Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Journal of fluid mechanics Ročník 807; s. 155 - 166
Hlavní autori:	Ling, Julia, Kurzawski, Andrew, Templeton, Jeremy
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cambridge, UK Cambridge University Press 25.11.2016
Predmet:	Anisotropy CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Fluid mechanics Navier-Stokes equations Reynolds number Turbulence Viscosity turbulent flows turbulence modelling turbulence theory
ISSN:	0022-1120, 1469-7645
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.
AbstractList	There exists significant demand for improved Reynolds-averaged Navier-Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated. There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. Furthermore, the Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.
Author	Kurzawski, Andrew Templeton, Jeremy Ling, Julia
Author_xml	– sequence: 1 givenname: Julia surname: Ling fullname: Ling, Julia email: jling@sandia.gov organization: Thermal/Fluids Science and Engineering Department, Sandia National Labs, Livermore, CA 94550, USA – sequence: 2 givenname: Andrew surname: Kurzawski fullname: Kurzawski, Andrew organization: Mechanical Engineering Department, University of Texas at Austin, Austin, TX 78712, USA – sequence: 3 givenname: Jeremy surname: Templeton fullname: Templeton, Jeremy organization: Thermal/Fluids Science and Engineering Department, Sandia National Labs, Livermore, CA 94550, USA
BackLink	https://www.osti.gov/servlets/purl/1333570$$D View this record in Osti.gov
BookMark	eNp1kM9LwzAYhoMouE1v_gFFr3YmaZu2Rxn-AkEQvXgJafJ1y2yTmaQb--_N2A4ievm-y_O8vLxjdGysAYQuCJ4STMqbZdtPKSZsykhxhEYkZ3Vasrw4RiOMKU0JofgUjb1fYkwyXJcj9PEKW2M75ROxBifmoJIwuGbowEhIequg67SZJ4PfXQWwSgwMTnTxhY11nz7Z6LBIoG9AqWhrsxZOi2ifoZNWdB7OD3-C3u_v3maP6fPLw9Ps9jmVGStDmuMqr1uqcNMKRpUgbSZrCliWomQVsEoWLZZYZISJiklCm4JWVBWgCtZISrMJutznWh8091IHkAtpjQEZOMmyrChxhK720MrZrwF84Es7OBN7cVJVeRFb1HWk6J6SznrvoOUxTQRtTXBCd5xgvhuax6H5bmgeh47S9S9p5XQv3PY_fHrARd84rebwo8pfwjelh5Fi
CitedBy_id	crossref_primary_10_1016_j_engappai_2023_107334 crossref_primary_10_1016_j_cma_2024_117187 crossref_primary_10_1002_nme_6828 crossref_primary_10_1007_s10409_021_01130_x crossref_primary_10_1088_1742_6596_2707_1_012104 crossref_primary_10_1016_j_jcp_2020_109951 crossref_primary_10_1080_00295639_2020_1712928 crossref_primary_10_1137_19M1251941 crossref_primary_10_1016_j_ijheatfluidflow_2022_109017 crossref_primary_10_1016_j_ijheatfluidflow_2022_109018 crossref_primary_10_1007_s00466_023_02342_7 crossref_primary_10_1016_j_cma_2018_09_010 crossref_primary_10_1021_acs_langmuir_5c00754 crossref_primary_10_1016_j_cma_2022_115436 crossref_primary_10_32604_cmes_2021_015747 crossref_primary_10_1016_j_ces_2021_116832 crossref_primary_10_1007_s40314_023_02547_9 crossref_primary_10_1016_j_physd_2020_132495 crossref_primary_10_1017_jfm_2024_81 crossref_primary_10_1007_s10494_019_00089_x crossref_primary_10_1016_j_ijheatfluidflow_2022_109004 crossref_primary_10_1016_j_flowmeasinst_2019_04_006 crossref_primary_10_1073_pnas_2016708118 crossref_primary_10_1016_j_ijheatfluidflow_2022_109008 crossref_primary_10_1029_2018WR024090 crossref_primary_10_1038_s42005_025_02149_3 crossref_primary_10_1016_j_compfluid_2022_105379 crossref_primary_10_1016_j_ocemod_2024_102325 crossref_primary_10_1017_jfm_2024_77 crossref_primary_10_1016_j_physa_2022_128327 crossref_primary_10_1063_5_0171217 crossref_primary_10_1080_19942060_2023_2288235 crossref_primary_10_1007_s10494_023_00482_7 crossref_primary_10_1016_j_ijheatfluidflow_2022_109038 crossref_primary_10_1016_j_jocs_2024_102404 crossref_primary_10_1017_jfm_2022_1069 crossref_primary_10_1177_09544100211027023 crossref_primary_10_1080_02286203_2024_2371682 crossref_primary_10_1029_2018EA000432 crossref_primary_10_1016_j_cma_2022_115457 crossref_primary_10_1016_j_oceaneng_2024_119779 crossref_primary_10_1016_j_energy_2025_135571 crossref_primary_10_1063_5_0212096 crossref_primary_10_1007_s12650_018_0519_x crossref_primary_10_1016_j_ijheatfluidflow_2022_109034 crossref_primary_10_1016_j_compfluid_2022_105382 crossref_primary_10_1017_jfm_2021_1012 crossref_primary_10_1109_ACCESS_2024_3430075 crossref_primary_10_1016_j_jcp_2024_113063 crossref_primary_10_2298_TSCI210313227Z crossref_primary_10_1016_j_compfluid_2020_104777 crossref_primary_10_1016_j_petrol_2022_110360 crossref_primary_10_1016_j_ast_2024_108955 crossref_primary_10_1016_j_mineng_2022_107884 crossref_primary_10_3390_jmse12112074 crossref_primary_10_1016_j_oceaneng_2021_109932 crossref_primary_10_1017_jfm_2020_453 crossref_primary_10_1016_j_cja_2019_04_004 crossref_primary_10_1016_j_nucengdes_2022_111716 crossref_primary_10_1016_j_matcom_2024_10_001 crossref_primary_10_1016_j_paerosci_2022_100849 crossref_primary_10_1016_j_ijheatmasstransfer_2023_124854 crossref_primary_10_1016_j_oceaneng_2022_113000 crossref_primary_10_1063_5_0218611 crossref_primary_10_1016_j_cnsns_2022_106664 crossref_primary_10_1016_j_energy_2023_128209 crossref_primary_10_1017_jfm_2019_358 crossref_primary_10_1073_pnas_2217744120 crossref_primary_10_3390_atmos12020157 crossref_primary_10_1016_j_ijheatmasstransfer_2022_122557 crossref_primary_10_1016_j_jcp_2019_109056 crossref_primary_10_1088_1751_8121_ad67bb crossref_primary_10_1002_fld_5284 crossref_primary_10_1073_pnas_2311808121 crossref_primary_10_1016_j_pecs_2022_101010 crossref_primary_10_1007_s10409_022_22302_x crossref_primary_10_1007_s10494_022_00321_1 crossref_primary_10_1103_PhysRevX_10_031056 crossref_primary_10_1016_j_ast_2024_109828 crossref_primary_10_1007_s10409_021_01143_6 crossref_primary_10_1016_j_applthermaleng_2018_08_041 crossref_primary_10_1146_annurev_fluid_010518_040547 crossref_primary_10_1016_j_ijhydene_2020_04_286 crossref_primary_10_1016_j_eswa_2024_124290 crossref_primary_10_1007_s00773_022_00914_5 crossref_primary_10_2514_1_J060866 crossref_primary_10_1007_s11082_024_07149_1 crossref_primary_10_1016_j_ces_2024_120950 crossref_primary_10_1016_j_combustflame_2019_02_019 crossref_primary_10_1017_jfm_2018_770 crossref_primary_10_1016_j_compfluid_2023_106113 crossref_primary_10_3847_1538_4357_ac3998 crossref_primary_10_1080_14685248_2017_1334907 crossref_primary_10_1080_14685248_2020_1757685 crossref_primary_10_1109_ACCESS_2020_2987324 crossref_primary_10_1017_jfm_2023_291 crossref_primary_10_1063_5_0033109 crossref_primary_10_1016_j_nucengdes_2024_113467 crossref_primary_10_1038_s41598_023_27426_5 crossref_primary_10_1016_j_jcp_2020_109957 crossref_primary_10_1088_1367_2630_ad6689 crossref_primary_10_1016_j_oceaneng_2024_118250 crossref_primary_10_1121_10_0026459 crossref_primary_10_3390_pr13041055 crossref_primary_10_1016_j_engstruct_2022_115149 crossref_primary_10_1016_j_powtec_2019_01_013 crossref_primary_10_1038_s41467_020_20779_9 crossref_primary_10_3390_en14165127 crossref_primary_10_2514_1_J057204 