Impact of source terms on reliability of CFD algorithms
Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also impact the reliability of CFD algorithms. A general recommendation is to treat negative values (sinks) implicitly, while positive values (sou...
Saved in:
| Published in | Computers & fluids Vol. 39; no. 10; pp. 1909 - 1922 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Ltd
01.12.2010
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0045-7930 1879-0747 |
| DOI | 10.1016/j.compfluid.2010.06.021 |
Cover
| Abstract | Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also impact the reliability of CFD algorithms. A general recommendation is to treat negative values (sinks) implicitly, while positive values (sources) should be evaluated explicitly. Although this provides improvements compared with evaluating all terms in the same manner, sources with positive values, in particular, often cause code reliability issues. The present paper addresses the reasons for these difficulties and combines a new source term evaluation method with time step limitation for convection and diffusion terms to give more robust capability. The method is verified by a combination of stability analyses followed by computational experiments to validate the stability findings in meaningful problems. The source Jacobian arising from a two-equation
k–
ω turbulence model is taken as an example to demonstrate our findings. |
|---|---|
| AbstractList | Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also impact the reliability of CFD algorithms. A general recommendation is to treat negative values (sinks) implicitly, while positive values (sources) should be evaluated explicitly. Although this provides improvements compared with evaluating all terms in the same manner, sources with positive values, in particular, often cause code reliability issues. The present paper addresses the reasons for these difficulties and combines a new source term evaluation method with time step limitation for convection and diffusion terms to give more robust capability. The method is verified by a combination of stability analyses followed by computational experiments to validate the stability findings in meaningful problems. The source Jacobian arising from a two-equation k-[Omega] turbulence model is taken as an example to demonstrate our findings. Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also impact the reliability of CFD algorithms. A general recommendation is to treat negative values (sinks) implicitly, while positive values (sources) should be evaluated explicitly. Although this provides improvements compared with evaluating all terms in the same manner, sources with positive values, in particular, often cause code reliability issues. The present paper addresses the reasons for these difficulties and combines a new source term evaluation method with time step limitation for convection and diffusion terms to give more robust capability. The method is verified by a combination of stability analyses followed by computational experiments to validate the stability findings in meaningful problems. The source Jacobian arising from a two-equation k– ω turbulence model is taken as an example to demonstrate our findings. |
| Author | Merkle, Charles L. Lian, Chenzhou Xia, Guoping |
| Author_xml | – sequence: 1 givenname: Chenzhou surname: Lian fullname: Lian, Chenzhou email: clian@purdue.edu – sequence: 2 givenname: Guoping surname: Xia fullname: Xia, Guoping – sequence: 3 givenname: Charles L. surname: Merkle fullname: Merkle, Charles L. |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23238731$$DView record in Pascal Francis |
