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Effects of finite spatial and temporal resolution in direct numerical simulations of incompressible isotropic turbulence

P. K. Yeung*

K. R. Sreenivasan

S. B. Pope

  • Schools of Aerospace Engineering and Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

  • Department of Mechanical and Aerospace Engineering, Department of Physics, and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA

  • Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA

  • *pk.yeung@ae.gatech.edu
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Phys. Rev. Fluids 3, 064603 – Published 18 June, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.064603

Abstract

As computing power has grown and turbulent flows at increasing Reynolds numbers are being computed by direct numerical simulations, conventional assumptions on adequate spatial and temporal resolutions are being continually challenged. We perform a systematic study of the resolution effects via numerical simulations at various spatial and temporal resolutions to clarify the proper scaling of dissipation and enstrophy (vorticity squared). Results show that inadequate resolution in space and/or time leads to overestimation of the likelihood and intensity of extreme fluctuations in dissipation and enstrophy. In order to capture rare events accurately, for instance, one needs to have not only grid resolutions that are increasingly smaller fractions of the Kolmogorov scale as the Reynolds number increases but also the Courant number that becomes increasingly smaller than that assumed to be adequate previously. Some comparisons are made with results obtained from an alternative approach where a stricter criterion for truncation in wave-number space allows aliasing errors to be removed completely. In contrast to prior work, the present data do not support the notion that dissipation and enstrophy probability density functions (PDFs) approach each other in the far tails at high Reynolds number. However the two PDFs are remarkably similar in form, being well described by stretched exponentials.

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References (20)

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Phys. Rev. Fluids 3, 064603– Published 18 June, 2018
  • Received 26 February 2018
Article part of CHORUS
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