Predictive near-wall modelling for turbulent boundary layers with arbitrary pressure gradients Article Swipe
Xiang I. A. Yang
,
Peng E. S. Chen
,
Wen Zhang
,
Robert F. Kunz
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1017/jfm.2024.565
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1017/jfm.2024.565
The mean flow in a turbulent boundary layer (TBL) deviates from the canonical law of the wall (LoW) when influenced by a pressure gradient. Consequently, LoW-based near-wall treatments are inadequate for such flows. Chen et al. ( J. Fluid Mech. , vol. 970, 2023, A3) derived a Navier–Stokes-based velocity transformation that accurately describes the mean flow in TBLs with arbitrary pressure gradients. However, this transformation requires information on total shear stress, which is not always readily available, limiting its predictive power. In this work, we invert the transformation and develop a predictive near-wall model. Our model includes an additional transport equation that tracks the Lagrangian integration of the total shear stress. Particularly noteworthy is that the model introduces no new parameters and requires no calibration. We validate the developed model against experimental and computational data in the literature, and the results are favourable. Furthermore, we compare our model with equilibrium models. These equilibrium models inevitably fail when there are strong pressure gradients, but they prove to be sufficient for boundary layers subjected to weak, moderate and even moderately high pressure gradients. These results compel us to conclude that history effects in mean flow, which negatively impact the validity of equilibrium models, can largely be accounted for by the material time derivative term and the pressure gradient term, both of which require no additional modelling.
Related Topics
Concepts
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1017/jfm.2024.565
- OA Status
- hybrid
- Cited By
- 6
- References
- 48
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4402521505
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4402521505Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1017/jfm.2024.565Digital Object Identifier
- Title
-
Predictive near-wall modelling for turbulent boundary layers with arbitrary pressure gradientsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-08-25Full publication date if available
- Authors
-
Xiang I. A. Yang, Peng E. S. Chen, Wen Zhang, Robert F. KunzList of authors in order
- Landing page
-
https://doi.org/10.1017/jfm.2024.565Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.1017/jfm.2024.565Direct OA link when available
- Concepts
-
Turbulence, Mechanics, Pressure gradient, Boundary layer, Boundary (topology), Flow separation, Materials science, Physics, Mathematical analysis, MathematicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
6Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 6Per-year citation counts (last 5 years)
- References (count)
-
48Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4402521505 |
|---|---|
| doi | https://doi.org/10.1017/jfm.2024.565 |
| ids.doi | https://doi.org/10.1017/jfm.2024.565 |
| ids.openalex | https://openalex.org/W4402521505 |
| fwci | 4.32477881 |
| type | article |
| title | Predictive near-wall modelling for turbulent boundary layers with arbitrary pressure gradients |
| awards[0].id | https://openalex.org/G7906798948 |
| awards[0].funder_id | https://openalex.org/F4320337345 |
| awards[0].display_name | |
| awards[0].funder_award_id | N000142012315 |
| awards[0].funder_display_name | Office of Naval Research |
| awards[1].id | https://openalex.org/G8293581535 |
| awards[1].funder_id | https://openalex.org/F4320321001 |
| awards[1].display_name | |
| awards[1].funder_award_id | 12225204,11988102 |
| awards[1].funder_display_name | National Natural Science Foundation of China |
| biblio.issue | |
| biblio.volume | 993 |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10360 |
| topics[0].field.id | https://openalex.org/fields/22 |
| topics[0].field.display_name | Engineering |
| topics[0].score | 1.0 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2206 |
| topics[0].subfield.display_name | Computational Mechanics |
| topics[0].display_name | Fluid Dynamics and Turbulent Flows |
| topics[1].id | https://openalex.org/T10173 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9997000098228455 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2206 |
| topics[1].subfield.display_name | Computational Mechanics |
| topics[1].display_name | Computational Fluid Dynamics and Aerodynamics |
| topics[2].id | https://openalex.org/T11371 |
