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Parameter-Free Symmetry-Preserving Regularization Modelling of Turbulent Natural Convection Flows

  • F. X. Trias
  • R. W. C. P. Verstappen
  • M. Soria
  • A. Oliva
Conference paper
Part of the Notes on Numerical Fluid Mechanics and Multidisciplinary Design book series (NNFM, volume 110)

Abstract

Since direct numerical simulations of natural convection flows cannot be performed at high Ra-numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the nonlinearity. The regularization method basically alters the convective terms to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yields a novel class of regularizations that restrain the convective production of smaller and smaller scales of motion by means of vortex stretching in an unconditional stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The regularization model is successfully tested for a 3D natural convection flow in air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4 at Ra = 1010 and 1011. Moreover, a method to dynamically determine the regularization parameter (local filter length) is also proposed and tested.

Keywords

Nusselt Number Natural Convection Rayleigh Number Direct Numerical Simulation Convective Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • F. X. Trias
    • 1
    • 2
  • R. W. C. P. Verstappen
    • 2
  • M. Soria
    • 1
  • A. Oliva
    • 1
  1. 1.Centre Tecnològic de Transferència de Calor, ETSEIATTechnical University of CataloniaTerrassaSpain
  2. 2.Institute of Mathematics and Computing ScienceUniversity of GroningenGroningenThe Netherlands

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