Spatiotemporally dynamic implicit large eddy simulation using machine learning classifiers

Romit Maulik, Omer San, Jamey D. Jacob

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this article, we utilize machine learning to dynamically determine if a point on the computational grid requires implicit numerical dissipation for large eddy simulation (LES). The decision making process is learnt through a priori training on quantities derived from direct numerical simulation (DNS) data. In particular, we compute eddy-viscosities obtained through the coarse-graining of DNS quantities and utilize their projection onto a Gaussian distribution to categorize areas that may require dissipation. If our learning determines that closure is necessary, an upwinded scheme is utilized for computing the non-linear Jacobian. In contrast, if it is determined that closure is unnecessary, a symmetric and second-order accurate energy and enstrophy preserving Arakawa scheme is utilized instead. This results in a closure framework that precludes the specification of any model-form for the small scale contributions of turbulence but deploys an appropriate numerical dissipation from explicit closure driven hypotheses. This methodology is deployed for the Kraichnan turbulence test-case and assessed through various statistical quantities such as angle-averaged kinetic energy spectra and vorticity structure functions. Our framework thus establishes a link between the use of explicit LES ideologies for closure and numerical dissipation-based modeling of turbulence leading to improved statistical fidelity of a posteriori simulations.

Original languageEnglish (US)
Article number132409
JournalPhysica D: Nonlinear Phenomena
StatePublished - May 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Cite this