| topics[2].field.id | https://openalex.org/fields/23 |
| topics[2].field.display_name | Environmental Science |
| topics[2].score | 0.9995999932289124 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2305 |
| topics[2].subfield.display_name | Environmental Engineering |
| topics[2].display_name | Wind and Air Flow Studies |
| funders[0].id | https://openalex.org/F4320321001 |
| funders[0].ror | https://ror.org/01h0zpd94 |
| funders[0].display_name | National Natural Science Foundation of China |
| funders[1].id | https://openalex.org/F4320333649 |
| funders[1].ror | |
| funders[1].display_name | Center for Turbulence Research, Stanford University |
| funders[2].id | https://openalex.org/F4320337345 |
| funders[2].ror | https://ror.org/00rk2pe57 |
| funders[2].display_name | Office of Naval Research |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C196558001 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7036095261573792 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q190132 |
| concepts[0].display_name | Turbulence |
| concepts[1].id | https://openalex.org/C57879066 |
| concepts[1].level | 1 |
| concepts[1].score | 0.658861517906189 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q41217 |
| concepts[1].display_name | Mechanics |
| concepts[2].id | https://openalex.org/C98156149 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6238720417022705 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q2414143 |
| concepts[2].display_name | Pressure gradient |
| concepts[3].id | https://openalex.org/C111603439 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5148448348045349 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q752193 |
| concepts[3].display_name | Boundary layer |
| concepts[4].id | https://openalex.org/C62354387 |
| concepts[4].level | 2 |
| concepts[4].score | 0.47740498185157776 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q875399 |
| concepts[4].display_name | Boundary (topology) |
| concepts[5].id | https://openalex.org/C77576233 |
| concepts[5].level | 3 |
| concepts[5].score | 0.4268471598625183 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q1545856 |
| concepts[5].display_name | Flow separation |
| concepts[6].id | https://openalex.org/C192562407 |
| concepts[6].level | 0 |
| concepts[6].score | 0.3996473550796509 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[6].display_name | Materials science |
| concepts[7].id | https://openalex.org/C121332964 |
| concepts[7].level | 0 |
| concepts[7].score | 0.2713640630245209 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[7].display_name | Physics |
| concepts[8].id | https://openalex.org/C134306372 |
| concepts[8].level | 1 |
| concepts[8].score | 0.12546038627624512 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[8].display_name | Mathematical analysis |
| concepts[9].id | https://openalex.org/C33923547 |
| concepts[9].level | 0 |
| concepts[9].score | 0.10069957375526428 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[9].display_name | Mathematics |
| keywords[0].id | https://openalex.org/keywords/turbulence |
| keywords[0].score | 0.7036095261573792 |
| keywords[0].display_name | Turbulence |
| keywords[1].id | https://openalex.org/keywords/mechanics |
| keywords[1].score | 0.658861517906189 |
| keywords[1].display_name | Mechanics |
| keywords[2].id | https://openalex.org/keywords/pressure-gradient |
| keywords[2].score | 0.6238720417022705 |
| keywords[2].display_name | Pressure gradient |
| keywords[3].id | https://openalex.org/keywords/boundary-layer |
| keywords[3].score | 0.5148448348045349 |
| keywords[3].display_name | Boundary layer |
| keywords[4].id | https://openalex.org/keywords/boundary |
| keywords[4].score | 0.47740498185157776 |
| keywords[4].display_name | Boundary (topology) |
| keywords[5].id | https://openalex.org/keywords/flow-separation |
| keywords[5].score | 0.4268471598625183 |
| keywords[5].display_name | Flow separation |
| keywords[6].id | https://openalex.org/keywords/materials-science |
| keywords[6].score | 0.3996473550796509 |
| keywords[6].display_name | Materials science |
| keywords[7].id | https://openalex.org/keywords/physics |
| keywords[7].score | 0.2713640630245209 |
| keywords[7].display_name | Physics |
| keywords[8].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[8].score | 0.12546038627624512 |
| keywords[8].display_name | Mathematical analysis |
| keywords[9].id | https://openalex.org/keywords/mathematics |
| keywords[9].score | 0.10069957375526428 |
| keywords[9].display_name | Mathematics |
| language | en |