crossref_primary_10_1088_1742_6596_1618_6_062059 crossref_primary_10_1016_j_enganabound_2022_10_009 crossref_primary_10_2514_1_J057894 crossref_primary_10_1016_j_neo_2020_09_008 crossref_primary_10_1016_j_ijheatmasstransfer_2022_122998 crossref_primary_10_1016_j_ijheatfluidflow_2022_109094 crossref_primary_10_1177_23977914251353307 crossref_primary_10_3390_su151813383 crossref_primary_10_1016_j_oceaneng_2024_118041 crossref_primary_10_1007_s42241_019_0093_2 crossref_primary_10_1016_j_buildenv_2023_111157 crossref_primary_10_3390_fluids9080178 crossref_primary_10_1016_j_ijheatfluidflow_2023_109140 crossref_primary_10_1016_j_jcp_2025_114067 crossref_primary_10_1016_j_jcp_2025_114068 crossref_primary_10_1016_j_applthermaleng_2025_126380 crossref_primary_10_1016_j_ijthermalsci_2024_109363 crossref_primary_10_1063_5_0074724 crossref_primary_10_1002_fld_5093 crossref_primary_10_1007_s00162_022_00603_4 crossref_primary_10_1016_j_ces_2020_115835 crossref_primary_10_1007_s00521_021_06784_z crossref_primary_10_1007_s10409_022_22315_x crossref_primary_10_1016_j_ijheatmasstransfer_2022_123622 crossref_primary_10_1088_1361_6587_adfd13 crossref_primary_10_1007_s10439_022_02911_6 crossref_primary_10_1016_j_cma_2021_114211 crossref_primary_10_1016_j_jcp_2020_110085 crossref_primary_10_1080_00295450_2021_1974279 crossref_primary_10_1007_s00162_019_00512_z crossref_primary_10_1007_s10409_023_23517_x crossref_primary_10_1088_1361_6501_ace98b crossref_primary_10_1017_jfm_2020_861 crossref_primary_10_1016_j_neunet_2024_106354 crossref_primary_10_1088_1367_2630_abadb3 crossref_primary_10_1016_j_jcp_2021_110116 crossref_primary_10_1016_j_icheatmasstransfer_2023_107210 crossref_primary_10_1007_s10409_022_22326_x crossref_primary_10_1016_j_actaastro_2020_05_021 crossref_primary_10_3390_math11173698 crossref_primary_10_1140_epje_s10189_023_00302_w crossref_primary_10_1073_pnas_2304669120 crossref_primary_10_1515_jnet_2021_0008 crossref_primary_10_1016_j_compfluid_2024_106443 crossref_primary_10_3390_jmse13091761 crossref_primary_10_3390_fluids9080191 crossref_primary_10_1016_j_ijmultiphaseflow_2025_105201 crossref_primary_10_1016_j_ast_2022_107931 crossref_primary_10_1016_j_neucom_2020_09_006 crossref_primary_10_1007_s11071_021_07118_3 crossref_primary_10_1109_TPAMI_2025_3581941 crossref_primary_10_1017_jfm_2024_272 crossref_primary_10_3390_en13225987 crossref_primary_10_1007_s11804_022_00278_7 crossref_primary_10_1016_j_compfluid_2019_104258 crossref_primary_10_1007_s10494_020_00124_2 crossref_primary_10_1016_j_ijheatfluidflow_2025_109970 crossref_primary_10_1016_j_jcp_2025_114277 crossref_primary_10_2166_hydro_2023_035 crossref_primary_10_1088_1742_6596_1715_1_012012 crossref_primary_10_1016_j_oceaneng_2023_115313 crossref_primary_10_1016_j_compfluid_2024_106215 crossref_primary_10_3390_aerospace9020096 crossref_primary_10_1016_j_ijhydene_2021_03_074 crossref_primary_10_1007_s10409_021_01147_2 crossref_primary_10_1038_s41598_022_09938_8 crossref_primary_10_1063_5_0084999 crossref_primary_10_3390_jmse11020239 crossref_primary_10_1016_j_geoen_2024_212938 crossref_primary_10_1016_j_ijheatfluidflow_2022_109047 crossref_primary_10_1063_5_0066077 crossref_primary_10_1016_j_energy_2022_125907 crossref_primary_10_1017_jfm_2018_147 crossref_primary_10_1146_annurev_fluid_010719_060214 crossref_primary_10_1177_03019233241278460 crossref_primary_10_1016_j_ijheatmasstransfer_2019_118931 crossref_primary_10_1063_5_0289270 crossref_primary_10_1016_j_fluid_2021_113012 crossref_primary_10_1073_pnas_2101784118 crossref_primary_10_1007_s10494_025_00643_w crossref_primary_10_1017_jfm_2020_820 crossref_primary_10_1017_jfm_2023_679 crossref_primary_10_1016_j_ast_2020_106452 crossref_primary_10_1016_j_jcp_2021_110153 crossref_primary_10_1016_j_ijheatfluidflow_2022_109072 crossref_primary_10_1186_s42774_022_00121_1 crossref_primary_10_3847_1538_4357_ad088c crossref_primary_10_1029_2018MS001472 crossref_primary_10_1016_j_ijheatfluidflow_2020_108615 crossref_primary_10_1080_00295450_2023_2185056 crossref_primary_10_1007_s00205_023_01849_w crossref_primary_10_1016_j_jocs_2020_101237 crossref_primary_10_1109_ACCESS_2021_3139622 crossref_primary_10_1016_j_jcp_2018_10_045 crossref_primary_10_1137_23M1615425 crossref_primary_10_1088_1873_7005_ac4f2d crossref_primary_10_1080_14685248_2024_2412602 crossref_primary_10_1016_j_compfluid_2024_106246 crossref_primary_10_1017_jfm_2023_446 crossref_primary_10_1016_j_engappai_2025_111788 crossref_primary_10_1017_jfm_2021_1045 crossref_primary_10_1016_j_proci_2025_105796 crossref_primary_10_1017_jfm_2021_812 crossref_primary_10_1063_5_0132433 crossref_primary_10_1103_PhysRevFluids_10_014601 crossref_primary_10_1103_PhysRevFluids_10_014603 crossref_primary_10_1063_5_0010917 crossref_primary_10_2514_1_J063251 crossref_primary_10_1109_TR_2022_3196272 crossref_primary_10_1073_pnas_2213638120 crossref_primary_10_1109_TIE_2022_3140489 crossref_primary_10_3390_biomimetics9020072 crossref_primary_10_1016_j_compfluid_2024_106259 crossref_primary_10_2514_1_J063263 crossref_primary_10_1016_j_cja_2021_07_027 crossref_primary_10_1016_j_jcp_2021_110781 crossref_primary_10_1016_j_jcp_2024_113638 crossref_primary_10_1061__ASCE_PS_1949_1204_0000696 crossref_primary_10_1177_09544062211042920 crossref_primary_10_1016_j_knosys_2024_111641 crossref_primary_10_1016_j_nucengdes_2022_112005 crossref_primary_10_1016_j_oceaneng_2019_106799 crossref_primary_10_1007_s00162_022_00609_y crossref_primary_10_1016_j_icheatmasstransfer_2021_105626 crossref_primary_10_1063_5_0062377 crossref_primary_10_1080_14685248_2020_1832230 crossref_primary_10_1088_1361_6463_ada167 crossref_primary_10_1111_cgf_13620 crossref_primary_10_1007_s00162_020_00528_w crossref_primary_10_1016_j_euromechflu_2025_204372 crossref_primary_10_1016_j_physrep_2021_07_001 crossref_primary_10_1016_j_ijthermalsci_2018_09_002 crossref_primary_10_1016_j_jcp_2020_109491 crossref_primary_10_1109_TNNLS_2023_3338619 crossref_primary_10_1007_s42241_019_0089_y crossref_primary_10_1016_j_compfluid_2024_106270 crossref_primary_10_1007_s10494_020_00170_w crossref_primary_10_1016_j_camwa_2023_06_038 crossref_primary_10_1016_j_energy_2020_119005 crossref_primary_10_1016_j_physd_2022_133454 crossref_primary_10_1029_2020GL087005 crossref_primary_10_1007_s12206_021_0342_5 crossref_primary_10_1103_PhysRevFluids_6_050502 crossref_primary_10_1103_PhysRevFluids_6_050501 crossref_primary_10_1080_17455030_2023_2265506 crossref_primary_10_1080_00295639_2022_2107864 crossref_primary_10_1103_PhysRevFluids_6_050504 crossref_primary_10_1016_j_ast_2024_109155 crossref_primary_10_1007_s42401_019_00026_w crossref_primary_10_1016_j_compfluid_2021_105113 crossref_primary_10_1016_j_anucene_2022_109367 crossref_primary_10_1115_1_4068396 crossref_primary_10_1063_5_0136830 crossref_primary_10_1063_5_0121344 