| BookMark | eNqNkD1PHDEQhq0IpBwfv4FtoqTZw16vPd4iBTrCh4REA7U1eG3wybu-2L5I_Ht8OkSRIqEazczzjjTPETmY42wJOWN0ySiT5-ulidPGha0flx2tUyqXtGNfyIIpGFoKPRyQBaW9aGHg9Cs5ynlNa8-7fkHgdtqgKU10TY7bZGxTbJpyE-cm2eDxyQdfXnfr1dVlg-E5Jl9epnxCDh2GbE_f6zF5vPr1sLpp7-6vb1cXd63pQZZWAAjLDEPg3El0VkonuRDdk-pA0REd75WkCgUMCoeBcdkDcKFU72BUyI_J9_3dTYq_tzYXPflsbAg427jNWnFWnxZCVPLHP0kGdADRi05W9Ns7itlgcAln47PeJD9hetUd77gCzioHe86kmHOy7gNhVO_k67X-kK938jWVusqvyZ9_JY0vWHycS0IfPpG_2OdtdfvH26Sz8XY2dvTJmqLH6P974w0Fw6Vw |
| CODEN | CPFLBI |
| CitedBy_id | crossref_primary_10_1016_j_ijheatmasstransfer_2022_123300 crossref_primary_10_2514_1_J053722 crossref_primary_10_1016_j_apm_2019_03_016 crossref_primary_10_2514_1_B35780 crossref_primary_10_1016_j_jcp_2017_10_011 crossref_primary_10_2514_1_J060481 crossref_primary_10_1016_j_combustflame_2021_111876 crossref_primary_10_1093_mnras_sts071 crossref_primary_10_1016_j_conbuildmat_2024_136566 crossref_primary_10_1016_j_jcp_2016_04_005 crossref_primary_10_1080_13647830_2022_2141138 crossref_primary_10_1063_5_0076657 crossref_primary_10_1016_j_fuel_2024_131600 crossref_primary_10_1016_j_jcp_2024_113166 crossref_primary_10_1063_1_4916673 crossref_primary_10_1016_j_ijmultiphaseflow_2023_104647 crossref_primary_10_1021_acs_energyfuels_4c02898 crossref_primary_10_1016_j_jcp_2020_109899 crossref_primary_10_1080_10618562_2015_1093624 crossref_primary_10_1080_13647830_2019_1599444 crossref_primary_10_1016_j_ijmultiphaseflow_2021_103865 crossref_primary_10_2514_1_J052070 crossref_primary_10_1016_j_compfluid_2016_02_010 crossref_primary_10_2514_1_J059784 crossref_primary_10_1016_j_conbuildmat_2024_135106 crossref_primary_10_1016_j_jcp_2014_07_047 crossref_primary_10_1007_s11242_016_0657_3 crossref_primary_10_1016_j_combustflame_2018_02_003 crossref_primary_10_2514_1_B37801 crossref_primary_10_1016_j_cej_2019_123964 crossref_primary_10_1016_j_combustflame_2020_08_014 |
| Cites_doi | 10.2514/2.870 10.1137/0733001 10.2514/6.1993-2906 10.2514/3.9519 10.1016/j.jcp.2009.03.040 10.1108/EUM0000000004033 10.1016/j.compfluid.2003.12.004 10.1063/1.858424 10.2514/1.2426 10.2514/3.9119 10.2514/3.10464 10.2514/6.2003-72 10.2514/6.1992-547 10.1016/0021-9991(86)90200-7 10.1016/0021-9991(87)90084-2 10.1006/jcph.1996.0211 10.2514/3.8291 10.1006/jcph.1997.5793 10.1016/0094-4548(74)90150-7 10.1016/j.jcp.2006.05.001 10.2514/6.1991-1552 10.1016/S0045-7930(98)00017-6 |
| ContentType | Journal Article |
| Copyright | 2010 Elsevier Ltd 2015 INIST-CNRS |
| Copyright_xml | – notice: 2010 Elsevier Ltd – notice: 2015 INIST-CNRS |
| DBID | AAYXX CITATION IQODW 7SC 7TB 7U5 8FD FR3 H8D JQ2 KR7 L7M L~C L~D 7UA C1K F1W H96 L.G |
| DOI | 10.1016/j.compfluid.2010.06.021 |
| DatabaseName | CrossRef Pascal-Francis Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Solid State and Superconductivity Abstracts Technology Research Database Engineering Research Database Aerospace Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Water Resources Abstracts Environmental Sciences and Pollution Management ASFA: Aquatic Sciences and Fisheries Abstracts Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources Aquatic Science & Fisheries Abstracts (ASFA) Professional |
| DatabaseTitle | CrossRef Aerospace Database Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Solid State and Superconductivity Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional Aquatic Science & Fisheries Abstracts (ASFA) Professional Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources ASFA: Aquatic Sciences and Fisheries Abstracts Water Resources Abstracts Environmental Sciences and Pollution Management |
| DatabaseTitleList | Aerospace Database Aquatic Science & Fisheries Abstracts (ASFA) Professional |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Physics |
| EISSN | 1879-0747 |
| EndPage | 1922 |
