A study on the numerical dissipation of the Spectral Difference method for freely decaying and wall-bounded turbulence

Abstract

Abstract This paper aims at understanding the numerical dissipation mechanisms related to the Spectral Difference (SD) method in the context of three-dimensional (3D) turbulence. The numerical dissipation stemming from the discretization of the convective terms is studied by performing inviscid computations of the transitional Taylor–Green vortex and isotropic turbulence configurations. The Taylor–Green vortex computations show that the increase in the order of accuracy restricts the numerical dissipation to smaller scales which, in turn, leads to a better representation of transitional mechanisms. However, isotropic turbulence computations using a fifth-order accuracy or above show obvious manifestations of under-resolution (such as the onset of oscillations and numerical noise), which suggests that the high-order numerical dissipation alone is unable to mimic the dissipation originating from sub-grid scales in the case freely decaying turbulence. Computations of the channel flow configuration at R e τ = 1000 at typical large-eddy simulation resolutions show that under-resolved SD discretizations using a high order of accuracy (fifth and sixth) lead to an excellent prediction of the wall-friction, the velocity profiles, the turbulent structures near the wall and the energy spectra, while lower order discretizations lead to an underestimation of the wall-friction and globally a poor representation of wall-bounded turbulence. The present study emphasizes the benefit of using high-order SD discretizations for an accurate representation of turbulent phenomena (namely, transitional and wall-bounded turbulence) but also the necessity of combining this approach with dynamic large-eddy simulation models or appropriate regularization techniques which would activate only where needed to recover physically consistent results, e.g. , in regions where fully developed turbulence is present.