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dc.contributor.authorTian, Y.
dc.contributor.authorLivescu, D.
dc.contributor.authorChertkov, M.
dc.date.accessioned2021-10-16T02:18:43Z
dc.date.available2021-10-16T02:18:43Z
dc.date.issued2021
dc.identifier.citationTian, Y., Livescu, D., & Chertkov, M. (2021). Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor. Physical Review Fluids, 6(9).
dc.identifier.issn2469-990X
dc.identifier.doi10.1103/PhysRevFluids.6.094607
dc.identifier.urihttp://hdl.handle.net/10150/662109
dc.description.abstractReduced models describing the Lagrangian dynamics of the velocity gradient tensor (VGT) in homogeneous isotropic turbulence (HIT) are developed under the physics-informed machine learning (PIML) framework. We consider the VGT at both Kolmogorov scale and coarse-grained scale within the inertial range of HIT. Building reduced models requires resolving the pressure Hessian and subfilter contributions, which is accomplished by constructing them using the integrity bases and invariants of the VGT. The developed models can be expressed using the extended tensor basis neural network (TBNN) introduced by Ling et al. [J. Fluid Mech. 807, 155 (2016)0022-112010.1017/jfm.2016.615]. Physical constraints, such as Galilean invariance, rotational invariance, and incompressibility condition, are thus embedded in the models explicitly. Our PIML models are trained on the Lagrangian data from a high-Reynolds number direct numerical simulation (DNS). To validate the results, we perform a comprehensive out-of-sample test. We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the "ground-truth"DNS data. A number of other important features describing the structure of HIT are reproduced by the model successfully. We have also identified challenges in modeling inertial range dynamics, which indicates that a richer modeling strategy is required. This helps us identify important directions for future research, in particular towards including inertial range geometry into the TBNN. © 2021 American Physical Society.
dc.language.isoen
dc.publisherAmerican Physical Society
dc.rightsCopyright © 2021 American Physical Society.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.titlePhysics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor
dc.typeArticle
dc.typetext
dc.contributor.departmentProgram in Applied Mathematics, University of Arizona
dc.identifier.journalPhysical Review Fluids
dc.description.noteImmediate access
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
dc.eprint.versionFinal published version
dc.source.journaltitlePhysical Review Fluids
refterms.dateFOA2021-10-16T02:18:43Z


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