| ExternalDocumentID | 23238731 10_1016_j_compfluid_2010_06_021 S0045793010001520 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1~. 1~5 29F 4.4 457 4G. 5GY 5VS 6TJ 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABXDB ABYKQ ACAZW ACDAQ ACGFS ACIWK ACKIV ACNNM ACRLP ADBBV ADEZE ADGUI ADIYS ADMUD ADTZH AEBSH AECPX AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AI. AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HLZ HVGLF HZ~ IHE J1W JJJVA KOM LG9 LY7 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 R2- RIG ROL RPZ SBC SDF SDG SDP SES SET SEW SPC SPCBC SPD SST SSW SSZ T5K T9H TN5 VH1 WUQ XPP ZMT ~G- AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 7TB 7U5 8FD FR3 H8D JQ2 KR7 L7M L~C L~D 7UA C1K F1W H96 L.G |
| ID | FETCH-LOGICAL-c476t-5775e1c1a733f6afe66f63552b82780daf348608a5798a9913647735884f7d8a3 |
| IEDL.DBID | AIKHN |
| ISSN | 0045-7930 |
| IngestDate | Tue Oct 07 09:20:44 EDT 2025 Thu Oct 02 12:05:22 EDT 2025 Mon Jul 21 09:14:42 EDT 2025 Wed Oct 01 03:04:16 EDT 2025 Thu Apr 24 22:51:41 EDT 2025 Fri Feb 23 02:29:47 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Keywords | Computational fluid dynamics Sink Reliability Source Source terms Algorithms Turbulent flow Pipe flow Digital simulation Convergent nozzle Modelling Numerical convergence Turbulence structure |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c476t-5775e1c1a733f6afe66f63552b82780daf348608a5798a9913647735884f7d8a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| PQID | 1709754526 |
| PQPubID | 23500 |
| PageCount | 14 |
| ParticipantIDs | proquest_miscellaneous_831201555 proquest_miscellaneous_1709754526 pascalfrancis_primary_23238731 crossref_primary_10_1016_j_compfluid_2010_06_021 crossref_citationtrail_10_1016_j_compfluid_2010_06_021 elsevier_sciencedirect_doi_10_1016_j_compfluid_2010_06_021 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2010-12-01 |
| PublicationDateYYYYMMDD | 2010-12-01 |
| PublicationDate_xml | – month: 12 year: 2010 text: 2010-12-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington |
| PublicationTitle | Computers & fluids |
| PublicationYear | 2010 |
| Publisher | Elsevier Ltd Elsevier |
| Publisher_xml | – name: Elsevier Ltd – name: Elsevier |
| References | turbulence models for aerodynamic flows. AIAA paper 93-2906. In: 24th AIAA fluid dynamics conference, Orlando (FL); July 1993. Huang PG, Coakley TJ, An implicit Navier–Stokes code for turbulent flow modeling, AIAA paper 92-0547. In: AIAA 30th aerospace sciences meeting, Reno (NV), 1992. Viviand (bib18) 1985 Sahu, Danberg (bib6) 1991; 24 Batten, Leschziner, Goldberg (bib11) 1997; 137 Merkle, Li, Sankaran (bib15) 2006 Choi, Merkle (bib21) 1985; 23 Moryossef, Levy (bib14) 2006; 220 Franz D. An introduction to the theory of fluid flows. ISBN:9783540713425, 2008. Steelant, Dick (bib8) 1994; 4 – Launder, Sharma (bib24) 1974; 1 Van Leer B, Lee WT, Roe PL, Characteristic time-stepping or local preconditioning of the euler equations, AIAA 91-1552-CP. In: Computational fluid dynamics conference, Honolulu; 1991. Greenberg, Le Roux (bib9) 1996; 33 Merkle, Deshpande, Sankaran (bib2) 1993 Briley, McDonald, Shamroth (bib19) 1983; 21 Sankaran V, Merkle CL. Dual time stepping and preconditioning for unsteady computations. AIAA 95-0078, 1995. Guerra, Gustafsson (bib20) 1986; 63 Du, Wu (bib12) 2004; 42 Guillard, Viozat (bib27) 1999; 28 Gerolymos (bib5) 1990; 28 Yakhot, Orszag, Thangam, Gatski, Speziale (bib25) 1992; 4 Menter FR. Zonal two equation Du, Wu (bib13) 2005; 34 Pandya SA, Sankaran V, Pulliam T. Implementation of preconditioned dual-time procedures in overflow. AIAA 2003-0072, 2003. Wilcox (bib4) 2006 Merci, Steelant, Vierendeels, Riemslagh, Dick (bib3) 2000; 38 Liu, Zheng (bib10) 1996; 128 Turkel (bib16) 1987; 72 Lian, Xia, Merkle (bib1) 2009; 228 Du (10.1016/j.compfluid.2010.06.021_bib12) 2004; 42 Merci (10.1016/j.compfluid.2010.06.021_bib3) 2000; 38 Briley (10.1016/j.compfluid.2010.06.021_bib19) 1983; 21 Launder (10.1016/j.compfluid.2010.06.021_bib24) 1974; 1 Moryossef (10.1016/j.compfluid.2010.06.021_bib14) 2006; 220 10.1016/j.compfluid.2010.06.021_bib17 Steelant (10.1016/j.compfluid.2010.06.021_bib8) 1994; 4 Du (10.1016/j.compfluid.2010.06.021_bib13) 2005; 34 10.1016/j.compfluid.2010.06.021_bib7 Greenberg (10.1016/j.compfluid.2010.06.021_bib9) 1996; 33 Wilcox (10.1016/j.compfluid.2010.06.021_bib4) 2006 Merkle (10.1016/j.compfluid.2010.06.021_bib15) 2006 Guerra (10.1016/j.compfluid.2010.06.021_bib20) 1986; 63 Merkle (10.1016/j.compfluid.2010.06.021_bib2) 1993 Batten (10.1016/j.compfluid.2010.06.021_bib11) 1997; 137 Yakhot (10.1016/j.compfluid.2010.06.021_bib25) 1992; 4 Sahu (10.1016/j.compfluid.2010.06.021_bib6) 1991; 24 Liu (10.1016/j.compfluid.2010.06.021_bib10) 1996; 128 Guillard (10.1016/j.compfluid.2010.06.021_bib27) 1999; 28 Choi (10.1016/j.compfluid.2010.06.021_bib21) 1985; 23 Viviand (10.1016/j.compfluid.2010.06.021_bib18) 1985 10.1016/j.compfluid.2010.06.021_bib23 10.1016/j.compfluid.2010.06.021_bib22 10.1016/j.compfluid.2010.06.021_bib28 10.1016/j.compfluid.2010.06.021_bib26 Gerolymos (10.1016/j.compfluid.2010.06.021_bib5) 1990; 28 Lian (10.1016/j.compfluid.2010.06.021_bib1) 2009; 228 Turkel (10.1016/j.compfluid.2010.06.021_bib16) 1987; 72 |
| References_xml | – volume: 220 start-page: 88 year: 2006 end-page: 108 ident: bib14 article-title: Unconditionally positive implicit procedure for two-equation turbulence models: application to publication-title: J Comput Phys – volume: 28 start-page: 1707 year: 1990 end-page: 1717 ident: bib5 article-title: Implicit multiple-grid solution of the compressible Navier–Stokes equation using publication-title: AIAA J – volume: 21 start-page: 1467 year: 1983 end-page: 1469 ident: bib19 article-title: A low mach number euler formulation and application to time-iterative LBI schemes publication-title: AIAA J – volume: 23 start-page: 1518 year: 1985 end-page: 1524 ident: bib21 article-title: Application of time-iterative schemes to incompressible flow publication-title: AIAA J – reference: Pandya SA, Sankaran V, Pulliam T. Implementation of preconditioned dual-time procedures in overflow. AIAA 2003-0072, 2003. – volume: 1 year: 1974 ident: bib24 article-title: Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc publication-title: Lett Heat Mass Transfer – start-page: 2006 year: 2006 end-page: 4575 ident: bib15 article-title: Multi-disciplinary computational analysis in propulsion publication-title: AIAA – volume: 137 year: 1997 ident: bib11 article-title: Average-state Jacobians and implicit methods for compressible viscous and turbulent flows publication-title: J Comput Phys – year: 1985 ident: bib18 article-title: Pseudo-unsteady systems for steady inviscid calculations publication-title: Numerical methods for the euler equations of fluid dynamics – reference: Sankaran V, Merkle CL. Dual time stepping and preconditioning for unsteady computations. AIAA 95-0078, 1995. – volume: 228 start-page: 4836 year: 2009 end-page: 4857 ident: bib1 article-title: Solution-limited time stepping to enhance reliability in CFD applications publication-title: J Comput Phys – reference: Huang PG, Coakley TJ, An implicit Navier–Stokes code for turbulent flow modeling, AIAA paper 92-0547. In: AIAA 30th aerospace sciences meeting, Reno (NV), 1992. – reference: – – reference: Menter FR. Zonal two equation – volume: 28 start-page: 63 year: 1999 end-page: 86 ident: bib27 article-title: On the behavior of upwind schemes in the low mach number limit publication-title: Comput Fluids – reference: Franz D. An introduction to the theory of