| locations[0].id | doi:10.1017/jfm.2024.565 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S152000018 |
| locations[0].source.issn | 0022-1120, 1469-7645 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0022-1120 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Journal of Fluid Mechanics |
| locations[0].source.host_organization | https://openalex.org/P4310311721 |
| locations[0].source.host_organization_name | Cambridge University Press |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310311721, https://openalex.org/P4310311702 |
| locations[0].source.host_organization_lineage_names | Cambridge University Press, University of Cambridge |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Journal of Fluid Mechanics |
| locations[0].landing_page_url | https://doi.org/10.1017/jfm.2024.565 |
| locations[1].id | pmh:oai:scholarsphere.psu.edu:5dd69dc9-6bc8-40b5-a319-c368ceb16e51 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306401507 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | ScholarSphere (Penn State Libraries) |
| locations[1].source.host_organization | https://openalex.org/I3130638595 |
| locations[1].source.host_organization_name | Pangasinan State University |
| locations[1].source.host_organization_lineage | https://openalex.org/I3130638595 |
| locations[1].license | cc-by |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | Article |
| locations[1].license_id | https://openalex.org/licenses/cc-by |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://scholarsphere.psu.edu/resources/5dd69dc9-6bc8-40b5-a319-c368ceb16e51 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5085025441 |
| authorships[0].author.orcid | https://orcid.org/0000-0003-4940-5976 |
| authorships[0].author.display_name | Xiang I. A. Yang |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Xiang I.A. Yang |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5057227607 |
| authorships[1].author.orcid | https://orcid.org/0000-0001-6387-4811 |
| authorships[1].author.display_name | Peng E. S. Chen |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Peng E.S. Chen |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5115596895 |
| authorships[2].author.orcid | https://orcid.org/0009-0008-1519-4692 |
| authorships[2].author.display_name | Wen Zhang |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Wen Zhang |
| authorships[2].is_corresponding | False |
| authorships[3].author.id | https://openalex.org/A5023802568 |
| authorships[3].author.orcid | https://orcid.org/0000-0001-9504-1945 |
| authorships[3].author.display_name | Robert F. Kunz |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Robert Kunz |
| authorships[3].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.1017/jfm.2024.565 |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Predictive near-wall modelling for turbulent boundary layers with arbitrary pressure gradients |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10360 |
| primary_topic.field.id | https://openalex.org/fields/22 |
| primary_topic.field.display_name | Engineering |
| primary_topic.score | 1.0 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2206 |
| primary_topic.subfield.display_name | Computational Mechanics |
| primary_topic.display_name | Fluid Dynamics and Turbulent Flows |
| related_works | https://openalex.org/W23615509, https://openalex.org/W4312680187, https://openalex.org/W2998556114, https://openalex.org/W325349126, https://openalex.org/W1909938025, https://openalex.org/W857103152, https://openalex.org/W2159633953, https://openalex.org/W2312672266, https://openalex.org/W2586315063, https://openalex.org/W2643927566 |
| cited_by_count | 6 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 6 |
| locations_count | 2 |
| best_oa_location.id | doi:10.1017/jfm.2024.565 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S152000018 |
| best_oa_location.source.issn | 0022-1120, 1469-7645 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 0022-1120 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | Journal of Fluid Mechanics |
| best_oa_location.source.host_organization | https://openalex.org/P4310311721 |
| best_oa_location.source.host_organization_name | Cambridge University Press |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310311721, https://openalex.org/P4310311702 |
| best_oa_location.source.host_organization_lineage_names | Cambridge University Press, University of Cambridge |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Journal of Fluid Mechanics |
| best_oa_location.landing_page_url | https://doi.org/10.1017/jfm.2024.565 |
| primary_location.id | doi:10.1017/jfm.2024.565 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S152000018 |
