Comparison of a spectral method with a higher-order finite difference method in direct numerical simulations of three-dimensional homogeneous turbulence

Katsunori Yoshimatsu, Takashi Ishihara, Yukio Kaneda, Satoshi Nakai, Hidetoshi Nishida, Nobuyuki Satafuka

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A finite difference method (FDM) is easier and cheaper to use than a spectral method (SM) in flows with complicated geometry, but is inferior to a SM in both accuracy and resolution. In this paper, effects of both accuracy and resolution in a FDM on the quality of incompressible turbulent flow description were studied by comparing a SM with a FDM in direct numerical simulations (DNS) of the three-dimensional freely decaying homogeneous turbulence with 1283 and 2563 grids. We adopted the higher-order method of lines and Fourier spectral method as a FDM and a SM, respectively. The value of the kinematic viscosity was determined so that the minimum value of Kmaxη in time was about 2 in the SM with 2563 grids. Here, Kmax and η are the maximum resolved wavenumber and the Kolmogorov length scale, respectively. The statistical quantities, such as the total energy, the energy dissipation ratio, obtained by the higher-order method of lines were in good agreement with those by the SM. Furthermore, comparing their DNS fields, we found that the performance of the 4th-order method of lines with 2563 grids was comparable to that of the SM with 1283 grids in which the minimum value of Kmaxη in time was about 1.

Original languageEnglish
Pages (from-to)541-546
Number of pages6
JournalNippon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B
Issue number679
Publication statusPublished - Mar 2003
Externally publishedYes



  • Computational fluid dynamics
  • Finite difference method
  • Spectral method
  • Three-dimensional flow
  • Turbulent flow

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering

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