A systematic study of the grid requirements for a spectral element method solver

In this paper, direct numerical simulation of fully developed turbulent channel flow is carried out at low Reynolds number, ������������������ = 180, in order to investigate in a spectral element method context the effect of grid refinement on turbulence statistics. Mean flow, turbulence intensities, skewness, viscous dissipation, and energy spectra were computed, alongside planar visualisations of the flow. The findings show ������0 continuity, present at shared nodes between adjacent spectral elements, creates at element interfaces potential artefacts in the averaged statistical quantities. However, grid convergence is fast for spatially-averaged terms, particularly for statistics of primitive variables, but may require additional grid resolution for derivative terms. The findings also show that statistical convergence with grid refinement occurs more quickly in the near-wall region (below ������+ <= 30) than in the outer region. These results are useful for robust interpretation of data generated using spectral element methods in turbulence physics.

Automated summary

In this paper, direct numerical simulation of fully developed turbulent channel flow is carried out at low Reynolds number to investigate the effect of grid refinement on turbulence statistics in a spectral element method context. The findings show that discontinuity at shared nodes between adjacent spectral elements creates potential artefacts in the averaged statistical quantities. Grid convergence is fast for spatially-averaged terms, particularly for statistics of primitive variables, but may require additional grid resolution for derivative terms. Statistical convergence with grid refinement occurs more quickly in the near-wall region than in the outer region.