Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor
dc.contributor.author | Tian, Y. | |
dc.contributor.author | Livescu, D. | |
dc.contributor.author | Chertkov, M. | |
dc.date.accessioned | 2021-10-16T02:18:43Z | |
dc.date.available | 2021-10-16T02:18:43Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Tian, 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.issn | 2469-990X | |
dc.identifier.doi | 10.1103/PhysRevFluids.6.094607 | |
dc.identifier.uri | http://hdl.handle.net/10150/662109 | |
dc.description.abstract | Reduced 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.iso | en | |
dc.publisher | American Physical Society | |
dc.rights | Copyright © 2021 American Physical Society. | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.title | Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor | |
dc.type | Article | |
dc.type | text | |
dc.contributor.department | Program in Applied Mathematics, University of Arizona | |
dc.identifier.journal | Physical Review Fluids | |
dc.description.note | Immediate access | |
dc.description.collectioninformation | This 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.version | Final published version | |
dc.source.journaltitle | Physical Review Fluids | |
refterms.dateFOA | 2021-10-16T02:18:43Z |