fluid flows. ISBN:9783540713425, 2008. – reference: turbulence models for aerodynamic flows. AIAA paper 93-2906. In: 24th AIAA fluid dynamics conference, Orlando (FL); July 1993. – volume: 34 year: 2005 ident: bib13 article-title: Mixed analytical/numerical method applied to the high reynolds number publication-title: Comput Fluids – volume: 128 year: 1996 ident: bib10 article-title: A strongly coupled time-marching method for solving the Navier–Stokes and publication-title: J Comput Phys – volume: 4 start-page: 99 year: 1994 end-page: 113 ident: bib8 article-title: Multigrid method for the compressible Navier–Stokes equations coupled to the publication-title: Int J Numer Methods Heat Fluid Flow – volume: 72 start-page: 277 year: 1987 end-page: 298 ident: bib16 article-title: Preconditioning methods for solving the incompressible and low speed compressible equations publication-title: J Comput Phys – year: 2006 ident: bib4 article-title: Turbulence modeling for CFD – volume: 63 start-page: 377 year: 1986 ident: bib20 article-title: A numerical method for incompressible and compressible flow problems with smooth solutions publication-title: J Comput Phys – volume: 33 start-page: 1 year: 1996 end-page: 16 ident: bib9 article-title: A well-balanced scheme for the numerical processing of source terms in hyperbolic equations publication-title: SIAM J Numer Anal – volume: 38 start-page: 2085 year: 2000 end-page: 2093 ident: bib3 article-title: Computational treatment of source terms in two-equation turbulence models publication-title: AIAA J – volume: 42 year: 2004 ident: bib12 article-title: Mixed analytical/numerical method for low-reynolds-number publication-title: AIAA J – volume: 4 start-page: 1510 year: 1992 end-page: 1520 ident: bib25 article-title: Development of turbulence models for shear flows by a double expansion technique publication-title: Phys Fluids A – volume: 24 start-page: 1744 year: 1991 end-page: 1751 ident: bib6 article-title: Navier–Stokes computations of transonic flows with a two-equation turbulence model publication-title: AIAA J – reference: Van Leer B, Lee WT, Roe PL, Characteristic time-stepping or local preconditioning of the euler equations, AIAA 91-1552-CP. In: Computational fluid dynamics conference, Honolulu; 1991. – year: 1993 ident: bib2 article-title: Efficient implementation of turbulence modeling in computational schemes publication-title: Proceedings of the second US national congress on computational mechanics – volume: 38 start-page: 2085 issue: 11 year: 2000 ident: 10.1016/j.compfluid.2010.06.021_bib3 article-title: Computational treatment of source terms in two-equation turbulence models publication-title: AIAA J doi: 10.2514/2.870 – volume: 33 start-page: 1 year: 1996 ident: 10.1016/j.compfluid.2010.06.021_bib9 article-title: A well-balanced scheme for the numerical processing of source terms in hyperbolic equations publication-title: SIAM J Numer Anal doi: 10.1137/0733001 – year: 1993 ident: 10.1016/j.compfluid.2010.06.021_bib2 article-title: Efficient implementation of turbulence modeling in computational schemes – ident: 10.1016/j.compfluid.2010.06.021_bib26 doi: 10.2514/6.1993-2906 – volume: 24 start-page: 1744 year: 1991 ident: 10.1016/j.compfluid.2010.06.021_bib6 article-title: Navier–Stokes computations of transonic flows with a two-equation turbulence model publication-title: AIAA J doi: 10.2514/3.9519 – volume: 228 start-page: 4836 year: 2009 ident: 10.1016/j.compfluid.2010.06.021_bib1 article-title: Solution-limited time stepping to enhance reliability in CFD applications publication-title: J Comput Phys doi: 10.1016/j.jcp.2009.03.040 – start-page: 2006 year: 2006 ident: 10.1016/j.compfluid.2010.06.021_bib15 article-title: Multi-disciplinary computational analysis in propulsion publication-title: AIAA – volume: 4 start-page: 99 issue: 12 year: 1994 ident: 10.1016/j.compfluid.2010.06.021_bib8 article-title: Multigrid method for the compressible Navier–Stokes equations coupled to the k–ε turbulence equations publication-title: Int J Numer Methods Heat Fluid Flow doi: 10.1108/EUM0000000004033 – volume: 34 issue: 1 year: 2005 ident: 10.1016/j.compfluid.2010.06.021_bib13 article-title: Mixed analytical/numerical method applied to the high reynolds number k–ε turbulence model publication-title: Comput Fluids doi: 10.1016/j.compfluid.2003.12.004 – volume: 4 start-page: 1510 issue: 7 year: 1992 ident: 10.1016/j.compfluid.2010.06.021_bib25 article-title: Development of turbulence models for shear flows by a double expansion technique publication-title: Phys Fluids A doi: 10.1063/1.858424 – volume: 42 issue: 6 year: 2004 ident: 10.1016/j.compfluid.2010.06.021_bib12 article-title: Mixed analytical/numerical method for low-reynolds-number k–ε turbulence models publication-title: AIAA J doi: 10.2514/1.2426 – volume: 23 start-page: 1518 year: 1985 ident: 10.1016/j.compfluid.2010.06.021_bib21 article-title: Application of time-iterative schemes to incompressible flow publication-title: AIAA J doi: 10.2514/3.9119 – volume: 28 start-page: 1707 issue: 10 year: 1990 ident: 10.1016/j.compfluid.2010.06.021_bib5 article-title: Implicit multiple-grid solution of the compressible Navier–Stokes equation using k–ε turbulence closure publication-title: AIAA J doi: 10.2514/3.10464 – ident: 10.1016/j.compfluid.2010.06.021_bib22 doi: 10.2514/6.2003-72 – ident: 10.1016/j.compfluid.2010.06.021_bib23 – ident: 10.1016/j.compfluid.2010.06.021_bib7 doi: 10.2514/6.1992-547 – year: 1985 ident: 10.1016/j.compfluid.2010.06.021_bib18 article-title: Pseudo-unsteady systems for steady inviscid calculations – volume: 63 start-page: 377 year: 1986 ident: 10.1016/j.compfluid.2010.06.021_bib20 article-title: A numerical method for incompressible and compressible flow problems with smooth solutions publication-title: J Comput Phys doi: 10.1016/0021-9991(86)90200-7 – volume: 72 start-page: 277 year: 1987 ident: 10.1016/j.compfluid.2010.06.021_bib16 article-title: Preconditioning methods for solving the incompressible and low speed compressible equations publication-title: J Comput Phys doi: 10.1016/0021-9991(87)90084-2 – ident: 10.1016/j.compfluid.2010.06.021_bib28 – volume: 128 issue: 2 year: 1996 ident: 10.1016/j.compfluid.2010.06.021_bib10 article-title: A strongly coupled time-marching method for solving the Navier–Stokes and k–ω turbulence model equations with multigrid publication-title: J Comput Phys doi: 10.1006/jcph.1996.0211 – year: 2006 ident: 10.1016/j.compfluid.2010.06.021_bib4 – volume: 21 start-page: 1467 issue: 24 year: 1983 ident: 10.1016/j.compfluid.2010.06.021_bib19 article-title: A low mach number euler formulation and application to time-iterative LBI schemes publication-title: AIAA J doi: 10.2514/3.8291 – volume: 137 issue: 1 year: 1997 ident: 10.1016/j.compfluid.2010.06.021_bib11 article-title: Average-state Jacobians and implicit methods for compressible viscous and turbulent flows publication-title: J Comput Phys doi: 10.1006/jcph.1997.5793 – volume: 1 issue: 2 year: 1974 ident: 10.1016/j.compfluid.2010.06.021_bib24 article-title: Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc publication-title: Lett Heat Mass Transfer doi: 10.1016/0094-4548(74)90150-7 – volume: 220 start-page: 88 issue: 1 year: 2006 ident: 10.1016/j.compfluid.2010.06.021_bib14 article-title: Unconditionally positive implicit procedure for two-equation turbulence models: application to k–ω turbulence models publication-title: J Comput Phys doi: 10.1016/j.jcp.2006.05.001 – ident: 10.1016/j.compfluid.2010.06.021_bib17 doi: 10.2514/6.1991-1552 – volume: 28 start-page: 63 issue: 1 year: 1999 ident: 10.1016/j.compfluid.2010.06.021_bib27 article-title: On the behavior of upwind schemes in the low mach number limit publication-title: Comput Fluids doi: 10.1016/S0045-7930(98)00017-6 |