| primary_location.source.issn | 0022-1120, 1469-7645 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0022-1120 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Journal of Fluid Mechanics |
| primary_location.source.host_organization | https://openalex.org/P4310311721 |
| primary_location.source.host_organization_name | Cambridge University Press |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310311721, https://openalex.org/P4310311702 |
| primary_location.source.host_organization_lineage_names | Cambridge University Press, University of Cambridge |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Journal of Fluid Mechanics |
| primary_location.landing_page_url | https://doi.org/10.1017/jfm.2024.565 |
| publication_date | 2024-08-25 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W2147102474, https://openalex.org/W2918335093, https://openalex.org/W1977917057, https://openalex.org/W2579523679, https://openalex.org/W3179511989, https://openalex.org/W2090255068, https://openalex.org/W4220937902, https://openalex.org/W2164742615, https://openalex.org/W4388731932, https://openalex.org/W4386165714, https://openalex.org/W2319329301, https://openalex.org/W2345668738, https://openalex.org/W2613424231, https://openalex.org/W2763903125, https://openalex.org/W4382561544, https://openalex.org/W4382561563, https://openalex.org/W4295530537, https://openalex.org/W4200390805, https://openalex.org/W2008252915, https://openalex.org/W3039112463, https://openalex.org/W4322618422, https://openalex.org/W2012342745, https://openalex.org/W2028277719, https://openalex.org/W4386417438, https://openalex.org/W3035271189, https://openalex.org/W2994296715, https://openalex.org/W6788522056, https://openalex.org/W2991263474, https://openalex.org/W4384523618, https://openalex.org/W1981574772, https://openalex.org/W3095542365, https://openalex.org/W4317568510, https://openalex.org/W4386485205, https://openalex.org/W2075853313, https://openalex.org/W2162588443, https://openalex.org/W2175905423, https://openalex.org/W1595241212, https://openalex.org/W4388727811, https://openalex.org/W4207035978, https://openalex.org/W2058534834, https://openalex.org/W2810249645, https://openalex.org/W2887938690, https://openalex.org/W1632204961, https://openalex.org/W4317651125, https://openalex.org/W3119990632, https://openalex.org/W3132007733, https://openalex.org/W3104091039, https://openalex.org/W2053590982 |
| referenced_works_count | 48 |
| abstract_inverted_index.( | 36 |
| abstract_inverted_index., | 40 |
| abstract_inverted_index.a | 4, 21, 46, 90 |
| abstract_inverted_index.In | 81 |
| abstract_inverted_index.J. | 37 |
| abstract_inverted_index.We | 125 |
| abstract_inverted_index.an | 97 |
| abstract_inverted_index.be | 166, 203 |
| abstract_inverted_index.by | 20, 206 |
| abstract_inverted_index.et | 34 |
| abstract_inverted_index.in | 3, 56, 135, 190 |
| abstract_inverted_index.is | 72, 113 |
| abstract_inverted_index.no | 118, 123, 221 |
| abstract_inverted_index.of | 14, 106, 198, 218 |
| abstract_inverted_index.on | 67 |
| abstract_inverted_index.to | 165, 172, 185 |
| abstract_inverted_index.us | 184 |
| abstract_inverted_index.we | 84, 144 |
| abstract_inverted_index.A3) | 44 |
| abstract_inverted_index.Our | 94 |
| abstract_inverted_index.The | 0 |
| abstract_inverted_index.al. | 35 |
| abstract_inverted_index.and | 88, 121, 132, 138, 175, 212 |
| abstract_inverted_index.are | 28, 141, 158 |
| abstract_inverted_index.but | 162 |
| abstract_inverted_index.can | 201 |
| abstract_inverted_index.for | 30, 168, 205 |
| abstract_inverted_index.its | 78 |
| abstract_inverted_index.law | 13 |
| abstract_inverted_index.new | 119 |
| abstract_inverted_index.not | 73 |
| abstract_inverted_index.our | 146 |
| abstract_inverted_index.the | 11, 15, 53, 86, 103, 107, 115, 127, 136, 139, 196, 207, 213 |
| abstract_inverted_index.970, | 42 |
| abstract_inverted_index.Chen | 33 |
| abstract_inverted_index.TBLs | 57 |
| abstract_inverted_index.both | 217 |
| abstract_inverted_index.data | 134 |
| abstract_inverted_index.even | 176 |
| abstract_inverted_index.fail | 155 |
| abstract_inverted_index.flow | 2, 55 |
| abstract_inverted_index.from | 10 |
| abstract_inverted_index.high | 178 |
| abstract_inverted_index.mean | 1, 54, 191 |
| abstract_inverted_index.such | 31 |
| abstract_inverted_index.term | 211 |
| abstract_inverted_index.that | 50, 101, 114, 187 |
| abstract_inverted_index.they | 163 |
| abstract_inverted_index.this | 63, 82 |
| abstract_inverted_index.time | 209 |
| abstract_inverted_index.vol. | 41 |
| abstract_inverted_index.wall | 16 |
