start-page: 80
  year: 2016
  end-page: 91
  ident: br0570
  article-title: A hybridized discontinuous Galerkin method on mapped deforming domains
  publication-title: Comput. Fluids
– volume: 79
  start-page: 1309
  year: 2009
  end-page: 1331
  ident: br0640
  article-title: Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities
  publication-title: Int. J. Numer. Methods Eng.
– volume: 141
  start-page: 199
  year: 1998
  end-page: 224
  ident: br0200
  article-title: The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems
  publication-title: J. Comput. Phys.
– volume: 322
  start-page: 448
  year: 2016
  end-page: 472
  ident: br0290
  article-title: An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods
  publication-title: J. Comput. Phys.
– volume: 60
  start-page: 5678
  year: 2022
  end-page: 5691
  ident: br0400
  article-title: Continuous artificial-viscosity shock capturing for hybrid discontinuous Galerkin on adapted meshes
  publication-title: AIAA J.
– volume: 229
  start-page: 1739
  year: 2010
  end-page: 1762
  ident: br0050
  article-title: Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows
  publication-title: J. Comput. Phys.
– volume: 6
  start-page: 57
  year: 2011
  end-page: 83
  ident: br0060
  article-title: Viscous shock capturing in a time-explicit discontinuous Galerkin method
  publication-title: Math. Model. Nat. Phenom.
– volume: 225
  start-page: 686
  year: 2007
  end-page: 713
  ident: br0230
  article-title: A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
  publication-title: J. Comput. Phys.
– volume: 376
  start-page: 54
  year: 2019
  end-page: 75
  ident: br0380
  article-title: Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows
  publication-title: J. Comput. Phys.
– volume: 332
  start-page: 99
  year: 2017
  end-page: 117
  ident: br0310
  article-title: Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows
  publication-title: J. Comput. Phys.
– volume: 410
  year: 2020
  ident: br0460
  article-title: Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method
  publication-title: J. Comput. Phys.
– volume: 5
  start-page: 1
  year: 1995
  end-page: 38
  ident: br0340
  article-title: Analysis and design of numerical schemes for gas dynamics, 2: artificial diffusion and discrete shock structure
  publication-title: Int. J. Comput. Fluid Dyn.
– volume: 30
  start-page: 321
  year: 1993
  end-page: 342
  ident: br0360
  article-title: Legendre pseudospectral viscosity method for nonlinear conservation laws
  publication-title: SIAM J. Numer. Anal.
– start-page: 1408
  year: 2006
  end-page: 1420
  ident: br0100
  article-title: Sub-cell shock capturing for discontinuous Galerkin methods
  publication-title: Collection of Technical Papers - 44th AIAA Aerospace Sciences Meeting, vol. 2
– volume: 26
  start-page: 907
  year: 2005
  end-page: 929
  ident: br0240
  article-title: Runge-Kutta discontinuous Galerkin method using WENO limiters
  publication-title: SIAM J. Sci. Comput.
– volume: 227
  start-page: 4330
  year: 2008
  end-page: 4353
  ident: br0250
  article-title: Runge-Kutta discontinuous Galerkin method using WENO limiters II: unstructured meshes
  publication-title: J. Comput. Phys.
– volume: 70
  start-page: 1262
  year: 2017
  end-page: 1289
  ident: br0220
  article-title: Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells
  publication-title: J. Sci. Comput.
– year: 2010
  ident: br0550
  article-title: A hybridizable discontinuous Galerkin method for the compressible Euler and Navier-Stokes equations
  publication-title: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition
– volume: 246
  start-page: 207
  year: 2013
  end-page: 220
  ident: br0090
  article-title: Directional artificial fluid properties for compressible large-eddy simulation
  publication-title: J. Comput. Phys.
– volume: 48
  start-page: 323
  year: 2004
  end-page: 338
  ident: br0070
  article-title: Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
  publication-title: Appl. Numer. Math.
– year: 2010
  ident: br0440
  article-title: Computation of flows with shocks using spectral difference scheme with artificial viscosity
  publication-title: 48th AIAA Aerospace Sciences Meeting
– volume: 203
  start-page: 379
  year: 2005
  end-page: 385
  ident: br0020
  article-title: Hyperviscosity for shock-turbulence interactions
  publication-title: J. Comput. Phys.