| SSID | ssj0004324 |
| Score | 2.174391 |
| Snippet | Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 1909 |
| SubjectTerms | Algorithms Computational fluid dynamics Computational methods in fluid dynamics Convection Diffusion Exact sciences and technology Flows in ducts, channels, nozzles, and conduits Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) Jacobians Mathematical models Physics Reliability Sink Source Turbulence Turbulence simulation and modeling Turbulent flows, convection, and heat transfer |
| Title | Impact of source terms on reliability of CFD algorithms |
| URI | https://dx.doi.org/10.1016/j.compfluid.2010.06.021 https://www.proquest.com/docview/1709754526 https://www.proquest.com/docview/831201555 |
| Volume | 39 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier E-journals (Freedom Collection) customDbUrl: eissn: 1879-0747 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0004324 issn: 0045-7930 databaseCode: ACRLP dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection customDbUrl: eissn: 1879-0747 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0004324 issn: 0045-7930 databaseCode: .~1 dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals [SCFCJ] customDbUrl: eissn: 1879-0747 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0004324 issn: 0045-7930 databaseCode: AIKHN dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1879-0747 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0004324 issn: 0045-7930 databaseCode: AKRWK dateStart: 19730101 isFulltext: true providerName: Library Specific Holdings |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PT9swGP3EyoUJTbAxURiVkXYNxHZiO9yqQlVAcBoSN8t2bJapS6r-OOyyvx07P7pVCHHgmtiJ9ex8fkne9z6A78ziPDE0iyyjNkpSqqJMaxq5xBJNnItNrc25u2eTh-TmMX3cglGXCxNklW3sb2J6Ha3bI-ctmuezogg5vknqV1eM63xg4t_bt_3-I0QPtofXt5P7f-mRlDRmzElwZ6TxhswrKLfddFXkrcyLncUEv7ZJ7c7UwkPnmpoXL8J3vSeN9-BTSybRsBnvPmzZ8jN8_M9i8Avw6zoNElUONd_pUYjFC1SVaG6nRePS_SecHo0vkZo-VfNi-fP34gAexlc_RpOoLZYQmYSzZZRynlpssOKUOqacZcwFMkG0IFzEuXI01JsSymMmlGeFwTie05Cn6nguFP0KvbIq7SEglaTE5EYYrTPPL3Sm_TVVToylCjPD-sA6dKRpncRDQYup7CRjv-QaVhlglUE8R3Af4nXHWWOm8XaXiw5-ubEupA_5b3cebEzY-qaeRlLBqW9w2s2g9I9V-FeiSlutFhLzOON1_fU-oFfaCIpJoJzp0XsGeQw7ZC2R-Qa95XxlTzzRWeoBfDj7iwftcn4GCMX9Ag |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT-MwELYQHNjVCsE-RHl6pb0GYjuxE26oUBUWemql3izbsZegblL1ceCyv309eRQqhDhwTTyJ9dkZf46_mUHoF7ckiwxLA8uZDaKYqSDVmgUuslRT50JTaXPuB7w_im7H8XgDddtYGJBVNr6_9umVt26unDdonk_zHGJ8o9jPrpBU8cDU79u3opgK2IGd_XvWeUDKufqYGXIzsnBN5AW6bTdZ5lkj8uJnISVvLVFfpmrugXN1xYtXzrtakXq7aKehkviy7u0e2rDFV_T5RYLBb0jcVEGQuHS4_kuPwRPPcVngmZ3kdY7uJ7jd7V1hNflTzvLFw9_5dzTqXQ-7_aAplRCYSPBFEAsRW2KIEow5rpzl3AGVoDqhIgkz5RhUm0qURyxRnhNC2njBIErViSxR7AfaLMrC7iOsPIgmM4nROvXsQqfaP1Nl1FimCDe8g3iLjjRNHnEoZzGRrWDsUa5glQCrBOkcJR0UrgyndSqN900uWvjl2qyQ3uG_b3yyNmCrl3oSyRLBfIOf7QhK_1HBSYkqbLmcSyLCVFTV1zsIv9EmYYQC4YwPPtLJU7TdH97fybubwe9D9ImuxDJHaHMxW9pjT3kW-qSa0v8BJPn9yg |
| 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=Impact+of+source+terms+on+reliability+of+CFD+algorithms&rft.jtitle=Computers+%26+fluids&rft.au=Lian%2C+Chenzhou&rft.au=Xia%2C+Guoping&rft.au=Merkle%2C+Charles+L&rft.date=2010-12-01&rft.issn=0045-7930&rft.volume=39&rft.issue=10&rft.spage=1909&rft.epage=1922&rft_id=info:doi/10.1016%2Fj.compfluid.2010.06.021&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0045-7930&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0045-7930&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0045-7930&client=summon |