| abstract_inverted_index.when | 18, 156 |
| abstract_inverted_index.with | 58, 148 |
| abstract_inverted_index.(LoW) | 17 |
| abstract_inverted_index.(TBL) | 8 |
| abstract_inverted_index.2023, | 43 |
| abstract_inverted_index.Fluid | 38 |
| abstract_inverted_index.Mech. | 39 |
| abstract_inverted_index.These | 151, 181 |
| abstract_inverted_index.flow, | 192 |
| abstract_inverted_index.layer | 7 |
| abstract_inverted_index.model | 95, 116, 129, 147 |
| abstract_inverted_index.prove | 164 |
| abstract_inverted_index.shear | 69, 109 |
| abstract_inverted_index.term, | 216 |
| abstract_inverted_index.there | 157 |
| abstract_inverted_index.total | 68, 108 |
| abstract_inverted_index.weak, | 173 |
| abstract_inverted_index.which | 71, 193, 219 |
| abstract_inverted_index.work, | 83 |
| abstract_inverted_index.always | 74 |
| abstract_inverted_index.compel | 183 |
| abstract_inverted_index.flows. | 32 |
| abstract_inverted_index.impact | 195 |
| abstract_inverted_index.invert | 85 |
| abstract_inverted_index.layers | 170 |
| abstract_inverted_index.model. | 93 |
| abstract_inverted_index.models | 153 |
| abstract_inverted_index.power. | 80 |
| abstract_inverted_index.strong | 159 |
| abstract_inverted_index.tracks | 102 |
| abstract_inverted_index.against | 130 |
| abstract_inverted_index.compare | 145 |
| abstract_inverted_index.derived | 45 |
| abstract_inverted_index.develop | 89 |
| abstract_inverted_index.effects | 189 |
| abstract_inverted_index.history | 188 |
| abstract_inverted_index.largely | 202 |
| abstract_inverted_index.models, | 200 |
| abstract_inverted_index.models. | 150 |
| abstract_inverted_index.readily | 75 |
| abstract_inverted_index.require | 220 |
| abstract_inverted_index.results | 140, 182 |
| abstract_inverted_index.stress, | 70 |
| abstract_inverted_index.stress. | 110 |
| abstract_inverted_index.However, | 62 |
| abstract_inverted_index.boundary | 6, 169 |
| abstract_inverted_index.conclude | 186 |
| abstract_inverted_index.deviates | 9 |
| abstract_inverted_index.equation | 100 |
| abstract_inverted_index.gradient | 215 |
| abstract_inverted_index.includes | 96 |
| abstract_inverted_index.limiting | 77 |
| abstract_inverted_index.material | 208 |
| abstract_inverted_index.moderate | 174 |
| abstract_inverted_index.pressure | 22, 60, 160, 179, 214 |
| abstract_inverted_index.requires | 65, 122 |
| abstract_inverted_index.validate | 126 |
| abstract_inverted_index.validity | 197 |
| abstract_inverted_index.velocity | 48 |
| abstract_inverted_index.LoW-based | 25 |
| abstract_inverted_index.accounted | 204 |
| abstract_inverted_index.arbitrary | 59 |
| abstract_inverted_index.canonical | 12 |
| abstract_inverted_index.describes | 52 |
| abstract_inverted_index.developed | 128 |
| abstract_inverted_index.gradient. | 23 |
| abstract_inverted_index.near-wall | 26, 92 |
| abstract_inverted_index.subjected | 171 |
| abstract_inverted_index.transport | 99 |
| abstract_inverted_index.turbulent | 5 |
| abstract_inverted_index.Lagrangian | 104 |
| abstract_inverted_index.accurately | 51 |
| abstract_inverted_index.additional | 98, 222 |
| abstract_inverted_index.available, | 76 |
| abstract_inverted_index.derivative | 210 |
| abstract_inverted_index.gradients, | 161 |
| abstract_inverted_index.gradients. | 61, 180 |
| abstract_inverted_index.inadequate | 29 |
| abstract_inverted_index.inevitably | 154 |
| abstract_inverted_index.influenced | 19 |
| abstract_inverted_index.introduces | 117 |
| abstract_inverted_index.modelling. | 223 |
| abstract_inverted_index.moderately | 177 |
| abstract_inverted_index.negatively | 194 |
| abstract_inverted_index.noteworthy | 112 |
| abstract_inverted_index.parameters | 120 |
| abstract_inverted_index.predictive | 79, 91 |
| abstract_inverted_index.sufficient | 167 |
| abstract_inverted_index.treatments | 27 |
| abstract_inverted_index.equilibrium | 149, 152, 199 |
| abstract_inverted_index.favourable. | 142 |
| abstract_inverted_index.information | 66 |
| abstract_inverted_index.integration | 105 |
| abstract_inverted_index.literature, | 137 |
| abstract_inverted_index.Furthermore, | 143 |
| abstract_inverted_index.Particularly | 111 |
| abstract_inverted_index.calibration. | 124 |
| abstract_inverted_index.experimental | 131 |
| abstract_inverted_index.Consequently, | 24 |
| abstract_inverted_index.computational | 133 |
| abstract_inverted_index.transformation | 49, 64, 87 |
| abstract_inverted_index.Navier–Stokes-based | 47 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 98 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile.value | 0.91488294 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |