TR2018-170

Reduced-order modeling of fully turbulent buoyancy-driven flows using the Green's function method


    •  Khodkar, A., Hassanzadeh, P., Nabi, S., Grover, P., "Reduced-order modeling of fully turbulent buoyancy-driven flows using the Green's function method", Physical Review Fluids, DOI: 10.1103/PhysRevFluids.4.013801, Vol. 4, No. 1, December 2018.
      BibTeX TR2018-170 PDF
      • @article{Khodkar2018dec,
      • author = {Khodkar, Amin and Hassanzadeh, Pedram and Nabi, Saleh and Grover, Piyush},
      • title = {Reduced-order modeling of fully turbulent buoyancy-driven flows using the Green's function method},
      • journal = {Physical Review Fluids},
      • year = 2018,
      • volume = 4,
      • number = 1,
      • month = dec,
      • doi = {10.1103/PhysRevFluids.4.013801},
      • url = {https://www.merl.com/publications/TR2018-170}
      • }
  • MERL Contact:
  • Research Areas:

    Control, Dynamical Systems

One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh Benard convection system in the turbulent regime with Rayleigh number Ra = 106. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green’s Function (GRF) method, which involves applying many localized, weak forcings to the system one at a time and calculating the responses using long-time averaged Direct Numerical Simulations (DNS), the system’s Linear Response Function (LRF) has been computed. Another matrix, called the Eddy Flux Matrix (EFM), that relates changes in the divergence of vertical eddy heat fluxes to changes in the state vector, has also been calculated. Using various tests, it is shown that the LRF and EFM can accurately predict the time-mean responses of temperature and eddy heat flux to external forcings, and that the LRF can well predict the forcing needed to change the mean flow in a specified way (inverse problem). The non-normality of the LRF is discussed and its eigen/singular vectors are compared with the leading Proper Orthogonal Decomposition (POD) modes of the DNS data. Furthermore, it is shown that if the LRF and EFM are simply scaled by the square-root of Rayleigh number, they perform equally well for flows at other Ra, at least in the investigated range of 5 x 105 <= Ra <= 1.25 x 106. The GRF method can be applied to develop 1D or 3D ROMs for any turbulent flow, and the calculated LRF and EFM can help with better analyzing and controlling the nonlinear system.

 

  • Related News & Events

    •  NEWS   Turbulent flow paper selected as "Editors Suggestion" in journal Physical Review Fluids
      Date: January 11, 2019
      Where: PHYSICAL REVIEW FLUIDS, 4, 013801 – Published 11 January 2019
      MERL Contact: Saleh Nabi
      Research Areas: Control, Dynamical Systems
      Brief
      • The journal Physical Review Fluids has recently instituted "...a service to our readers, we are formally marking a small number of papers published in Physical Review Fluids that the editors and referees find of particular interest, importance, or clarity." The following paper with MERL authors Saleh Nabi and Piyush Grover was so honored in the January 2019 issue: "Reduced-order modeling of fully turbulent buoyancy-driven flows using the Green's function method.".
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