crossref_primary_10_1016_j_cma_2021_114424 crossref_primary_10_3390_math9161843 crossref_primary_10_1073_pnas_1814058116 crossref_primary_10_1016_j_paerosci_2018_10_001 crossref_primary_10_1088_1742_6596_1037_2_022009 crossref_primary_10_1016_j_cherd_2022_12_035 crossref_primary_10_1103_PhysRevE_103_053107 crossref_primary_10_2514_1_J063222 crossref_primary_10_1016_j_buildenv_2025_113535 crossref_primary_10_1103_qqxr_ly55 crossref_primary_10_1016_j_icheatmasstransfer_2018_04_005 crossref_primary_10_1007_s11814_021_0979_x crossref_primary_10_1038_s41598_021_90734_1 crossref_primary_10_1016_j_buildenv_2024_112103 crossref_primary_10_1111_cgf_13619 crossref_primary_10_1103_PhysRevFluids_10_024603 crossref_primary_10_1002_nme_7310 crossref_primary_10_1103_PhysRevFluids_10_024605 crossref_primary_10_1016_j_compfluid_2022_105611 crossref_primary_10_1016_j_jcp_2024_112982 crossref_primary_10_1017_jfm_2025_10332 crossref_primary_10_1016_j_cej_2022_138036 crossref_primary_10_3390_w13040423 crossref_primary_10_1007_s00521_020_05461_x crossref_primary_10_1016_j_nucengdes_2019_04_023 crossref_primary_10_1016_j_camwa_2020_08_012 crossref_primary_10_1063_5_0260447 crossref_primary_10_1002_ceat_202200564 crossref_primary_10_1017_jfm_2025_209 crossref_primary_10_1007_s12650_024_00974_2 crossref_primary_10_1007_s42979_021_00867_3 crossref_primary_10_1016_j_euromechflu_2025_204333 crossref_primary_10_1016_j_compfluid_2022_105620 crossref_primary_10_1016_j_cja_2023_09_003 crossref_primary_10_1007_s10494_025_00668_1 crossref_primary_10_1029_2023MS003658 crossref_primary_10_1029_2020GL088376 crossref_primary_10_1016_j_renene_2021_11_097 crossref_primary_10_1007_s40997_023_00615_3 crossref_primary_10_1007_s12206_022_1223_2 crossref_primary_10_1016_j_jcp_2021_110567 crossref_primary_10_1016_j_partic_2023_12_012 crossref_primary_10_1038_s41598_021_92278_w crossref_primary_10_1007_s42405_023_00598_0 crossref_primary_10_3390_su141911996 crossref_primary_10_1109_TGRS_2023_3281784 crossref_primary_10_1145_3514228 crossref_primary_10_1155_2022_9873112 crossref_primary_10_2514_1_J063407 crossref_primary_10_1002_nme_5583 crossref_primary_10_1016_j_cma_2022_115396 crossref_primary_10_1063_5_0253703 crossref_primary_10_1016_j_cma_2023_116543 crossref_primary_10_3389_fhpcp_2024_1444337 crossref_primary_10_3390_pr11030890 crossref_primary_10_2514_1_J062572 crossref_primary_10_1017_jfm_2019_700 crossref_primary_10_2514_1_J064745 crossref_primary_10_1016_j_cma_2020_113401 crossref_primary_10_1016_j_physd_2022_133630 crossref_primary_10_1038_s42003_020_01638_1 crossref_primary_10_1016_j_jcp_2025_113995 crossref_primary_10_1109_JAS_2024_124335 crossref_primary_10_1016_j_ress_2025_111353 crossref_primary_10_1038_s41597_021_01034_2 crossref_primary_10_1016_j_compfluid_2022_105651 crossref_primary_10_1073_pnas_1909854116 crossref_primary_10_1016_j_oceaneng_2019_106712 crossref_primary_10_1016_j_paerosci_2025_101130 crossref_primary_10_1051_epjconf_202124703013 crossref_primary_10_1016_j_jcp_2022_111090 crossref_primary_10_1016_j_actaastro_2024_01_022 crossref_primary_10_1186_s42774_021_00085_8 crossref_primary_10_1016_j_jcp_2020_109413 crossref_primary_10_1016_j_apenergy_2024_124703 crossref_primary_10_1155_2020_8888811 crossref_primary_10_1016_j_neunet_2023_03_014 crossref_primary_10_1016_j_jcp_2022_111081 crossref_primary_10_1063_5_0220444 crossref_primary_10_1016_j_nexres_2025_100618 crossref_primary_10_2514_1_J060131 crossref_primary_10_1016_j_jcp_2019_109209 crossref_primary_10_1016_j_jppr_2024_02_002 crossref_primary_10_1146_annurev_chembioeng_060817_084025 crossref_primary_10_1016_j_jcp_2021_110922 crossref_primary_10_1016_j_ultsonch_2025_107298 crossref_primary_10_1016_j_euromechflu_2025_204307 crossref_primary_10_2514_1_J058291 crossref_primary_10_1016_j_cma_2021_113927 crossref_primary_10_1080_14685248_2021_1999459 crossref_primary_10_1016_j_jcp_2023_112243 crossref_primary_10_1016_j_camwa_2023_01_002 crossref_primary_10_1016_j_compfluid_2023_105993 crossref_primary_10_1016_j_jcis_2021_11_195 crossref_primary_10_1007_s10596_020_09963_4 crossref_primary_10_1007_s10409_021_01150_7 crossref_primary_10_1016_j_jcp_2021_110733 crossref_primary_10_1016_j_camwa_2025_07_037 crossref_primary_10_1029_2022MS003105 crossref_primary_10_1007_s10444_018_9590_z crossref_primary_10_1007_s00162_021_00580_0 crossref_primary_10_1016_j_paerosci_2021_100725 crossref_primary_10_1016_j_ast_2023_108632 crossref_primary_10_1017_jfm_2021_53 crossref_primary_10_1007_s00521_021_06633_z crossref_primary_10_1051_e3sconf_202345902005 crossref_primary_10_1063_5_0207453 crossref_primary_10_1016_j_engappai_2024_108981 crossref_primary_10_1016_j_compstruc_2025_107839 crossref_primary_10_3390_w15030472 crossref_primary_10_1109_TASC_2024_3420184 crossref_primary_10_1007_s00162_025_00737_1 crossref_primary_10_1017_jfm_2021_398 crossref_primary_10_3389_fphy_2024_1452876 crossref_primary_10_1007_s10409_021_01119_6 crossref_primary_10_1017_jfm_2022_1020 crossref_primary_10_2514_1_J058486 crossref_primary_10_1109_JTEHM_2018_2886021 crossref_primary_10_1016_j_combustflame_2021_111486 crossref_primary_10_1016_j_jcp_2021_110717 crossref_primary_10_1063_5_0276641 crossref_primary_10_1016_j_oceaneng_2022_111436 crossref_primary_10_3389_fenrg_2023_1163043 crossref_primary_10_1002_ceat_202300040 crossref_primary_10_1007_s00162_019_00485_z crossref_primary_10_1140_epje_s10189_023_00267_w crossref_primary_10_1016_j_jcp_2023_112016 crossref_primary_10_1145_3768158 crossref_primary_10_1016_j_cma_2025_117810 crossref_primary_10_1016_j_combustflame_2025_114241 crossref_primary_10_1016_j_jcp_2023_112272 crossref_primary_10_1016_j_neunet_2023_04_017 crossref_primary_10_1063_5_0251597 crossref_primary_10_1063_5_0273361 crossref_primary_10_1109_ACCESS_2020_2979794 crossref_primary_10_1016_j_ces_2021_116886 crossref_primary_10_1016_j_oceaneng_2021_109058 crossref_primary_10_1016_j_cma_2025_117804 crossref_primary_10_1109_TAES_2021_3056086 crossref_primary_10_3390_fluids8070212 crossref_primary_10_1016_j_engappai_2023_106127 crossref_primary_10_1016_j_ast_2023_108542 crossref_primary_10_1016_j_anucene_2024_110679 crossref_primary_10_1007_s11831_024_10145_z crossref_primary_10_1016_j_arcontrol_2021_03_009 crossref_primary_10_1063_5_0077050 crossref_primary_10_1016_j_ijheatmasstransfer_2024_126150 crossref_primary_10_2514_1_J062711 crossref_primary_10_1038_s43588_022_00264_7 crossref_primary_10_1063_5_0265759 crossref_primary_10_1029_2022MS003424 crossref_primary_10_3390_en14051465 crossref_primary_10_3847_1538_4357_ad1c55 crossref_primary_10_1017_jfm_2018_872 crossref_primary_10_2514_1_J058462 crossref_primary_10_1016_j_apenergy_2021_116641 crossref_primary_10_1146_annurev_fluid_121021_031431 crossref_primary_10_1063_1_5067313 crossref_primary_10_1002_fld_5125 crossref_primary_10_1017_jfm_2021_148 crossref_primary_10_1287_moor_2020_1118 crossref_primary_10_1016_j_taml_2021_100244 crossref_primary_10_1017_jfm_2017_823 crossref_primary_10_1016_j_jcp_2020_109811 crossref_primary_10_1016_j_neunet_2025_107455 crossref_primary_10_1007_s00162_023_00663_0 crossref_primary_10_1016_j_biosystemseng_2019_11_006 crossref_primary_10_1016_j_jocs_2022_101906 crossref_primary_10_1002_fld_5375 crossref_primary_10_1088_2632_2153_ad7d60 crossref_primary_10_1088_1361_6501_ad3fd3 crossref_primary_10_1007_s00162_018_0480_2 crossref_primary_10_2514_1_J057108 crossref_primary_10_1016_j_compfluid_2020_104645 crossref_primary_10_3390_computation8010015 crossref_primary_10_1063_5_0134198 crossref_primary_10_1016_j_eswa_2022_117038 crossref_primary_10_1134_S1995080224605654 crossref_primary_10_1177_09544062211028264 crossref_primary_10_1007_s11071_019_04915_9 crossref_primary_10_1016_j_envsoft_2024_106182 crossref_primary_10_1016_j_ijheatmasstransfer_2022_123115 crossref_primary_10_1016_j_powtec_2022_117303 crossref_primary_10_1016_j_ijheatmasstransfer_2024_126149 crossref_primary_10_1088_1572_9494_ac60f9 crossref_primary_10_1016_j_cpc_2025_109754 crossref_primary_10_1016_j_engappai_2024_109922 crossref_primary_10_3390_fluids7030111 crossref_primary_10_1134_S0021894423030094 crossref_primary_10_1016_j_ijheatfluidflow_2023_109204 crossref_primary_10_2514_1_J059302 crossref_primary_10_1155_er_3241787 crossref_primary_10_1029_2021MS002847 crossref_primary_10_1016_j_ijheatmasstransfer_2025_127539 crossref_primary_10_1080_00295450_2023_2178251 crossref_primary_10_1111_mice_13000 crossref_primary_10_1016_j_cma_2025_117782 crossref_primary_10_1017_jfm_2019_238 crossref_primary_10_1017_jfm_2017_637 crossref_primary_10_1017_jfm_2023_179 crossref_primary_10_1016_j_cpc_2024_109220 crossref_primary_10_1063_5_0056549 crossref_primary_10_2514_1_J060976 crossref_primary_10_1016_j_ymssp_2024_111297 crossref_primary_10_1016_j_ast_2023_108354 crossref_primary_10_1016_j_oceaneng_2023_114743 crossref_primary_10_1016_j_ast_2022_108054 crossref_primary_10_1109_TKDE_2021_3079836 crossref_primary_10_1016_j_jcp_2020_109859 crossref_primary_10_1016_j_buildenv_2020_106671 crossref_primary_10_3390_math12081188 crossref_primary_10_1016_j_cja_2023_06_031 crossref_primary_10_1007_s10494_023_00506_2 crossref_primary_10_1016_j_jhydrol_2023_130350 crossref_primary_10_3390_en16041755 crossref_primary_10_1063_5_0278635 crossref_primary_10_1016_j_energy_2023_129405 crossref_primary_10_1109_OJCOMS_2025_3560319 crossref_primary_10_1016_j_jcp_2024_113157 crossref_primary_10_1007_s10494_019_00011_5 crossref_primary_10_3389_fonc_2022_850731 crossref_primary_10_1017_jfm_2016_803 crossref_primary_10_2514_1_J058638 crossref_primary_10_1145_3611383 crossref_primary_10_1016_j_compfluid_2024_106506 crossref_primary_10_1088_1742_6596_1522_1_012022 crossref_primary_10_1016_j_combustflame_2021_111758 crossref_primary_10_1016_j_compchemeng_2022_108111 crossref_primary_10_3390_fluids10080193 crossref_primary_10_1017_jfm_2023_154 crossref_primary_10_1063_5_0056569 crossref_primary_10_1016_j_cma_2024_117478 crossref_primary_10_1186_s40323_025_00284_8 crossref_primary_10_1063_5_0253128 crossref_primary_10_3390_jmse9040376 crossref_primary_10_3390_machines13060496 crossref_primary_10_1017_jfm_2019_205 crossref_primary_10_2514_1_J059741 crossref_primary_10_3390_en13010258 crossref_primary_10_1016_j_jcp_2022_111037 crossref_primary_10_1016_j_compfluid_2019_03_022 crossref_primary_10_1007_s10494_024_00623_6 crossref_primary_10_3390_aerospace12030238 crossref_primary_10_1016_j_finel_2022_103895 crossref_primary_10_1103_PhysRevFluids_10_034606 crossref_primary_10_1016_j_xphs_2024_09_015 crossref_primary_10_2514_1_J055595 crossref_primary_10_1063_5_0280752 crossref_primary_10_1137_18M1192184 crossref_primary_10_1016_j_buildenv_2021_108315 crossref_primary_10_1016_j_cma_2024_116807 crossref_primary_10_1016_j_cryogenics_2025_104142 crossref_primary_10_1017_jfm_2020_725 crossref_primary_10_1063_5_0282938 crossref_primary_10_1016_j_ast_2024_108896 crossref_primary_10_1016_j_compfluid_2020_104473 crossref_primary_10_1007_s10915_023_02401_4 crossref_primary_10_1016_j_compfluid_2019_104318 crossref_primary_10_1016_j_compfluid_2019_104319 crossref_primary_10_1016_j_oceaneng_2023_113693 crossref_primary_10_1103_8t52_mtb9 crossref_primary_10_1007_s00366_024_02057_0 crossref_primary_10_1016_j_taml_2020_01_006 crossref_primary_10_2514_1_J059721 crossref_primary_10_1088_1742_6596_2099_1_012020 crossref_primary_10_3390_en15228719 crossref_primary_10_1029_2021WR030163 crossref_primary_10_1007_s10494_019_00013_3 crossref_primary_10_1016_j_ast_2022_108089 crossref_primary_10_5194_npg_27_373_2020 crossref_primary_10_1016_j_ijft_2025_101073 crossref_primary_10_2514_1_J060919 crossref_primary_10_1073_pnas_2305765120 crossref_primary_10_1016_j_ijheatfluidflow_2021_108822 crossref_primary_10_1016_j_taml_2024_100496 crossref_primary_10_1016_j_jocs_2022_101741 crossref_primary_10_1038_s43588_024_00643_2 crossref_primary_10_1017_jfm_2019_254 crossref_primary_10_1088_1742_6596_2151_1_012011 crossref_primary_10_1016_j_egyai_2025_100567 crossref_primary_10_1088_2632_2153_ad7191 crossref_primary_10_1016_j_compfluid_2020_104497 crossref_primary_10_1146_annurev_fluid_010719_060317 crossref_primary_10_1016_j_jcp_2019_108910 crossref_primary_10_1016_j_neucom_2020_01_088 crossref_primary_10_3390_en14040984 crossref_primary_10_1007_s10409_021_09057_z crossref_primary_10_1103_PhysRevFluids_7_024305 crossref_primary_10_1007_s10494_020_00234_x crossref_primary_10_1016_j_compfluid_2021_104950 crossref_primary_10_1063_5_0216747 crossref_primary_10_1016_j_combustflame_2021_111973 crossref_primary_10_1016_j_ijheatfluidflow_2019_04_014 crossref_primary_10_5802_crmeca_240 crossref_primary_10_1007_s40997_023_00632_2 crossref_primary_10_1137_21M1401243 crossref_primary_10_3390_app14188382 crossref_primary_10_1109_ACCESS_2020_2970143 crossref_primary_10_1016_j_ijheatfluidflow_2019_108454 crossref_primary_10_1007_s11071_025_11773_1 crossref_primary_10_1103_PhysRevFluids_6_094607 crossref_primary_10_3390_fluids7050154 crossref_primary_10_1016_j_jcp_2019_05_024 crossref_primary_10_1007_s42241_018_0156_9 crossref_primary_10_1017_aer_2020_83 crossref_primary_10_1186_s42774_024_00197_x crossref_primary_10_1016_j_ijhydene_2023_04_311 crossref_primary_10_2514_1_J056640 crossref_primary_10_1007_s10462_024_10874_4 crossref_primary_10_1080_19942060_2024_2374316 crossref_primary_10_1016_j_jcp_2021_110296 crossref_primary_10_1016_j_pnucene_2022_104339 crossref_primary_10_1016_j_compfluid_2023_106054 crossref_primary_10_1016_j_compfluid_2020_104431 crossref_primary_10_1016_j_ast_2023_108198 crossref_primary_10_1017_jfm_2023_590 crossref_primary_10_1017_jfm_2025_91 crossref_primary_10_1155_2020_8855314 crossref_primary_10_1063_5_0058346 crossref_primary_10_1080_19942060_2023_2237611 