Research Group



CURRENT MEMBERS



FORMER MEMBERS

  • Dave Wells (PhD, 2015)       Postdoc
    Rensselaer Polytechnic Institute

  • Omer San (postdoc, 2012-2014)   Assistant Professor
    Oklahoma State University

  • Erich Foster (PhD, 2013)       Postdoc
    Sandia National Laboratories

  • Zhu Wang (PhD, 2012)       Assistant Professor
    University of South Carolina

  • Haofeng Yu (PhD, 2011)       Actuary Director at AIG


Traian Iliescu

Professor
Department of Mathematics
Virginia Tech
428 McBryde Hall
Blacksburg, VA 24061-0123
Email: iliescu@vt.edu
Phone: (540) 231-5296
Fax: (540) 231-5960

LES-ROM

For the past few years, together with my students and collaborators, I have been trying to bridge two reseach fields: reduced order modeling (ROM) and large eddy simulation (LES). We are not the first to try this (see, e.g., Lumley's pioneering work). We are, however, the first (to our knowledge) to use explicit spatial filtering to develop ROM closure models of LES type. Here are some of our accomplishments:
  •       (I) first dynamic subgrid-scale ROM closure model (this is state-of-the-art in LES)
  •       (II) first variational multiscale ROM closure model of eddy viscosity type
  •       (III) first structural ROM closure model: the approximate deconvolution ROM
  •       (IV) first rigorous error estimates for explicit ROM spatial filters


Data-Driven ROM

Together with our collaborators, we have recently proposed a hybrid ROM framework, in which the Galerkin projection is used to model the evolution of the dominant modes and a data-driven (calibration) approach is used to model the effect of the discarded modes (i.e., solve the ROM closure problem). ROM spatial filtering is employed to find an explicit formula for the interaction between the resolved and unresolved modes. The available full order model data and a least-squares problem are used to construct the ROM closure model, i.e., to model the effect of the unresolved modes. The resulting calibrated-filtered ROM framework can be applied to general nonlinear PDEs.



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