– volume: 228
  start-page: 7368
  year: 2009
  end-page: 7374
  ident: br0080
  article-title: Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks
  publication-title: J. Comput. Phys.
– volume: 82
  start-page: 398
  year: 2016
  end-page: 416
  ident: br0150
  article-title: Dilation-based shock capturing for high-order methods
  publication-title: Int. J. Numer. Methods Fluids
– volume: 93
  start-page: 1490
  year: 2021
  end-page: 1519
  ident: br0490
  article-title: The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows
  publication-title: Int. J. Numer. Methods Fluids
– volume: 229
  start-page: 1213
  year: 2010
  end-page: 1237
  ident: br0320
  article-title: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves
  publication-title: J. Comput. Phys.
– volume: 228
  start-page: 7368
  issue: 19
  year: 2009
  ident: 10.1016/j.jcp.2023.112507_br0080
  article-title: Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2009.06.040
– volume: 48
  start-page: 323
  issue: 3–4
  year: 2004
  ident: 10.1016/j.jcp.2023.112507_br0070
  article-title: Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
  publication-title: Appl. Numer. Math.
  doi: 10.1016/j.apnum.2003.11.002
– volume: 98
  start-page: 111
  year: 2013
  ident: 10.1016/j.jcp.2023.112507_br0120
  article-title: Computation of flows with shocks using the spectral difference method with artificial viscosity: Part I
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2013.12.013
– volume: 95
  start-page: 143
  year: 2021
  ident: 10.1016/j.jcp.2023.112507_br0500
  article-title: A least-squares formulation of the moving discontinuous Galerkin finite element method with interface condition enforcement
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2020.09.012
– volume: 82
  start-page: 398
  issue: 7
  year: 2016
  ident: 10.1016/j.jcp.2023.112507_br0150
  article-title: Dilation-based shock capturing for high-order methods
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.4223
– volume: 246
  start-page: 207
  year: 2013
  ident: 10.1016/j.jcp.2023.112507_br0090
  article-title: Directional artificial fluid properties for compressible large-eddy simulation
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2013.03.026
– year: 2011
  ident: 10.1016/j.jcp.2023.112507_br0160
  article-title: An adaptive shock-capturing HDG method for compressible flows
– volume: 70
  start-page: 1262
  issue: 3
  year: 2017
  ident: 10.1016/j.jcp.2023.112507_br0220
  article-title: Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells
  publication-title: J. Sci. Comput.
  doi: 10.1007/s10915-016-0287-5
– year: 2018
  ident: 10.1016/j.jcp.2023.112507_br0140
  article-title: A physics-based shock capturing method for unsteady laminar and turbulent flows
– volume: 295
  start-page: 715
  year: 2015
  ident: 10.1016/j.jcp.2023.112507_br0210
  article-title: Entropy-bounded discontinuous Galerkin scheme for Euler equations
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2015.04.026
– volume: 77
  start-page: 1566
  issue: 3
  year: 2018
  ident: 10.1016/j.jcp.2023.112507_br0530
  article-title: Hybridized discontinuous Galerkin methods for wave propagation
  publication-title: J. Sci. Comput.
  doi: 10.1007/s10915-018-0811-x
– volume: 5
  start-page: 1
  year: 1995
  ident: 10.1016/j.jcp.2023.112507_br0340
  article-title: Analysis and design of numerical schemes for gas dynamics, 2: artificial diffusion and discrete shock structure
  publication-title: Int. J. Comput. Fluid Dyn.
  doi: 10.1080/10618569508940734
– volume: 365
  start-page: 105
  year: 2018
  ident: 10.1016/j.jcp.2023.112507_br0450
  article-title: An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2018.03.029
– volume: 225
  start-page: 686
  issue: 1
  year: 2007
  ident: 10.1016/j.jcp.2023.112507_br0230
  article-title: A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2006.12.017
– volume: 141
  start-page: 199
  issue: 2
  year: 1998
  ident: 10.1016/j.jcp.2023.112507_br0200
  article-title: The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.1998.5892
– volume: 54
  start-page: 341
  issue: 3
  year: 1986
  ident: 10.1016/j.jcp.2023.112507_br0350
  article-title: A new finite element formulation for computational fluid dynamics: II. Beyond SUPG
  publication-title: Comput. Methods Appl. Mech. Eng.
  doi: 10.1016/0045-7825(86)90110-6
– volume: 26
  start-page: 907
  issue: 3
  year: 2005
  ident: 10.1016/j.jcp.2023.112507_br0240
  article-title: Runge-Kutta discontinuous Galerkin method using WENO limiters
  publication-title: SIAM J. Sci. Comput.
  doi: 10.1137/S1064827503425298
– volume: 169
  start-page: 111
  issue: 1
  year: 2001
  ident: 10.1016/j.jcp.2023.112507_br0170
  article-title: A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.2001.6718
– volume: 6
  start-page: 57
  issue: 3
  year: 2011
  ident: 10.1016/j.jcp.2023.112507_br0060
  article-title: Viscous shock capturing in a time-explicit discontinuous Galerkin method
  publication-title: Math. Model. Nat. Phenom.
  doi: 10.1051/mmnp/20116303
– volume: 28
  start-page: 753
  issue: 2
  year: 2021
  ident: 10.1016/j.jcp.2023.112507_br0410
  article-title: Hybridisable discontinuous Galerkin formulation of compressible flows
  publication-title: Arch. Comput. Methods Eng.
  doi: 10.1007/s11831-020-09508-z
– volume: 60
  start-page: 3060
  issue: 5
  year: 2022
  ident: 10.1016/j.jcp.2023.112507_br0620
  article-title: Large-eddy simulation of transonic buffet using matrix-free discontinuous Galerkin method
  publication-title: AIAA J.
  doi: 10.2514/1.J060459
– volume: 229
  start-page: 1213
  issue: 4
  year: 2010
  ident: 10.1016/j.jcp.2023.112507_br0320
  article-title: Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2009.10.028
– volume: 52
  start-page: 411
  issue: 186
  year: 1989
  ident: 10.1016/j.jcp.2023.112507_br0180
  article-title: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework
  publication-title: Math. Comput.
– volume: 183
  start-page: 508
  issue: 2
  year: 2002
  ident: 10.1016/j.jcp.2023.112507_br0390
  article-title: Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
  publication-title: J. Comput. Phys.
  doi: 10.1006/jcph.2002.7206
– volume: 195
  start-page: 594
  issue: 2
  year: 2004
  ident: 10.1016/j.jcp.2023.112507_br0010
  article-title: A high-wavenumber viscosity for high-resolution numerical methods
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2003.10.012
– volume: 226
  start-page: 879
  issue: 1
  year: 2007
  ident: 10.1016/j.jcp.2023.112507_br0190
  article-title: Limiters for high-order discontinuous Galerkin methods
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2007.05.011
– volume: 79
  start-page: 1309
  issue: 11
  year: 2009
  ident: 10.1016/j.jcp.2023.112507_br0640
  article-title: Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities
  publication-title: Int. J. Numer. Methods Eng.
  doi: 10.1002/nme.2579
– volume: 19
  issue: 5
  year: 2007
  ident: 10.1016/j.jcp.2023.112507_br0430
  article-title: Artificial fluid properties for large-eddy simulation of compressible turbulent mixing
  publication-title: Phys. Fluids
  doi: 10.1063/1.2728937
– volume: 87
  start-page: 95
  issue: 309
  year: 2018
  ident: 10.1016/j.jcp.2023.112507_br0590
  article-title: An entropy stable, hybridizable discontinuous Galerkin method for the compressible Navier-Stokes equations
  publication-title: Math. Comput.
  doi: 10.1090/mcom/3199
– volume: 322
  start-page: 448
  year: 2016
  ident: 10.1016/j.jcp.2023.112507_br0290
  article-title: An entropy-residual shock detector for solving conservation laws using high-order discontinuous Galerkin methods
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2016.06.052
– volume: 228
  start-page: 4965
  issue: 14
  year: 2009
  ident: 10.1016/j.jcp.2023.112507_br0420
  article-title: A modified artificial viscosity approach for compressible turbulence simulations
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2009.04.009
– year: 2011
  ident: 10.1016/j.jcp.2023.112507_br0540
  article-title: Navier-Stokes solution using hybridizable discontinuous Galerkin methods
– volume: 89
  start-page: 362
  issue: 9
  year: 2019
  ident: 10.1016/j.jcp.2023.112507_br0480
  article-title: A moving discontinuous Galerkin finite element method for flows with interfaces
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.4697
– year: 2011
  ident: 10.1016/j.jcp.2023.112507_br0510
  article-title: Dissipation-based continuation: a globalization for inexact-Newton solvers
– volume: 93
  start-page: 1490
  issue: 5
  year: 2021
  ident: 10.1016/j.jcp.2023.112507_br0490
  article-title: The moving discontinuous Galerkin finite element method with interface condition enforcement for compressible viscous flows
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.4939
– volume: 222
  start-page: 246
  issue: 1
  year: 2007
  ident: 10.1016/j.jcp.2023.112507_br0030
  article-title: An artificial nonlinear diffusivity method for supersonic reacting flows with shocks
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2006.07.020
– volume: 98
  start-page: 122
  year: 2014
  ident: 10.1016/j.jcp.2023.112507_br0130
  article-title: Computation of flows with shocks using the spectral difference method with artificial viscosity, II: modified formulation with local mesh refinement
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2014.01.024
– volume: 21
  start-page: 232
  year: 1950
  ident: 10.1016/j.jcp.2023.112507_br0330
  article-title: A method for the numerical calculation of hydrodynamic shocks
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1699639
– volume: 338
  start-page: 771
  issue: 2
  year: 2015
  ident: 10.1016/j.jcp.2023.112507_br0610
  article-title: Vanishing viscosity solutions of the compressible Euler equations with spherical symmetry and large initial data
  publication-title: Commun. Math. Phys.
  doi: 10.1007/s00220-015-2376-y
– volume: 30
  start-page: 321
  year: 1993
  ident: 10.1016/j.jcp.2023.112507_br0360
  article-title: Legendre pseudospectral viscosity method for nonlinear conservation laws
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0730016
– volume: 231
  start-page: 5955
  issue: 18
  year: 2012
  ident: 10.1016/j.jcp.2023.112507_br0520
  article-title: Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2012.02.033
– volume: 26
  start-page: 30
  year: 1989
  ident: 10.1016/j.jcp.2023.112507_br0370
  article-title: Convergence of spectral methods for nonlinear conservation laws
  publication-title: SIAM J. Numer. Anal.
  doi: 10.1137/0726003
– volume: 139
  start-page: 80
  year: 2016
  ident: 10.1016/j.jcp.2023.112507_br0570
  article-title: A hybridized discontinuous Galerkin method on mapped deforming domains
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2016.04.004
– volume: 229
  start-page: 1739
  issue: 5
  year: 2010
  ident: 10.1016/j.jcp.2023.112507_br0050
  article-title: Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2009.11.005
– start-page: 1408
  year: 2006
  ident: 10.1016/j.jcp.2023.112507_br0100
  article-title: Sub-cell shock capturing for discontinuous Galerkin methods
– volume: 332
  start-page: 99
  year: 2017
  ident: 10.1016/j.jcp.2023.112507_br0310
  article-title: Explicit discontinuous spectral element method with entropy generation based artificial viscosity for shocked viscous flows
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2016.11.042
– volume: 336
  start-page: 308
  year: 2017
  ident: 10.1016/j.jcp.2023.112507_br0580
  article-title: The hybridized discontinuous Galerkin method for implicit large-eddy simulation of transitional turbulent flows
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2017.02.015
– volume: 98
  start-page: 3
  year: 2014
  ident: 10.1016/j.jcp.2023.112507_br0560
  article-title: A comparison of hybridized and standard DG methods for target-based hp-adaptive simulation of compressible flow
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2014.03.023
– volume: 410
  year: 2020
  ident: 10.1016/j.jcp.2023.112507_br0460
  article-title: Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2020.109385
– volume: 72
  start-page: 883
  year: 2013
  ident: 10.1016/j.jcp.2023.112507_br0280
  article-title: Higher-order and adaptive discontinuous Galerkin methods with shock-capturing applied to transonic turbulent delta wing flow
  publication-title: Int. J. Numer. Methods Fluids
  doi: 10.1002/fld.3762
– volume: 454
  year: 2022
  ident: 10.1016/j.jcp.2023.112507_br0470
  article-title: Implicit shock tracking for unsteady flows by the method of lines
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2021.110906
– volume: 227
  start-page: 9498
  issue: 22
  year: 2008
  ident: 10.1016/j.jcp.2023.112507_br0040
  article-title: Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2008.06.034
– volume: 376
  start-page: 54
  year: 2019
  ident: 10.1016/j.jcp.2023.112507_br0380
  article-title: Shock capturing for discontinuous Galerkin methods with application to predicting heat transfer in hypersonic flows
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2018.09.016
– year: 2010
  ident: 10.1016/j.jcp.2023.112507_br0550
  article-title: A hybridizable discontinuous Galerkin method for the compressible Euler and Navier-Stokes equations
– start-page: 3061
  year: 2013
  ident: 10.1016/j.jcp.2023.112507_br0110
  article-title: Shock capturing for high-order discontinuous Galerkin simulation of transient flow problems
– volume: 229
  start-page: 1810
  issue: 5
  year: 2010
  ident: 10.1016/j.jcp.2023.112507_br0270
  article-title: Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2009.11.010
– volume: 161
  start-page: 223
  issue: 1
  year: 2005
  ident: 10.1016/j.jcp.2023.112507_br0600
  article-title: Vanishing viscosity solutions of nonlinear hyperbolic systems
  publication-title: Ann. Math.
  doi: 10.4007/annals.2005.161.223
– volume: 98
  start-page: 152
  year: 2014
  ident: 10.1016/j.jcp.2023.112507_br0300
  article-title: Shock capturing with entropy-based artificial viscosity for staggered grid discontinuous spectral element method
  publication-title: Comput. Fluids
  doi: 10.1016/j.compfluid.2014.01.022
– year: 2023
  ident: 10.1016/j.jcp.2023.112507_br0630
  article-title: Implicit large eddy simulation of hypersonic boundary-layer transition for a flared cone
– volume: 203
  start-page: 379
  issue: 2
  year: 2005
  ident: 10.1016/j.jcp.2023.112507_br0020
  article-title: Hyperviscosity for shock-turbulence interactions
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2004.09.011
– volume: 227
  start-page: 4330
  issue: 9
  year: 2008
  ident: 10.1016/j.jcp.2023.112507_br0250
  article-title: Runge-Kutta discontinuous Galerkin method using WENO limiters II: unstructured meshes
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2007.12.024
– year: 2010
  ident: 10.1016/j.jcp.2023.112507_br0440
  article-title: Computation of flows with shocks using spectral difference scheme with artificial viscosity
– volume: 248
  start-page: 200
  year: 2013
  ident: 10.1016/j.jcp.2023.112507_br0260
  article-title: Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
  publication-title: J. Comput. Phys.
  doi: 10.1016/j.jcp.2013.04.012
– volume: 60
  start-page: 5678
  issue: 10
  year: 2022
  ident: 10.1016/j.jcp.2023.112507_br0400
  article-title: Continuous artificial-viscosity shock capturing for hybrid discontinuous Galerkin on adapted meshes
  publication-title: AIAA J.
  doi: 10.2514/1.J061783
SSID ssj0008548
Score 2.5091708
Snippet We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach...
SourceID unpaywall
osti
crossref
elsevier
SourceType Open Access Repository
Enrichment Source
Index Database
Publisher
StartPage 112507
SubjectTerms Adaptive viscosity
Conservation laws
Discontinuous Galerkin methods
Finite element methods
Shock capturing
Shock waves
SummonAdditionalLinks – databaseName: Unpaywall
  dbid: UNPAY
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlZ3fa9RAEMeHen0oPlhrK56_GNAnS2qSzU_fDrWUQosPHtSnsLvZhashOe5ylvrsH-5MdlNFpKXvO2RhZnc-ZL47A_A21JqwIKfzLcsySERsA6V0GqR1EhoTWlsOjefPzrOTeXJ6kV5swZvxLQzLKjsK7kFTqRaqWXTv45gTtXgA21lKwD2B7fn5l9k3J96IAkacoaZZhkFM-D_WLgcV16XmppSx4KcyKc-M_X_2mfA3H8LOpl3K6yvZNH8lmeNd-DRuz2lLvh9tenWkf_7TufGO_T-GRx4yceaiYg-2TPsEdj1woj_O6334NWtR1nLJVx7-WKw1K7iucTXMp1_5F5o4th1H4lskXsR248o8DY6Bi51Fzbps_4cXG3m1_oCzP9Vx7Du0CwZcNE6xjm549foA5sefv348CfxYhkCLLO8DrUUkDJGbiOJY5hQFiiAricpcy7rIZFRHKiMO1FZkWtR1XebkJ1VkQunQZlY8hUnbteYZYFowP0lDjFkQyVil60JZhiYTl7JMphCO7qq071nOozOaahSnXVbk4Yo9XDkPT-HdjcnSNey4bXEyxkDlicORREUJ5TazF-xjNuFOu5olSWTj_TyFw5swunsLz--1-iVM-tXGvCIQ6tVrfxB-AzXKCQA
  priority: 102
  providerName: Unpaywall
Title An adaptive viscosity regularization approach for the numerical solution of conservation laws: Application to finite element methods
URI https://dx.doi.org/10.1016/j.jcp.2023.112507
https://www.osti.gov/biblio/2202503
UnpaywallVersion submittedVersion
Volume 494
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Baden-Württemberg Complete Freedom Collection (Elsevier)
  customDbUrl:
  eissn: 1090-2716
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0008548
  issn: 0021-9991
  databaseCode: GBLVA
  dateStart: 20110101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier ScienceDirect Freedom Collection
  customDbUrl:
  eissn: 1090-2716
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0008548
  issn: 0021-9991
  databaseCode: AIKHN
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Elsevier SD Complete Freedom Collection [SCCMFC]
  customDbUrl:
  eissn: 1090-2716
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0008548
  issn: 0021-9991
  databaseCode: ACRLP
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVESC
  databaseName: Science Direct
  customDbUrl:
  eissn: 1090-2716
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0008548
  issn: 0021-9991
  databaseCode: .~1
  dateStart: 19950101
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
– providerCode: PRVLSH
  databaseName: Elsevier Journals
  customDbUrl:
  mediaType: online
  eissn: 1090-2716
  dateEnd: 99991231
  omitProxy: true
  ssIdentifier: ssj0008548
  issn: 0021-9991
  databaseCode: AKRWK
  dateStart: 19660801
  isFulltext: true
  providerName: Library Specific Holdings
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ3PaxQxFMdDWQ_Vg9qquFbLO3hSxs4kmV_ehmJZW1w8dKGehiSTwJZhdtkfll48-Yf73iTTHyAVPA0zJBDykpcPk-97j7H3sTGIBTnub1WWkRTcRVqbNEobGVsbO1f2iee_TbPJTJ5epBc77HiIhSFZZfD93qf33jp8OQqzebSczynGl1MMPbpeSirCyQ9LmVMVg0-_bmUeRSq9NyYpArYebjZ7jdeloZSVXFAgTUoVZf9-No0WuN2esN1tt1TXV6pt7xxBJ8_Z08COUPnh7bEd2-2zZ4EjIezS9Qv2u-pANWpJngx-zteGhFnXsOrLzq9C4CUM2cQBsRUQA6Hb-tubFob1CAsHhuTW4ccttOpq_Rmq20tv2CzAzYlbwXohOvia1OuXbHby5fx4EoVqC5ERWb6JjBGJsAhkIuFc5WhcjewkkzI3qikylTSJzhDvjBOZEU3TlDlOqi4yoU3sMidesVG36OxrBmlBWKQsomOBgOK0aQrtiIUsL1Upxywe5rk2IRU5VcRo60FzdlmjaWoyTe1NM2YfbrosfR6OhxrLwXj1vcVU4znxULcDMjR1oQS6hpRG2Idz4kQxZh9v7P_vIbz5vyEcsMf05vUyb9los9rad0g9G33YL-tD9qj6ejaZ4nM2_V79-APH1QNz
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnZ3La9wwEIeHsD2kPfRdsk3azqGnFje25GduS2jYtklOCeRmJFmCDca77KMhl57yh2fGkpMWSgq92hIIjTT6bP1mBuBjbAxhQUH7W1VVlErhIq1NFmVNGlsbO1f1iedPTvPpefr9IrvYgsMhFoZllcH3e5_ee-vwZD_M5v5iNuMYX8Ex9OR6OamIID_8KM1EwV9gX37d6zzKLPXumLUI1Hy42uxFXpeGc1YKyZE0GZeU_fvhNJrTfnsC25tuoa6vVNv-dgYdPYenAR5x4sf3ArZs9xKeBZDEsE1Xr-Bm0qFq1IJdGf6crQwrs65x2dedX4bISxzSiSNxKxIHYrfx1zctDgsS5w4N663Dn1ts1dXqACf3t964nqObMbii9Up09EWpV6_h_Ojr2eE0CuUWIiPzYh0ZIxNpichkIoQqyLqa4ClNqsKopsxV0iQ6J74zTuZGNk1TFTSpusylNrHLnXwDo27e2R3ArGQuUpbYsSRCcdo0pXYMQ1ZUqkrHEA_zXJuQi5xLYrT1IDq7rMk0NZum9qYZw6e7LgufiOOhxulgvPqP1VTTQfFQt102NHfhDLqGpUbURwgGRTmGz3f2__cQ3v7fED7A9vTs5Lg-_nb6Yxce8xsvntmD0Xq5se8Igdb6fb_EbwGavQNY
linkToUnpaywall http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlZ3fa9RAEMeHen0oPlhrK56_GNAnS2qSzU_fDrWUQosPHtSnsLvZhashOe5ylvrsH-5MdlNFpKXvO2RhZnc-ZL47A_A21JqwIKfzLcsySERsA6V0GqR1EhoTWlsOjefPzrOTeXJ6kV5swZvxLQzLKjsK7kFTqRaqWXTv45gTtXgA21lKwD2B7fn5l9k3J96IAkacoaZZhkFM-D_WLgcV16XmppSx4KcyKc-M_X_2mfA3H8LOpl3K6yvZNH8lmeNd-DRuz2lLvh9tenWkf_7TufGO_T-GRx4yceaiYg-2TPsEdj1woj_O6334NWtR1nLJVx7-WKw1K7iucTXMp1_5F5o4th1H4lskXsR248o8DY6Bi51Fzbps_4cXG3m1_oCzP9Vx7Du0CwZcNE6xjm549foA5sefv348CfxYhkCLLO8DrUUkDJGbiOJY5hQFiiAricpcy7rIZFRHKiMO1FZkWtR1XebkJ1VkQunQZlY8hUnbteYZYFowP0lDjFkQyVil60JZhiYTl7JMphCO7qq071nOozOaahSnXVbk4Yo9XDkPT-HdjcnSNey4bXEyxkDlicORREUJ5TazF-xjNuFOu5olSWTj_TyFw5swunsLz--1-iVM-tXGvCIQ6tVrfxB-AzXKCQA
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=An+adaptive+viscosity+regularization+approach+for+the+numerical+solution+of+conservation+laws%3A+Application+to+finite+element+methods&rft.jtitle=Journal+of+computational+physics&rft.au=Nguyen%2C+Ngoc+Cuong&rft.au=Vila-P%C3%A9rez%2C+Jordi&rft.au=Peraire%2C+Jaime&rft.date=2023-12-01&rft.issn=0021-9991&rft.volume=494&rft.spage=112507&rft_id=info:doi/10.1016%2Fj.jcp.2023.112507&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jcp_2023_112507
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9991&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9991&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9991&client=summon