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...
Saved in:
| Published in | Journal of computational physics Vol. 494; no. C; p. 112507 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Elsevier Inc
01.12.2023
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 1090-2716 |
| DOI | 10.1016/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 |