crossref_primary_10_1016_j_nucengdes_2024_113721 crossref_primary_10_1155_2022_9034773 crossref_primary_10_2166_hydro_2024_373 crossref_primary_10_1016_j_ijheatfluidflow_2021_108816 crossref_primary_10_1108_HFF_12_2023_0726 crossref_primary_10_1016_j_jcp_2025_114388 crossref_primary_10_1088_1674_1056_ac9cb9 crossref_primary_10_1016_j_ijheatmasstransfer_2018_12_070 crossref_primary_10_1007_s11082_023_06107_7 crossref_primary_10_1140_epje_s10189_023_00314_6 crossref_primary_10_1016_j_ijheatmasstransfer_2025_126893 crossref_primary_10_1017_jfm_2025_10618 crossref_primary_10_2514_1_J065567 crossref_primary_10_1007_s10494_019_00028_w crossref_primary_10_1016_j_jcp_2022_111205 crossref_primary_10_1016_j_cagd_2022_102087 crossref_primary_10_1017_jfm_2020_948 crossref_primary_10_1029_2018MS001351 crossref_primary_10_1016_j_nucengdes_2022_112059 crossref_primary_10_3390_vehicles6030063 crossref_primary_10_1109_JSEN_2025_3538625 crossref_primary_10_1007_s00707_021_02951_4 crossref_primary_10_1016_j_jcp_2025_114125 crossref_primary_10_1016_j_ijheatfluidflow_2023_109242 crossref_primary_10_1080_14685248_2019_1706742 crossref_primary_10_1007_s10115_023_01864_z crossref_primary_10_3389_fphy_2024_1347657 crossref_primary_10_1016_j_asoc_2025_113394 crossref_primary_10_1186_s42774_021_00088_5 crossref_primary_10_1038_s41598_022_16463_1 crossref_primary_10_1142_S0218202525500125 crossref_primary_10_1016_j_cma_2020_113375 crossref_primary_10_1016_j_ijheatfluidflow_2024_109377 crossref_primary_10_3390_aerospace10070599 crossref_primary_10_1002_gamm_202100002 crossref_primary_10_1017_jfm_2022_738 crossref_primary_10_3390_app12136718 crossref_primary_10_3934_fods_2021013 crossref_primary_10_1016_j_taml_2024_100503 crossref_primary_10_1016_j_jcp_2023_112173 crossref_primary_10_1186_s40323_020_00153_6 crossref_primary_10_1007_s10494_025_00667_2 crossref_primary_10_1063_5_0213412 crossref_primary_10_1017_jfm_2022_744 crossref_primary_10_1063_5_0236511 crossref_primary_10_1016_j_ast_2025_110750 crossref_primary_10_3390_app12105194 crossref_primary_10_1017_flo_2024_15 crossref_primary_10_1016_j_ymssp_2021_108709 crossref_primary_10_1016_j_ast_2024_109014 crossref_primary_10_1016_j_acha_2024_101717 crossref_primary_10_1063_5_0190452 crossref_primary_10_1002_hyp_14565 crossref_primary_10_1016_j_ijheatfluidflow_2022_108983 crossref_primary_10_1063_5_0132326 crossref_primary_10_1063_5_0211680 crossref_primary_10_1016_j_ces_2021_117268 crossref_primary_10_1109_ACCESS_2020_2976199 crossref_primary_10_1007_s00397_023_01412_0 crossref_primary_10_3390_math9161939 crossref_primary_10_1016_j_compfluid_2022_105707 crossref_primary_10_3390_math12101417 crossref_primary_10_1016_j_applthermaleng_2025_127412 crossref_primary_10_1016_j_ijheatfluidflow_2024_109348 crossref_primary_10_1007_s10494_017_9807_0 crossref_primary_10_1103_PhysRevFluids_6_094401 crossref_primary_10_1016_j_apenergy_2019_114025 crossref_primary_10_1016_j_neunet_2024_106401 crossref_primary_10_1016_j_oceaneng_2024_116717 crossref_primary_10_12677_AAM_2022_119670 crossref_primary_10_1016_j_oceaneng_2022_110650 crossref_primary_10_1145_3689037 crossref_primary_10_1007_s10462_024_10867_3 crossref_primary_10_1017_jfm_2020_1028 crossref_primary_10_1016_j_cageo_2021_104833 crossref_primary_10_1038_s41598_020_61450_z crossref_primary_10_1038_s42256_020_00272_0 crossref_primary_10_1063_5_0259567 crossref_primary_10_2514_1_J064416 crossref_primary_10_1631_FITEE_2000435 crossref_primary_10_1109_ACCESS_2019_2960451 crossref_primary_10_1007_s10494_024_00539_1 crossref_primary_10_1038_s41598_023_29525_9 crossref_primary_10_1061_JAEEEZ_ASENG_6214 crossref_primary_10_1016_j_renene_2022_10_013 crossref_primary_10_1016_j_ast_2021_106576 crossref_primary_10_1016_j_paerosci_2019_100554 crossref_primary_10_1007_s00466_023_02434_4 crossref_primary_10_1017_jfm_2025_10488 crossref_primary_10_1103_PhysRevE_111_055302 crossref_primary_10_1016_j_supflu_2023_106051 crossref_primary_10_1103_PhysRevFluids_8_054602 crossref_primary_10_1088_1674_1056_ac5e98 crossref_primary_10_1115_1_4069140 crossref_primary_10_2514_1_J064422 crossref_primary_10_1080_14685248_2024_2361738 crossref_primary_10_1016_j_ces_2019_115357 crossref_primary_10_1016_j_jcp_2024_112869 crossref_primary_10_3390_en12142716 crossref_primary_10_1016_j_compfluid_2021_105213 crossref_primary_10_1007_s11831_025_10378_6 crossref_primary_10_1103_PhysRevLett_126_098302 crossref_primary_10_3390_app13126891 crossref_primary_10_1016_j_apor_2023_103587 crossref_primary_10_1016_j_asoc_2023_110013 crossref_primary_10_1016_j_cnsns_2019_04_025 crossref_primary_10_1109_ACCESS_2025_3602021 crossref_primary_10_1109_ACCESS_2018_2888733 crossref_primary_10_1016_j_taml_2025_100623 crossref_primary_10_1016_j_pnucene_2024_105097 crossref_primary_10_2514_1_J061375 crossref_primary_10_1029_2020MS002301 crossref_primary_10_1109_ACCESS_2020_2993562 crossref_primary_10_1029_2022MS003034 crossref_primary_10_1017_dce_2022_37 crossref_primary_10_1016_j_compfluid_2023_105835 crossref_primary_10_1038_s41598_019_47747_8 crossref_primary_10_1146_annurev_fluid_031221_105530 crossref_primary_10_1016_j_physd_2020_132409 crossref_primary_10_1016_j_taml_2022_100359 crossref_primary_10_1063_5_0212949 crossref_primary_10_1016_j_energy_2022_124440 crossref_primary_10_2514_1_J064610 crossref_primary_10_1088_2632_2153_add8de crossref_primary_10_1038_s41563_020_00913_0 crossref_primary_10_1016_j_icheatmasstransfer_2022_105890 crossref_primary_10_1016_j_ijheatmasstransfer_2021_120976 crossref_primary_10_1088_1873_7005_ade8a2 crossref_primary_10_1103_PhysRevFluids_8_064603 crossref_primary_10_1016_j_compfluid_2021_105266 crossref_primary_10_1016_j_engappai_2024_108896 crossref_primary_10_1016_j_ast_2022_107328 crossref_primary_10_1017_jfm_2019_822 crossref_primary_10_2514_1_J062203 crossref_primary_10_1007_s10409_022_09001_w crossref_primary_10_1007_s10973_021_10931_y crossref_primary_10_1016_j_cma_2024_117441 crossref_primary_10_1088_2632_2153_acb19c crossref_primary_10_1017_jfm_2019_814 crossref_primary_10_3390_fluids6020072 crossref_primary_10_3390_ijtpp7020016 crossref_primary_10_1016_j_jcp_2019_01_021 crossref_primary_10_1063_5_0239178 crossref_primary_10_4271_2021_01_0407 crossref_primary_10_1016_j_applthermaleng_2022_118449 crossref_primary_10_1016_j_jcp_2024_113341 crossref_primary_10_1016_j_combustflame_2019_10_031 crossref_primary_10_1063_5_0252753 crossref_primary_10_1063_5_0127808 crossref_primary_10_1186_s40323_021_00213_5 crossref_primary_10_1063_1_5138681 crossref_primary_10_1002_aic_17715 crossref_primary_10_2514_1_J062664 crossref_primary_10_1063_5_0142198 crossref_primary_10_1080_14685248_2022_2060508 crossref_primary_10_1016_j_powtec_2018_11_092 crossref_primary_10_1002_we_70030 crossref_primary_10_1007_s00348_023_03736_2 crossref_primary_10_1016_j_compfluid_2022_105354 crossref_primary_10_1016_j_apor_2025_104661 crossref_primary_10_1007_s00162_020_00518_y crossref_primary_10_1186_s13636_024_00376_0 crossref_primary_10_1073_pnas_1900358116 crossref_primary_10_1155_2021_5575722 crossref_primary_10_1016_j_ces_2020_116235 crossref_primary_10_2514_1_J059474 crossref_primary_10_3390_fluids7020056 crossref_primary_10_1017_aer_2024_123 crossref_primary_10_1051_meca_2024023 crossref_primary_10_3390_math11244926 crossref_primary_10_1016_j_procir_2024_08_302 crossref_primary_10_1016_j_taml_2021_100280 crossref_primary_10_1016_j_taml_2022_100381 crossref_primary_10_1016_j_compfluid_2023_105864 crossref_primary_10_3389_fmars_2021_672477 crossref_primary_10_1016_j_taml_2022_100389 crossref_primary_10_1016_j_taml_2022_100387 crossref_primary_10_1017_jfm_2019_867 crossref_primary_10_1007_s00707_025_04325_6 crossref_primary_10_1016_j_jcp_2018_08_016 crossref_primary_10_1016_j_actaastro_2022_04_007 crossref_primary_10_1016_j_compfluid_2021_105298 crossref_primary_10_3390_su162411039 crossref_primary_10_3389_fsufs_2024_1363744 crossref_primary_10_1007_s11630_024_2035_8 crossref_primary_10_1016_j_engappai_2023_107483 crossref_primary_10_1080_10618562_2022_2113520 crossref_primary_10_1016_j_ast_2025_110166 crossref_primary_10_1016_j_jcp_2018_08_029 crossref_primary_10_1103_PhysRevResearch_7_013202 crossref_primary_10_1080_17455030_2023_2192818 crossref_primary_10_1016_j_oceaneng_2022_111791 crossref_primary_10_1063_5_0053590 crossref_primary_10_1016_j_compfluid_2023_105883 crossref_primary_10_1016_j_scs_2023_104881 crossref_primary_10_1063_5_0263211 crossref_primary_10_1007_s00162_020_00529_9 crossref_primary_10_2514_1_J062870 crossref_primary_10_1088_1674_4527_ac449d crossref_primary_10_3390_aerospace9100578 crossref_primary_10_3390_aerospace11070592 crossref_primary_10_1016_j_compfluid_2022_105592 crossref_primary_10_1007_s42241_020_0077_2 crossref_primary_10_1002_msd2_70031 crossref_primary_10_1109_ACCESS_2025_3580485 crossref_primary_10_3390_en16052343 crossref_primary_10_1177_09544100221097521 crossref_primary_10_1063_5_0122165 crossref_primary_10_1007_s11082_023_04715_x
Cites_doi	10.1016/j.jcp.2015.11.012 10.1016/0142-727X(95)00079-6 10.1017/S0022112093002034 10.1016/j.jcp.2016.05.003 10.1038/nature16961 10.1063/1.4915065 10.2514/6.2014-2085 10.1038/nature14539 10.2514/6.2015-1287 10.1017/jfm.2011.193 10.2514/6.2003-149 10.1063/1.4927765 10.1017/S0022112009992242 10.1006/jcph.2002.7146 10.1007/BF00251667 10.1017/S0022112075003382 10.1017/S0022112099007004 10.1109/MSP.2012.2205597 10.1016/j.ijheatfluidflow.2010.05.006 10.1115/1.4031698 10.2514/6.2015-2460 10.2514/6.2013-259 10.1063/1.869966
ContentType	Journal Article
Copyright	Cambridge University Press 2016. This is a work of the U.S. Government and is not subject to copyright protection in the United States.
Copyright_xml	– notice: Cambridge University Press 2016. This is a work of the U.S. Government and is not subject to copyright protection in the United States.
CorporateAuthor	Sandia National Lab. (SNL-CA), Livermore, CA (United States)
CorporateAuthor_xml	– name: Sandia National Lab. (SNL-CA), Livermore, CA (United States)
DBID	AAYXX CITATION 3V. 7TB 7U5 7UA 7XB 88I 8FD 8FE 8FG 8FK 8G5 ABJCF ABUWG AEUYN AFKRA ARAPS AZQEC BENPR BGLVJ BHPHI BKSAR C1K CCPQU DWQXO F1W FR3 GNUQQ GUQSH H8D H96 HCIFZ KR7 L.G L6V L7M M2O M2P M7S MBDVC P5Z P62 PCBAR PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U S0W OIOZB OTOTI
DOI	10.1017/jfm.2016.615
DatabaseName	CrossRef ProQuest Central (Corporate) Mechanical & Transportation Engineering Abstracts Solid State and Superconductivity Abstracts Water Resources Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Research Library (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest One Sustainability ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials - QC ProQuest Central Technology collection Natural Science Collection Earth, Atmospheric & Aquatic Science Collection Environmental Sciences and Pollution Management ProQuest One Community College ProQuest Central ASFA: Aquatic Sciences and Fisheries Abstracts Engineering Research Database ProQuest Central Student ProQuest Research Library Aerospace Database Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources SciTech Premium Collection Civil Engineering Abstracts Aquatic Science & Fisheries Abstracts (ASFA) Professional ProQuest Engineering Collection Advanced Technologies Database with Aerospace Research Library Science Database Engineering Database Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Earth, Atmospheric & Aquatic Science Database Proquest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic DELNET Engineering & Technology Collection OSTI.GOV - Hybrid OSTI.GOV
DatabaseTitle	CrossRef Research Library Prep ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials SciTech Premium Collection ProQuest Central China Water Resources Abstracts Environmental Sciences and Pollution Management ProQuest One Applied & Life Sciences ProQuest One Sustainability Natural Science Collection ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database ProQuest Technology Collection ProQuest One Academic UKI Edition Solid State and Superconductivity Abstracts Engineering Research Database ProQuest One Academic ProQuest One Academic (New) Aquatic Science & Fisheries Abstracts (ASFA) Professional Technology Collection Technology Research Database ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Central (Alumni Edition) ProQuest One Community College Research Library (Alumni Edition) ProQuest Central Earth, Atmospheric & Aquatic Science Collection Aerospace Database ProQuest Engineering Collection ProQuest Central Korea ProQuest Research Library Advanced Technologies Database with Aerospace Civil Engineering Abstracts ProQuest Central Basic ProQuest Science Journals ProQuest SciTech Collection Advanced Technologies & Aerospace Database Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources ASFA: Aquatic Sciences and Fisheries Abstracts ProQuest DELNET Engineering and Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni)
DatabaseTitleList	Research Library Prep CrossRef
Database_xml	– sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering Physics
DocumentTitleAlternate	J. Ling, A. Kurzawski and J. Templeton Turbulence modelling using deep neural networks
EISSN	1469-7645
EndPage	166
ExternalDocumentID	1333570 4321477043 10_1017_jfm_2016_615
GroupedDBID	-2P -DZ -E. -~6 -~X .DC .FH 09C 09E 0E1 0R~ 29K 3V. 4.4 5GY 5VS 74X 74Y 7~V 88I 8FE 8FG 8FH 8G5 8R4 8R5 AAAZR AABES AABWE AACJH AAGFV AAKTX AAMNQ AARAB AASVR AATMM AAUIS AAUKB ABBXD ABGDZ ABITZ ABJCF ABJNI ABKKG ABMWE ABQTM ABQWD ABROB ABTCQ ABUWG ABVKB ABXAU ABZCX ACBEA ACBMC ACDLN ACGFO ACGFS ACGOD ACIMK ACIWK ACUIJ ACYZP ACZBM ACZUX ACZWT ADCGK ADDNB ADFEC ADFRT ADKIL ADVJH AEBAK AEHGV AEMTW AENEX AENGE AEUYN AEYYC AFFUJ AFKQG AFKRA AFLOS AFLVW AFRAH AFUTZ AFZFC AGABE AGBYD AGJUD AGLWM AHQXX AHRGI AIDUJ AIGNW AIHIV AIOIP AISIE AJ7 AJCYY AJPFC AJQAS ALMA_UNASSIGNED_HOLDINGS ALVPG ALWZO AQJOH ARABE ARAPS ATUCA AUXHV AZQEC BBLKV BENPR BGHMG BGLVJ BHPHI BKSAR BLZWO BMAJL BPHCQ BQFHP C0O CBIIA CCPQU CCQAD CFAFE CHEAL CJCSC CS3 D-I DC4 DOHLZ DU5 DWQXO E.L EBS EJD F5P GNUQQ GUQSH HCIFZ HG- HST HZ~ I.6 I.7 IH6 IOEEP IS6 I~P J36 J38 J3A JHPGK JQKCU KCGVB KFECR L6V L98 LK5 LW7 M-V M2O M2P M7R M7S NIKVX O9- OYBOY P2P P62 PCBAR PQQKQ PROAC PTHSS PYCCK Q2X RAMDC RCA RNS ROL RR0 S0W S6- S6U SAAAG SC5 T9M TAE TN5 UT1 WFFJZ WH7 WQ3 WXU WYP ZE2 ZMEZD ZYDXJ ~02 AAYXX ABUFD ABXHF ADMLS AFFHD AKMAY CITATION PHGZM PHGZT PQGLB 7TB 7U5 7UA 7XB 8FD 8FK C1K F1W FR3 H8D H96 KR7 L.G L7M MBDVC PKEHL PQEST PQUKI PRINS Q9U AAEED ABBJB ABTRL ACCHT ACQFJ ACREK ACUYZ ACWGA ADGEJ ADOCW AFKSM AGOOT AIAFM OIOZB OTOTI WXY ZJOSE
ID	FETCH-LOGICAL-c367t-40849f2d0bfa62da1f3c92e0c7a768e68c5f0c0a316a86c12b5282d5ed56bc223
IEDL.DBID	BENPR
ISICitedReferencesCount	1176
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000386452000009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0022-1120
IngestDate	Mon Jul 03 03:57:20 EDT 2023 Sat Aug 16 05:41:12 EDT 2025 Tue Nov 18 22:18:18 EST 2025 Sat Nov 29 04:24:12 EST 2025 Tue Jan 21 06:22:06 EST 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Keywords	turbulent flows turbulence modelling turbulence theory
Language	English
License	https://www.cambridge.org/core/terms
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c367t-40849f2d0bfa62da1f3c92e0c7a768e68c5f0c0a316a86c12b5282d5ed56bc223
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 AC04-94AL85000 USDOE National Nuclear Security Administration (NNSA) SAND-2016-7345J
OpenAccessLink	https://www.osti.gov/servlets/purl/1333570
PQID	1884540899
PQPubID	34769
PageCount	12
ParticipantIDs	osti_scitechconnect_1333570 proquest_journals_1884540899 crossref_citationtrail_10_1017_jfm_2016_615 crossref_primary_10_1017_jfm_2016_615 cambridge_journals_10_1017_jfm_2016_615
PublicationCentury	2000
PublicationDate	2016-11-25
PublicationDateYYYYMMDD	2016-11-25
PublicationDate_xml	– month: 11 year: 2016 text: 2016-11-25 day: 25
PublicationDecade	2010
PublicationPlace	Cambridge, UK
PublicationPlace_xml	– name: Cambridge, UK – name: Cambridge – name: United States
PublicationTitle	Journal of fluid mechanics
PublicationTitleAlternate	J. Fluid Mech
PublicationYear	2016
Publisher	Cambridge University Press
Publisher_xml	– name: Cambridge University Press
References	2010; 31 2016c; 138 2002; 182 1996; 17 2015; 27 2015; 521 2010; 644 2016; 305 2000; 403 2016; 529 2013; 30 2007; 8 1999; 11 2012; 29 2012; 25 1975; 72 1965; 18 2016a; 318 1993; 254 2011; 681 S0022112016006157_r3 S0022112016006157_r25 S0022112016006157_r2 S0022112016006157_r27 S0022112016006157_r5 S0022112016006157_r4 S0022112016006157_r26 S0022112016006157_r28 S0022112016006157_r21 S0022112016006157_r20 S0022112016006157_r23 S0022112016006157_r22 Banerjee (S0022112016006157_r1) 2007; 8 Ling (S0022112016006157_r10) 2016b Karpathy (S0022112016006157_r7) 2014 S0022112016006157_r6 S0022112016006157_r9 S0022112016006157_r8 S0022112016006157_r14 S0022112016006157_r16 S0022112016006157_r15 S0022112016006157_r18 S0022112016006157_r17 S0022112016006157_r19 Ling (S0022112016006157_r11) 2016c; 138 Snoek (S0022112016006157_r24) 2012; 25 S0022112016006157_r12 Maas (S0022112016006157_r13) 2013; 30
References_xml	– volume: 521 start-page: 436 year: 2015 end-page: 444 article-title: Deep learning publication-title: Nature – volume: 27 year: 2015 article-title: Flow topologies and turbulence scales in a jet-in-cross-flow publication-title: Phys. Fluids – volume: 29 start-page: 82 year: 2012 end-page: 97 article-title: Deep neural networks for acoustic modeling in speech recognition: the shared views of four research groups publication-title: IEEE Signal Process. Mag. – volume: 31 start-page: 805 year: 2010 end-page: 819 article-title: A numerical study of scalar dispersion downstream of a wall-mounted cube using direct simulations and algebraic flux models publication-title: Intl J. Heat Fluid Flow – volume: 254 start-page: 59 year: 1993 end-page: 78 article-title: On explicit algebraic stress models for complex turbulent flows publication-title: J. Fluid Mech. – volume: 318 start-page: 22 year: 2016a end-page: 35 article-title: Machine learning strategies for systems with invariance properties publication-title: J. Comput. Phys. – volume: 11 start-page: 943 year: 1999 end-page: 945 article-title: Direct numerical simulation of turbulent channel flow up to Re = 590 publication-title: Phys. Fluids – volume: 18 start-page: 282 year: 1965 end-page: 292 article-title: On isotropic integrity bases publication-title: Arch. Rational Mech. Anal. – volume: 644 start-page: 107 year: 2010 end-page: 122 article-title: Reynolds number dependence of mean flow structure in square duct turbulence publication-title: J. Fluid Mech. – volume: 182 start-page: 1 year: 2002 end-page: 26 article-title: Neural network modeling for near wall turbulent flow publication-title: J. Comput. Phys. – volume: 529 start-page: 484 year: 2016 end-page: 489 article-title: Mastering the game of Go with deep neural networks and tree search publication-title: Nature – volume: 305 start-page: 758 year: 2016 end-page: 774 article-title: A paradigm for data-driven predictive modeling using field inversion and machine learning publication-title: J. Comput. Phys. – volume: 8 start-page: 1 year: 2007 end-page: 27 article-title: Presentation of anisotropy properties of turbulence invariants versus eigenvalue approaches publication-title: J. Turbul. – volume: 681 start-page: 205 year: 2011 end-page: 240 article-title: Instability of streaks in wall turbulence with adverse pressure gradient publication-title: J. Fluid Mech. – volume: 27 year: 2015 article-title: Evaluation of machine learning algorithms for prediction of regions of high RANS uncertainty publication-title: Phys. Fluids – volume: 403 start-page: 89 year: 2000 end-page: 132 article-title: An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows publication-title: J. Fluid Mech. – volume: 72 start-page: 331 year: 1975 end-page: 340 article-title: A more general effective-viscosity hypothesis publication-title: J. Fluid Mech. – volume: 138 year: 2016c article-title: Analysis of turbulent scalar flux models for a discrete hole film cooling flow publication-title: J. Turbomach. – volume: 25 start-page: 2951 year: 2012 end-page: 2959 article-title: Practical Bayesian optimization of machine learning algorithms publication-title: Adv. Neural Inform. Proc. Syst. – volume: 17 start-page: 108 year: 1996 end-page: 115 article-title: Development and application of a cubic eddy-viscosity model of turbulence publication-title: Intl J. Heat Fluid Flow – volume: 30 start-page: 1 year: 2013 end-page: 6 article-title: Rectifier nonlinearities improve neural network acoustic models publication-title: Proc. ICML – ident: S0022112016006157_r17 doi: 10.1016/j.jcp.2015.11.012 – ident: S0022112016006157_r2 doi: 10.1016/0142-727X(95)00079-6 – volume-title: ASME Turbo Expo 2016 year: 2016b ident: S0022112016006157_r10 – ident: S0022112016006157_r6 doi: 10.1017/S0022112093002034 – ident: S0022112016006157_r9 doi: 10.1016/j.jcp.2016.05.003 – ident: S0022112016006157_r3 doi: 10.1038/nature16961 – ident: S0022112016006157_r22 doi: 10.1063/1.4915065 – ident: S0022112016006157_r20 doi: 10.2514/6.2014-2085 – ident: S0022112016006157_r8 doi: 10.1038/nature14539 – ident: S0022112016006157_r26 doi: 10.2514/6.2015-1287 – ident: S0022112016006157_r14 doi: 10.1017/jfm.2011.193 – ident: S0022112016006157_r4 doi: 10.2514/6.2003-149 – volume: 25 start-page: 2951 year: 2012 ident: S0022112016006157_r24 article-title: Practical Bayesian optimization of machine learning algorithms publication-title: Adv. Neural Inform. Proc. Syst. – start-page: 1725 volume-title: Proc. IEEE Conf. on Computer Vision and Pattern Recognition year: 2014 ident: S0022112016006157_r7 – volume: 30 start-page: 1 year: 2013 ident: S0022112016006157_r13 article-title: Rectifier nonlinearities improve neural network acoustic models publication-title: Proc. ICML – ident: S0022112016006157_r12 doi: 10.1063/1.4927765 – ident: S0022112016006157_r18 doi: 10.1017/S0022112009992242 – ident: S0022112016006157_r15 doi: 10.1006/jcph.2002.7146 – ident: S0022112016006157_r23 doi: 10.1007/BF00251667 – ident: S0022112016006157_r19 doi: 10.1017/S0022112075003382 – ident: S0022112016006157_r27 doi: 10.1017/S0022112099007004 – ident: S0022112016006157_r5 doi: 10.1109/MSP.2012.2205597 – ident: S0022112016006157_r21 doi: 10.1016/j.ijheatfluidflow.2010.05.006 – volume: 138 year: 2016c ident: S0022112016006157_r11 article-title: Analysis of turbulent scalar flux models for a discrete hole film cooling flow publication-title: J. Turbomach. doi: 10.1115/1.4031698 – volume: 8 start-page: 1 year: 2007 ident: S0022112016006157_r1 article-title: Presentation of anisotropy properties of turbulence invariants versus eigenvalue approaches publication-title: J. Turbul. – ident: S0022112016006157_r28 doi: 10.2514/6.2015-2460 – ident: S0022112016006157_r25 doi: 10.2514/6.2013-259 – ident: S0022112016006157_r16 doi: 10.1063/1.869966
SSID	ssj0013097
Score	2.6936703
Snippet	There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of... There exists significant demand for improved Reynolds-averaged Navier-Stokes (RANS) turbulence models that are informed by and can represent a richer set of...
SourceID	osti proquest crossref cambridge
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	155
SubjectTerms	Anisotropy CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Fluid mechanics Navier-Stokes equations Reynolds number Turbulence Viscosity
Title	Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
URI	https://www.cambridge.org/core/product/identifier/S0022112016006157/type/journal_article https://www.proquest.com/docview/1884540899 https://www.osti.gov/servlets/purl/1333570
Volume	807
WOSCitedRecordID	wos000386452000009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1469-7645 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0013097 issn: 0022-1120 databaseCode: P5Z dateStart: 20010101 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Earth, Atmospheric & Aquatic Science Database customDbUrl: eissn: 1469-7645 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0013097 issn: 0022-1120 databaseCode: PCBAR dateStart: 20010101 isFulltext: true titleUrlDefault: https://search.proquest.com/eaasdb providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database (subscription) customDbUrl: eissn: 1469-7645 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0013097 issn: 0022-1120 databaseCode: M7S dateStart: 20010101 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1469-7645 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0013097 issn: 0022-1120 databaseCode: BENPR dateStart: 20010101 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Research Library customDbUrl: eissn: 1469-7645 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0013097 issn: 0022-1120 databaseCode: M2O dateStart: 20010101 isFulltext: true titleUrlDefault: https://search.proquest.com/pqrl providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database customDbUrl: eissn: 1469-7645 dateEnd: 20241207 omitProxy: false ssIdentifier: ssj0013097 issn: 0022-1120 databaseCode: M2P dateStart: 20010101 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dSxwxEB_0tFAfql5bej2VPFR8KFuzX8nuU9Gi9KFeD7UgvizZSbZY7N7VPQ_87zuzlzstYl98CQsbSOA3mY9k5jcAH0onc5PoKshiTIKETDJ9lTpIUOswx1KhaguFv-nBILu4yIf-wq3xaZVzndgqajtCviPfD7OMyeIoPPg8_hNw1yh-XfUtNJZhhZnKkg6sHB4Nhqf37wgy13O-cPIspE99Z9LoXxUXoofqk-KWuPfECv8YqM6IDtojNd3anuP15-56A155r1MczMRkE5Zc3YV174EKf76bLqw9oCfswos2PRSb13B56u7q0bVthCHRJxVkBZmq8ratWBJtNx0uaxecRf9TWOfGgokyacl6lmbeCL7wFe536UjTWXFVTylIZ4l7Az-Oj86_fA18V4YAY6UnFHBmSV5FVpaVUZE1YRVjHjmJ2lDo4lSGaSVRmjhUJlMYRmVKYZ1NnU1VieSNvIVOPardOxCKNYBFpSObJLmVpjI2TnVkcrQUOac92FvAUviz1RSzvDRdEIAFA1gQgD34OAetQE9uzj02rp-YvbuYPZ6Rejwxr8_4F-SMMKMucuoRTgoK62mXsgdbc8wfbG4B-Pv__-7DS16GyxqjdAs6k5tbtw2rOJ1cNTc7Xo53YPkk-t6OQx71GY3D9PIvgMv_aA
linkProvider	ProQuest
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9RADLWqBQQcKCwglhaYAxUHFJhMkpnkgBACqlbdripUpIpLOvFMUFHJLpttUf8UvxE7H9siVG49cIuUkfL1_GxP7GeA54WXmY1NGaQRxkFMLpmOChPEaEyYYaFRN43CYzOZpAcH2d4K_Op7YbissufEhqjdFHmP_HWYpiwWR-nB29mPgKdG8d_VfoRGC4sdf_aTUrb6zfYH-r4bSm1-3H-_FXRTBQKMtFlQwpTGWamcLEqrlbNhGWGmvERjKfT2OsWklChtFGqbagxVkVBa4hLvEl2gYqEDovxrMWVCbFe7au_8r4XMTK9OTnGM7ArtWaL6W8lt76F-pXkA77mMwx_ucDAls_7LKTSebnP1f3tHd-FOF1OLd60R3IMVXw1htYuvRcde9RBuXxBfHMKNpvgV6_vw5ZM_q6bHrhaWDJsI1glyxMVJ048lmllB3LQvuEfgq3DezwTLgNIlq7aIvha8nS3898ITjztxVJ3aOe8W-Qfw-Uqe_CEMqmnlH4HQzG8OtVEujjMnbWldlBhlM3QRBb4jeLGEQd4xR523VXcmJ8DkDJicADOClz1Icuyk23mCyPElqzeWq2etZMkl69YYbzmFWqwXjFxYhYs8jCK6SzmC9R5jF25uCbDH_z79DG5u7e-O8_H2ZGcNbvEluYFTJeswWMxP_BO4jqeLo3r-tLEgAYdXDcffjJRXUg
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=Reynolds+averaged+turbulence+modelling+using+deep+neural+networks+with+embedded+invariance&rft.jtitle=Journal+of+fluid+mechanics&rft.au=Ling%2C+Julia&rft.au=Kurzawski%2C+Andrew&rft.au=Templeton%2C+Jeremy&rft.date=2016-11-25&rft.pub=Cambridge+University+Press&rft.issn=0022-1120&rft.eissn=1469-7645&rft.volume=807&rft.spage=155&rft.epage=166&rft_id=info:doi/10.1017%2Fjfm.2016.615&rft.externalDocID=10_1017_jfm_2016_615
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0022-1120&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0022-1120&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0022-1120&client=summon